Koji Ikuta
The International Journal of Robotics Research http://ijr.sagepub.com
Safety Evaluation Method of Design and Control for Human-Care Robots Koji Ikuta, Hideki Ishii and Makoto Nokata The International Journal of Robotics Research 2003; 22; 281 DOI: 10.1177/0278364903022005001 The online version of this article can be found at: http://ijr.sagepub.com/cgi/content/abstract/22/5/281
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Koji Ikuta Hideki Ishii Department of Micro System Engineering School of Engineering Nagoya University Japan
Makoto Nokata
Safety Evaluation Method of Design and Control for Human-Care Robots
Department of Robotics Faculty of Science and Engineering Ritsumeikan University Japan
Abstract We propose the world’s first general method of evaluating safety for human-care robots. In the case of a careless collision between a robot and a human, impact force and impact stress are chosen as evaluation measures, and a danger-index is defined to quantitatively evaluate the effectiveness of each safety strategy used for design and control. As a result, this proposed method allows us to assess the contribution of each safety strategy to the overall safety performance of a human-care robot. In addition, a new type of three-dimensional robot simulation system for danger evaluation is constructed on a PC. The system simplifies the danger evaluation of both the design and control of various types of human-care robots to quantify the effectiveness of various safety strategies.
KEY WORDS—human-care robot, safety evaluation, danger index, safety design and control
ation measures which describe the degree of safety. Then, we apply our method to evaluate several safety design/control strategies, and we prove the viability of our safety evaluation method. Finally, we construct a new type of three-dimensional (3D) robot simulation system for danger evaluation on a PC, and we realize an easily designed robot, controlling safety.
2. Safety Strategy for Human-Care Robots 2.1. Injury to Humans from Human-Care Robots We have given thorough consideration to the possibility of injury to humans from human-care robots and machines. The causes of injury may be classified as follows: 1. mechanical injury • shock—internal bleeding, fracture of a bone; • scar—bleeding, contagion;
1. Introduction An aged society is not far in the future. Human-care robots must be realized to nurse aged and disabled people. Humancare robots will need to work around humans and to touch them. So, conventional safety strategies for industrial robots cannot be applied to human-care robots. It is now necessary to make a new study of safety in the areas where humans and machines will exist together. In this paper, we investigate human injury caused by robots and machines, and then we classify the safety design and control strategy for robots. Next, we propose a method for evaluating safety for human-care robots and we define evaluThe International Journal of Robotics Research Vol. 22, No. 5, May 2003, pp. 281-297, ©2003 Sage Publications
2. electric injury • electric shock—death from shock, burn; • electromagnetic wave—cancer, leukemia; 3. acoustic injury • boom—hardness of hearing; • low frequency sound—insomnia, neurosis. In this research, as the subject of our study we have chosen the safety strategy to prevent mechanical injury. Although protecting humans from electric and acoustic injury is possible by making use of insulators or soundproofing materials, it is very difficult to isolate the mechanical damage in the 281
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robot working space. In order to secure human-care robots which work around humans, many types of design and control strategies are indispensable. But many complex and difficult problems are conformed in the design of the robot. 2.2. Classification of Safety Strategies We classify safety strategies as follows: 1. pre-contact safety strategy; 2. post-contact safety strategy. Pre-contact safety strategies consider minimizing human injury before human–robot collision. Post-contact safety strategies aim to reduce potential injuries after collisions. In analogy to car safety strategy, the former strategy corresponds to avoiding a collision by means of an Antilock Brake System (ABS), the latter strategy to absorbing the shock by means of an air bag or side door beam. From the point of view of a human-care robot user or designer, this discussion can be classified as follows: 1. safety design strategy (minimizing injury by design); 2. safety control strategy (minimizing injury by control). Table 1 shows the classification of safety strategies, clearly showing the details. We have already developed cybernetic actuators (Ikuta et al. 1991) and non-contact magnetic gear (Ikuta, Makita, and Arimoto 1991), which have force limiting functions as safety designs. Other strategies have been devised, such as force limiting equipment using electrorheological fluid (Saito and Sugimoto 1997), force control, shock absorption cover (Suita et al. 1995), and chamfering, etc. Thus far, little research has been carried out on safety evaluation methods; some of the research to date measures the danger inherent in different actuator arrangements (Dohi 1996) and safety in human control (Saito et al. 1996).
Table 1. Classification of Safety Strategies
International safety standards have defined safety as “freedom from unacceptable risk of harm”, and thus estimate only the risk of harm (International Organization for Standardization 1990). This estimation method lacks a quantitative basis because it relies on the use of insufficiently provable data. Furthermore, the estimation methods of safety vary with the researchers. As a result, we cannot compare the various strategies. So we have carried out only one separate case study from beginning to end. The reasons for this are attributable to the vagueness of the concept of safety. Everyone thinks that it is difficult to calculate the degree of safety or dangerousness and the contribution of each safety design and control strategy to the overall safety performance of robots. So nobody tries to do it. As a result, the aim of this study is to propose a method to evaluate safety for various robots on the same scale in order to compare and investigate them quantitatively. A detailed or complicated method limits the evaluated objects and contents. In order to evaluate various types of robot, the method should be simple and must use the simplified model, calculating general physical quantity.
3. Proposal of Evaluation Measures 3.1. Necessity for Quantitative Evaluation of Safety It is necessary to define “evaluation measures” for devising various safety strategies of human-care robots. Evaluation measures enable us to compare the effect of each safety strategy on the same scale and to optimize the design and control of human-care robots. In the field of information science, Shannon (1948) has defined information as the degree of entropy, thereby advancing information theory remarkably. In the robotics field, Yoshikawa (1985) and Uchiyama defined the measure of manipulability, which has enabled us to compare the manipulation performance of various kinds of robot uniformly. The former definition does not express enough about the quality of the information; the latter does not express various kinds of control performance completely. But we cannot deny their contribution to science and engineering. If we overcome some different opinions and define the general evaluation measures of human-care robots, we will be able to achieve similar effects. 3.2. Selection of Evaluation Measures In the event of careless collision between robots and humans, the degree of dangerousness can be expressed as eq. (2) by using only main factors such as design and control: Dangerousness
=
{f (design) · g(control)} (1) ×(a rate of accident incidence).
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Ikuta, Ishii and Nokata / Safety Evaluation Method In the International Organization for Standardization (ISO), this has been analyzed by the risk management of the rate of accident incidence caused by human error, manipulation and so on. Their main aim is how to reduce the probability of accident and how to estimate it. Little attention has been paid to the relation between the design or control of humancare robots and the danger of injury. In this research, we aim to study “what design or control can minimize human injury” at the occurrence of an accident. In other words, our aim is to make a quantitative evaluation of the effectiveness of safety design or control strategies, and to minimize the dangerousness on the condition that the rate of accident incidence is 1. So what should the evaluation measures be? A human-care robot works around humans who move irregularly. We consider an appropriate safety strategy while adapting the classified design/control safety strategy mentioned previously. A safety design strategy is a means for reducing the injury to a human after an irregular collision. A safety control strategy is a means for minimizing the injury before a human–robot collision. Therefore, it is important to estimate not the occurrence rate but the injury due to collision. No matter what the cause of collision accident may be, the shock of mechanical injury depends on the impact force, and the scar depends on impact stress. Namely, we consider impact force and stress as evaluation measures.
4. Safety Evaluation Method Using Evaluation Measures In this section, we propose a safety evaluation method using evaluation measures for human-care robots. 4.1. Safety Evaluation of Safety Design Strategy First, we define the critical impact force Fc as a minimal impact force that causes injury to humans. Next, we define the danger-index α as the producible impact force F against Fc in eq. (2): α=
F Fc
(α ≥ 0).
injury to a human is output. The index is dependent on the transfer function. In this system, several factors are connected with each other in series. The characteristic of the whole system can be expressed as the multiplication of each transfer function. So the total danger-index of the whole robot αall is expressed by the multiplication shown in eq. (3), a calculation which is made possible by quantifying the effect of safety strategies on the same scale: αall =
n
αi .
(3)
i=1
Here, n is the total number of safety strategies and i is the number of safety strategies. As an example, we consider the case of reducing impact force using a perfect shock absorption material. Even if a robot which has a dangerous shape or other factors collides with a human, the impact force to the human is qualitatively zero because it is isolated by the material. The danger-index αj (1, 2, . . . j . . . , n) about the shock absorption material is expressed as zero by using the proposed evaluation method of safety. The total danger-index multiplied by each index results in zero, so it is obvious to agree the usual. But too many safety strategies will cause a lowering of the ability of robot work or operation. This problem can be solved by devising a safety strategy on condition that required working ability is satisfied, or calculating the optimum solution between eq. (3) and efficiency of robot working. This is an advantage produced by a quantitative evaluation of dangerousness. The improvement rate η can be calculated as follows, by using impact force and the danger-index before improvement as F0 and α0 respectively: η=
α0 F0 Fc F0 = = , α Fc F F
ηall =
n α0 i=1
(2)
Strictly speaking, the value of force Fc varies according to age, sex and body part. But we use one representative value for realizing the generality of safety evaluation. In exceptional cases such as body parts where Fc is very low, such as eyes, these cases are treated as a singular point. Another evaluation is needed for such points. Next, we consider the overall danger-index provided by several safety strategies. We express the characteristic of safety strategies for minimizing the impact force by using a block chart, which is popular in the control field. For example, producible impact force is input, a safety strategy is a factor, its danger-index is transfer function, and
283
αi
.
(4)
(5)
In eq. (4) Fc is canceled. So we can simply compare before and after safety strategies. The algorithm of our proposed evaluation method is as follows: 1. investigating the factor of damage to a human as evaluation measures; 2. calculating the impact force F of each safety strategy; 3. calculating the danger-index α from eq. (2); 4. executing the safety evaluation by using the total danger-index;
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5. discussing the review of the safety strategy or not from the result. This method enables us to evaluate the effect of each or all safety strategies. 4.2. Expansion into Safety Control Strategy For safety control strategies, it is possible to employ impact force as an evaluation measure. So each danger-index can be calculated in the same way as the safety design strategy (Section 4.1). The premises are as follows: 1. robots are always controlled without collision with a human; 2. robots can be controlled just before collision even if the collision is unexpected.
4.3. Expansion for Evaluating Various Types of Danger In order to discuss the safety of the many types of humancare robots or equipment, various types of danger must be considered and examined. Most have a tendency to be independent. So it is difficult to measure them on the same scale even if they can be quantified. Thus, we propose the evaluation method of safety strategy for human-care equipment in general by expanding the method described above. First, a suitable evaluation measure S is defined for each safety strategy the same as impact force. If critical impact values of damage to human Sc is given, the danger-index is as follows: α=
S Sc
(α ≥ 0).
When we evaluate several strategies together which have the same evaluation measures, the total danger-index can be calculated by multiplying eq. (13)
The following equations are derived similar to eqs. (2)–(5): F∗ α∗ = Fc
(α ∗ ≥ 0)
n
∗ αall =
αi∗
(6)
(7)
i=1
η∗ =
α0 F0 = ∗ ∗ α F
∗ ηall =
n
ηi∗ .
(8)
(9)
i=1
We use “*” in these equations in order to distinguish them from the safety design strategy. When safety design and control strategy are carried out at the same time, the total dangerindex of the whole robot can be expressed in multiplication equations the same as eqs.(7) and (9): αall =
i=1
ηall
αall =
αi
αj∗
(10)
j =1
m n α0 α0 = . αi j =1 αj∗ i=1
(11)
By using these equations, it is possible to optimize both safety design and safety control and to evaluate them at the same time. In the case of treating scar, impact force is replaced with impact stress.
n
αi ,
(13)
i=1
where N is the total number of safe strategies and i is the number of the safety strategy. The general danger-index Gα , which considers several evaluation measures, is obtained by additional equations because these values are independent of each other. Gα =
ci α(Si )all .
(14)
i
The weight coefficient ci is defined by measuring individual properties of humans. For an example of another safety strategy, if the dangerous factor is an electric shock, the evaluation measure is determined as a current I (A) because the damage to humans is dependent on it. If the minimal current value which produces the damage to humans is defined as the critical current value Ic , the danger-index becomes the same as eq. (12): α(I ) =
n
m
(12)
I . Ic
(15)
The improvement rate can be calculated in the same way as impact force. The total danger-index can be calculated by multiplying eq. (15): α(I )all =
n
α(I )i .
(16)
i=1
In addition, it is possible to quantify burn (temperature, T (K), e.g., radio knife), fall (moment, M (N m−1 ), e.g., wheel chair), pressing (pressure, P (Pa), e.g., holding in robot arms) and noise (decibel (dB)) in spite of I (A) by the general
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danger-index of these evaluation measures, which are independent of each other, by summation of eq. (14): Gα = c1 α(I )all + c2 α(T )all + c3 α(M)all + · · · .
(17)
There are several ways to decide ci ; one is by using a medical benefit or medical insurance. For example, critical impact force Fc causes injury which will take four weeks to heal completely; critical current Ic causes injury which will take two weeks to heal completely. We can fix on a cforce value which is twice as large as ccurrent . By using this method, not only impact force F but also many types of safety or dangerousness can be evaluated quantitatively. It is possible to realize the correlation between safety and practical use, such as function, workspace, work efficiency, and so on, using simultaneous equations with their estimated equations and eq. (17). Fig. 1. Manipulator covered with soft material.
5. Deriving Danger-Indices of Robot Design Methods In this section, we give examples of safety design strategy to show the practical derivation of a danger-index. We propose a linear approximate model of each safety strategy and solve it individually. The aim of the approximation is to extract only the effect of a safety factor and to remove the effects of other factors, as much as possible. Usually, we make models and equations which satisfy all effects of boundary conditions at the same time. But this requires reconsideration of the model or the equation when the conditions are changed. If many phenomena are considered, it makes the equation complicated and increases unknown variables. To execute the evaluation and the comparison of safety strategies, it is necessary not only to consider all phenomena strictly but also to quantify the safety with the aim of wide use. As a result, we work out the danger-index of the safety strategy by using a linear approximate model individually. This research supposes a sudden collision between human and robot, so we discuss each safety strategy for reducing the damage from the collision. 5.1. Effect of Reducing the Weight We consider a strategy of reducing a robot weight in order to minimize the impact force. Impact force F is derived as eq. (18) by Newton’s equation of motion. This impact force F of the robot against the critical force yields the danger-index α, eq. (19): F = ma
(18)
ma . Fc
(19)
α=
As an example, a danger-index is shown when robot material is changed. For a robot whose main material is steel (density, 7.86 × 103 kg m−3 ) and whose weight is 20 kg moving at 1 m s−2 , if the material is replaced with aluminum (density, 2.69 × 103 kg m−3 ), the robot weight becomes 6.7 kg and its danger-index α is 0.34. Or, if replaced with a plastic (density, 1.40 × 103 kg m−3 ), the weight becomes 3.5 kg and its index α is 0.18. In short, if the weight is reduced by half, α is also halved. 5.2. Effect of Absorbing Impact Force We consider a strategy of absorbing impact force by soft material as shown in Figure 1. Generally speaking, several humanrelated parameters need to be set in the case of working out the time response of material deformation. But we employ the same boundary conditions in order to purpose the safety evaluation method and calculate the maximum impact force in a collision. If the approach speed of the robot is reduced from v to v , the impact force F is derived from momentum as in eq. (20): F =
mv − mv
. dt
(20)
The collision between human and robot can be expressed by a linear approximate model (Figure 2), and the following equation of motion is obtained: mx¨ + cx˙ + kx = 0
(x = xrg − xrs ).
(21)
This model shows damped oscillation, so the solution of eq. (21) is as follows:
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Fig. 2. Model of the collision between human and robot. Fig. 3. Manipulator with compliant joints.
x = e−ζ ωn t C cos(ωd t − β) where
(22)
5.3. Effect of Joint Compliance It is an effective strategy to have compliance in each joint as in Figure 3. Rotational motion around the joint is produced by collision, and impact force F can be calculated using
ωn = k/m, ωd = ωn 1 − ζ 2
F3 =
√ ζ = c/2 mk and
C=
a02 +
(x = a0 , x˙ = v0 at t = 0). Equation (23) is obtained by differentiating eq. (22): x˙ = Ce−ζ ωn t (−ζ ωn cos(ωd t − β) − ωd sin(ωd t − β)) . (23) When the speed after collision v is 0, the impact force becomes maximum. So the collision time dt is obtained as −1
I θ¨ + C θ˙ + Kθ = 0
(27)
tan−1 (−ζ ωn /ωd ) + π/2 , (28) ωd √ √ √ where ωn is K/I , ωd = ωn 1 − ζ 2 , ζ is C/2 I K, and dt =
α=
(24)
As a result, the danger-index α is derived as mv . α= Fc dt
(26)
where I is the moment of inertia and l is the distance from joint to contact point. The collision time can be obtained in the same manner as in Section 5.2. So eqs. (28) and (29) are derived by replacing eq. (21) with
v0 + a 0 ζ ωn v 0 + a 0 ζ ωn , β = tan−1 ωd a0 ωd
tan (−ζ ωn /ωd ) + π/2 dt = . ωd
I ω − I ω
l dt
I θ˙ . Fc dt
(29)
5.4. Minimizing Impact Stress Caused by Shape (25)
In this equation, the time response is not considered. But the most dangerous situation is considered because maximum value is obtained. For example, the danger-index of a robot, which moves at α = 1.0, is reduced to 0.05 by covering it with rubber (thickness 10 mm, Young’s modulus 5.0 Mpa).
This strategy is to design robot shape for minimizing impact stress. Impact stress σ is calculated by σ =
F A
(30)
where A is contact area. Strictly, contact area A is dependent not only on the shape but also on the material specification.
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Table 2. Safety Design Strategies and Danger-Indices
Fig. 4. Deformation area under the collision between human and robot. So we calculate the danger-index α by using the rate of deformation λ (eq. (31)) which considers the possession space of human A1 (outline, y = human(x)) and deformation space A2 (outline, y = robot (x)) in order to extract the effect of shape (Figure 3): 2l −l (human(x) − robot (x)) dx A2 λ= . (31) = 2 l l A1 2 ( − human(x)) dx l 2 − 2
As a result, the danger-index is as follows: λ (32) λc where λc is the critical rate of deformation. As an example, we consider a collision with a human head (φ = 0.2 m) and other things, such as (1) a kitchen knife (width 50 mm, thickness 2 mm), (2) a bat (φ = 0.1 m) and (3) a curved surface (y = −0.5x 2 ). Each danger-index α is (1) 24.08, (2) 4.8 and (3) 0.92 as compared with a flat surface. So it is possible to evaluate the dangerousness of shapes. α=
5.5. Effect of Reducing Surface Friction It is possible to release impact force by slipping on the surface with less friction: F = µN
(33)
µN (34) Fc where µ is the coefficient of friction, and N is the vertical force. As an example, we compare robots which are covered with iron, nylon and Teflon. If the robot’s surface material, iron (µ = 0.5), is replaced with nylon (µ = 0.2) or Teflon (µ = 0.04), each danger-index α is 0.4 and 0.08. Danger-indices of the above safety design strategies are integrated in Table 2. Those indices can be calculated by inputting each design parameter to the equations in it. α=
6. Examples of Evaluating Practical Robot Design We now explain how to apply safety strategies to the practical design of robots. 6.1. Case 1 The following safety designs are executed in the case of a conventional robot (Figure 5(1), arm length 0.25 m, weight 1.8 kg):
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Fig. 5. Safety design of manipulator and the danger-indices (case 1).
1. shape—not sharp to humans;
Fig. 6. Safety design of manipulators and the danger-indices (case 2).
2. weight—light weight material; 3. cover—soft material such as rubber. As a result, a new robot (Figure 5(2)) is obtained. Its roundish shape can be seen: weight, 0.9 kg; shape, y = 0.25x 2 ; surface, rubber (E = 0.5 MPa, thickness 0.1 m). We evaluate the effect of the weight, the shape and the surface of these robots by the evaluation method proposed in the previous section. In the case of collision between a human and a central part of the robot at angular velocity 1.57 rad s−1 , each danger-index of weight, surface material and shape is calculated by eqs. (19), (25) and (32), respectively. The result of such a calculation is shown in Figure 5. We employed the producible impact force of a conventional robot as the critical impact force. The danger-index of the whole robot αall is 0.031. This result reveals that the redesigned robot is 32.78 times as safe as a conventional robot. 6.2. Case 2 As the next example, we evaluate the three types of robot that are shown in Figure 6. Each design specification is as follows: 1. one-joint manipulator robot (material, steel; 3 = 200.0 GPa);
2. one-joint manipulator robot, covered with rubber on the surface (thickness, 0.1 m); 3. ten-joint manipulator robot, with flexible joint covered with rubber. (The full length and the cross-section of the robot are 1 m and 0.1 × 0.1 m2 . The Young’s modulus of rubber is 0.5 MPa.) The calculation results are also shown in Figure 6. When robots 2 and 3 take the same motion of robot 1, the total danger-indices are αall2 = 0.1 and αall3 = 0.024, and the total safe indices are ηall2 = 10.0 and ηall3 = 41.7. As shown by the above, we have been able to quantify the safety of the practically designed robot by using the method of safety evaluation which we have proposed. The subject of the next study will be to verify these findings experimentally.
7. Deriving Danger-Indices of Robot Control Methods In this section, we give examples of safety control strategies to show the practical derivation of a danger-index. We make each danger-index equation kinematically on some assumption to make the effect of it clear as a first trial. If dynamical analysis
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Ikuta, Ishii and Nokata / Safety Evaluation Method or consideration of extra parameters are needed, the safety is evaluated by replacing just the equation of impact force F in eq. (2).
289
and α ∗ are 0.59 s, 24.15 N and 0.049, respectively. The improvement rate η∗ , obtained from eq. (9), is 3.01. The result revealed quantitatively that the danger was decreased almost to 30%.
7.1. Effect of Keeping Distance Sufficient distance produces enough time to reduce impact force by braking, actions to avert collision, and so on. We discuss the effect of keeping distance when the approaching speed of a robot (mass m) is reduced at acceleration a from distance l. The time until collision 4t is obtained by eq. (35), when v > 0 and a > 0: a4t 2 2
(35)
v 2 2l − . a a
(36)
l = v4t − v 4t = − a
The collision speed becomes v −a4t, and the impact force F ∗ and the danger-index α ∗ are expressed as in eqs. (37) and (38). We assume that the impact force does not become a negative value: F∗ = m
(v − a4t) − v
dt
F∗ (v − a4t) − v
α = =m . Fc Fc dt ∗
(37)
7.2. The Effect of Approaching Velocity Human damage caused by approaching velocity is expressed as a time change of the momentum. Therefore, the impact force and danger-index are shown in the following equation: F∗ =
mv − mv
dt
α∗ =
mv − mv
. Fc dt
(39)
Velocity after collision v and contact time dt are determined by shape, material, and so on. For the purpose of picking up the effect of velocity and generally evaluating the danger of the robot, velocity after collision v and contact time dt are substituted by 0 m s−1 and 1 s obtained from the normalization technique of impact force. When a robot (mass 10 kg) comes close to a human at a velocity of 5 m s−1 , the impact force F0 , calculated from eq. (39), is 50 N. Thus, the danger-index α0 is 0.102. If the velocity is reduced from 5 to 1 m s−1 , F ∗ becomes 10 N, and α ∗ becomes 0.020. Thus, a high improvement rate, η∗ = 5, can be obtained. 7.3. The Effect of Posture
(38)
Here, we examine nursing work by a multi-joint manipulator. First, the “normalization technique of impact force” is introduced in order to pick up the effect of distance. In eqs. (35)–(38), acceleration a has no influence on the effect of distance and differs between every robot. Velocity after collision v cannot be specifically determined before the collision. The normalization technique determines these parameters. They are provided by the assumption that impact force is 1 N (normalized impact force). Therefore, unknown parameters in these equations, obtained from this technique, should be a = 1 m s−2 , v = 0 m s−1 , dt = 1.0 s. We consider a concrete example of a robot (mass, 10 kg) approaching a human from a distance of 0.5 m at a velocity of 2 m s−1 . The time until collision 4t, calculated from eq. (36), is 0.27 s. The impact force F0 , obtained from eq. (37), is 64.65 N. The critical impact force Fc is 490 N, i.e., 10% of the force which the human head can withstand without injury (Uehara et al. 2002). A safety factor of 10 on Fc is introduced on our own terms. Strictly speaking, the value of Fc changes according to age, sex and body part. But we use 490 N as one representative value for realizing the generality of danger evaluation. If another value of Fc is needed, the safety is evaluated by replacing just the equation of impact force F in eq. (2). The danger-index α0 calculated from eq. (38) is 0.13. When the robot is set up 1.0 m away from a human, 4t, F ∗
Postures with a minimum momentum of inertia and minimum stiffness improve safety against collisions between humans and robots. 7.3.1. Posture of Minimum Momentum of Inertia Impact force differs according to the posture of a manipulator, namely the momentum of inertia. When the robot (with momentum of inertia I ) works at angular acceleration θ¨ and collides with a human at the point of length r from the base, the impact force and danger-index are expressed as follows: F∗ =
I θ¨ r
α∗ =
F∗ I θ¨ = . Fc Fc r
(40)
In this paper, I is not a 3×3 matrix but a simple value because motions of the robot are limited on single plane. To provide examples with a multi-joint manipulator, we calculate the danger-indices of the three postures shown in Figure 7 using the above equations and the normalization technique of impact force. We decide that θ¨ is 2 rad s−1 because the arm (6 = 1 m, m = 1 kg), which collides at the point r = 0.5 m, produces an impact force of 1 N. The momenta of inertia are (a) 8.75, (b) 6.57 and (c) 2.75, so the impact forces, calculated from eq. (40), are (a) 35 N, (b) 26.3 N and (c) 11 N. The danger-indices are (a) 0.071, (b) 0.053 and (c) 0.022. The improvement rates for (b) and (c) are 1.33 and 3.18, respectively.
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THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / May 2003 Table 3. Safety Control Strategies and Danger-Indices
Fig. 7. Safety effect on the posture with inertial moment.
The above calculations are shown in Table 3. The dangerindex can be easily calculated merely by substituting each control parameter.
Fig. 8. Safety effect on the posture with joint compliance.
8. Examples of Evaluating Practical Robot Control
7.3.2. Posture of Minimum Stiffness
We apply our danger-evaluation method to a multi-articular manipulator. The danger-index for each strategy is calculated and evaluated when a manipulator comes close to a human, as shown in Figure 9.
When each joint has some compliance, the whole stiffness differs according to the posture of the manipulator. When a robot with a whole stiffness of k collides against a human and pushes into him δr, the impact force and danger-index are expressed as follows: F ∗ = kδr
kδr α∗ = . Fc
(41)
δr differs according to several robot and human parameters. We use δr = 0.01 m (k = 1.0 × 102 N m−1 ) obtained from the normalization technique of impact force. We calculate the danger-indexes of the three postures shown in Figure 8. The stiffness of ky at (a), which collides directly above, is infinity, so the impact force Fy is maximum. The stiffness of the side is kx = 0.2 × 102 N m−1 when the joint stiffness k is 1.0 × 102 N m−1 and the length of the arm 6 is 1 m. Impact force, calculated from eq. (41), is 0.2 N. The danger-indices should be 0.4 × 10−3 , 0.59 × 10−3 and 2.0 × 10−3 , respectively. These results mean that the upright posture (a) is the softest and minimizes the impact force of collisions from the side.
8.1. Indication of Danger-Index The robot moves around the human. A new method is required to indicate the danger-index because the index of control strategies is dependent on direction and time. The circle shown in Figure 9 plots the danger-index of each direction from the human. The circle line indicates α ∗ = F ∗ /Fc = 1. When the danger-index crosses over the line, it means that the robot will always injure the human. We call this the “danger-index chart”. This chart can clarify the danger of every direction at all times. The safety of control can be quantitatively improved by decreasing the danger of the direction. Figure 10 shows the danger-chart in the world of space and time, with the danger-index charted at all times on the time axis. As the chart expresses, the danger-index in time and space increases as the area of the danger-index (black area) grows larger. We call this index calculated from eqs. (42) and (43), the ‘time–space danger-chart”:
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Ikuta, Ishii and Nokata / Safety Evaluation Method
Fig. 9. Indication of danger-index under each posture.
291
Fig. 11. Danger-index chart (the human is at point B).
Fig. 10. Schematic diagram of danger-chart in the world of space and time. Fig. 12. Danger-index chart (the human is at point C).
A=
t2 2π
α ∗ (t, θ )δθ δt
(42)
α ∗ (t, θ ) dθ dt.
(43)
t=t1 θ=0
t2 2π → t=t1 θ=0
The features are shown as follows: 1. easy understanding the danger of every direction at all times; 2. evaluation overall danger using the shape and volume; 3. useful for optimizing safety control. The maximum impact force produced in Figure 9 is applied as the critical impact force Fc in order to calculate the danger-index. We did this so that we could compare it with the following similar control strategies. If it becomes necessary to evaluate a concrete example, the same result can be obtained by replacing Fc with the actual value.
8.2. Relationship of the Position Between the Human and the Robot The danger-indices of human positions B, C and D shown are calculated from eq. (38). Each result is shown in Figures 11, 12 and 13. When the robot arrives at posture 4, the danger-index of human position C reaches its maximum, α ∗ (C) = 2.44. The index passes over the circular line of α ∗ = 1, which means that the situation is extremely dangerous. The dangerindices of human positions B and D are α ∗ (B) = 0.57 and α ∗ (D) = 0.45, respectively. This means that the danger is only slight since the index is inside the circle. 8.3. Relationship Between the Approaching Velocity and Danger-Index When a human is at position A in Figure 9, the danger-indices of approaching velocities 2v and v/2 are calculated from eq. (39). Each result is shown in Figure 14. The maximum danger-indices are α ∗ (2v) = 2.68 and α ∗ (0.5v) = 0.42, respectively. In the case where a robot approaches at twice the initial velocity, the index already reaches 1 when the robot approaches at posture 2. Here, there is a clear need for some kind of control, for example, a reduction in velocity.
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Fig. 16. Speed curve of the robot tip (cases A and B). Fig. 13. Danger-index chart (the human is at point D). 8.4. Relationship Between the Momentum of Inertia and Danger-Index Equation (40) is used to calculate the danger-indices when the inertia of the robot is 2I and 0.5I , respectively. We changed the mass of each robot to 2 and 0.5 m in order to fix other parameters. The results are shown in Figure 15. The maximum values of each danger-index are α ∗ (2I ) = 1.67 and α ∗ (0.5I ) = 0.67. As a result, it is easy for us to judge whether or not the robot’s posture is safe. This assists us in the discussion of safety posture. 8.5. Controlling Approaching Velocity and Time–Space Danger-Chart
Fig. 14. Danger-index chart (approaching speeds are 2v and 0.5v).
Figure 17 shows the time–space danger-chart when the tip of a robot approaches with speed curves A and B shown in Figure 16. Even if a robot moves quickly, safety can be maintained by planning a suitable approaching velocity. As a result, optimized control becomes possible.
9. Development of Safe Human-Care Robots Using a Robot Simulator for Danger Evaluation
Fig. 15. Danger-index chart (inertial moments are 2I and 0.5I ).
When developing human-care robots, the effectiveness of necessary safety strategies has to be quantified and the safety of humans assured. Every time we modify an actual robot to enhance safety and evaluate the safety strategies used, great effort and cost go into the new development and construction. On the other hand, the use of a computerized robot model and simulation of danger evaluation make it easier to modify design, improve control strategies and evaluate the effectiveness of safety strategies applied. Less effort and cost will be required in the long run through such means. The features are shown as follows: 1. calculating danger-index of various robots; 2. easy modification of robot design and control; 3. less effort and cost.
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Fig. 18. Development process of human-care robots by using a danger-evaluation simulator.
Fig. 17. Results of the danger-chart in the world of space and time.
A robot simulator for danger evaluation must be capable of a number of functions including the ability to simulate a robot’s desired motions and to evaluate and indicate danger using a prescribed danger evaluation method. It should also serve to facilitate the design and easy modification of new robots. As shown in Figure 18, a robot simulator can make it possible to efficiently develop such robots with due consideration for the safety of humans. According to this concept, we have developed a robot simulator which assists us in the design and simulation of humancare robots, and calculates and shows the danger-index. 9.1. Robot Simulator for Danger-Evaluation This robot simulator works on a Windows PC and is capable of modeling and simulating robots, calculating the danger-index in the course of operations required of them, and indicating danger visually using danger and time–space danger-charts. The graphic user interface (GUI) of this simulator is shown in Figure 19. The main window, which is in the middle of the screen, performs the following functions, much as normal CAD/CAE systems do: 1. it helps us to design robots with friendly GUI; 2. it perceives and displays the motions of robots and other moving things. Danger-charts are shown at the right of the screen. They display quantified danger to multiple persons numerically or
Fig. 19. Graphic user interface of the robot simulator.
graphically. Danger in time and in space represented threedimensionally can be evaluated by observing the figure from various angles using a mouse. The sphere or cylinder is the limit of α = 1.0. Danger-index values shown outside this limit indicate that the person will suffer injury if the robot collides with him or her at that time. It is important therefore to devise safety strategies to ensure that the danger-index value remains within the sphere or cylinder. A simulation is practiced in the following way: 1. design the robots’ parts; 2. connect the parts using appropriate joints and give them motion; 3. select the subject’s or subjects’ motion, then execute a danger-evaluating simulation; 4. judge the result with graphs and numerical values;
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Fig. 22. Types of joints.
We then give motion to each joint by deciding its velocity pattern which fixes its displacement at a point of time by spline interpolation. The effectiveness of safety control strategies, such as reducing velocity in the direction of people or changing an approaching posture or course, is quantified by modifying motions of the joints.
Fig. 20. Shapes of parts.
9.4. Deciding a Person’s Motion and Calculating Danger-Indices
Fig. 21. Properties of a part (e.g., box).
5. if necessary, perform safety design/control strategies, and then carry out the simulation again. From here, procedures involved in the design of the simulator are explained in detail. 9.2. Modeling of the Robots’ Parts First of all, we create rough designs of the robot’s component parts. The shape of each can be chosen from among the five types shown in Figure 20. Its rough position and size are decided using a mouse. Then we decide the exact properties of each, such as position, size, mass, elasticity, and so on. The properties of a box are shown in Figure 21 as an example. The effectiveness of safety design strategies, such as reducing weight by using lightweight material or hollow structure and absorbing impact force with a soft substance, is quantified by calculating those properties exactly. 9.3. Connecting the Parts and Giving Motions The parts are connected using appropriate joints. Each joint is chosen from among three types shown in Figure 22.
This robot simulator treats a person as a moving point to which a critical force is applied, and is able to define multiple points. So it can evaluate danger toward each part of a person, or many people at once. In the dynamic coexistent space of the human and robot above-stated, the danger-index is calculated as eq. (38). The effectiveness of safety design strategies is evaluated by mass m and impact time dt computed from elasticity, and the effectiveness of safety control strategies is evaluated by relative velocity v and time to spare δt computed from distance. A constant a indicates the effect of time to spare. The dangerindex is calculated by dividing producible impact force computed as mentioned above by the critical impact force Fc . The whole danger can be evaluated by calculating the danger-index at all points of time and in all directions. 9.5. Indicating Danger-Index This robot simulator expands a danger-index chart to three dimensions, and is able to prepare multiple windows to show graphs and numerical values. The spherical danger-index chart shown in Figure 23(a) indicates danger toward a point on a person at a point in time synchronizing with its motion displayed in the main window. Now, we need to consider a time–space danger-chart. The sequence of spherical danger-index charts shown in Figure 23(b) makes the whole danger during the operation, but it is troublesome to judge the result without seeing all graphs. This robot simulator projects each spherical danger-index chart onto a plane and arranges all the projected danger-index charts along the time axis as shown in Figure 24. The danger during the
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Fig. 23. Indication of danger-index. Fig. 25. Simulation result of the initial state.
Fig. 24. Dimension contracted time–space danger-index.
Fig. 26. Time–space danger-index for increasing surface elasticity.
operation can be judged objectively by properly determining the plane. Repeating evaluation and modification in this way, the designer can optimize design and control of the human-care robot before building the actual machine.
9.6.1. Safety Design Strategy (Soft Material)
9.6. Examples of Danger Evaluation Simulations We carried out experiments to design a manipulator, to evaluate danger, to modify properties, and to improve safety, as described above. We modeled PA-10 by Mitsubishi. The manipulator was operated to approach a person with a load on a plane. Figure 25 shows the results obtained when we carried out this simulation. The dotted line is the course of the tip. During these simulations the critical impact force was 50 N, the impact time was 0.3 s, and the operation took 3 s. The time–space danger-chart shown on the right is the sequence of spherical danger-index charts projected from this side of the screen. The maximum danger-index value was 1.67, which was sharply over one. This means that the situation is extremely dangerous because a person will be injured if the manipulator collides with him. In the following, we show the results of the simulation with modified parameters as various safety design and control strategies were performed.
As an example of a safety design strategy, we carried out simulations increasing elasticity. Figure 26 shows the result obtained by increasing the impact time twice to 0.6 s as the manipulator was covered with soft material such as rubber. The danger was reduced by half while the maximum dangerindex value decreased to 0.84, which was less than 1. The cost of such a safety strategy is relatively high, but is sure to reduce danger. 9.6.2. Safety Control Strategy (Approaching Posture and Course) As an example of a safety control strategy, we changed the approaching posture and course. Figure 27 shows the result obtained when we modified the motion on the same plane as the initial simulation. Without delaying the operation, the maximum danger-index value was decreased to 0.93, which was less than 1. It seems that the posture of the bending manipulator cut down the velocity toward the person. Figure 28 shows the result obtained by rounding the approaching course to the side of the screen. The maximum danger-index value was decreased to 0.76, which was the smallest of all examples. Such safety control strategies are difficult to control properly, but need not be excessively costly and are very efficient.
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Fig. 27. Simulation result of improving to safe motion. Fig. 30. Simulation results under a dynamic environment.
10. Conclusions
Fig. 28. Simulation result of rounding frontward.
Fig. 29. The robot brings the tip part close to a cared person under a dynamic environment.
We have undertaken a new study of safety in the coexistent space of human and machine in order to realize a human-care robot for the nursing of the aged or disabled. First, the human injury from robot and machine was investigated thoroughly, and we found that it was important to treat safety strategies in the light of mechanical injury. Also, we grouped them as safety design and control strategy according to the difference in their contents. In order to take every safety strategy into consideration, impact force and stress were chosen as evaluation measures for quantifying safety. We proposed the evaluation method of safety and defined danger-index, improvement rate, and total evaluation index. Discussions of some safety strategies proved the viability of our safety evaluation method. In addition, we constructed a new type of 3D robot simulation system for danger evaluation on a PC. By simplifying the evaluation of danger in the stages of both design and control of human-care robots, the system makes it easy to quantify the effectiveness of various safety strategies. As a result, we were able to discuss the successful design and control optimization of robot safety. We believe that this method allows us to assess the contribution of each safety strategy to the overall safety performance of human-care robots.
References These experiments show that the effectiveness of various safety strategies can be easily evaluated quantitatively with our simulator. Furthermore, by calculating danger when performing several types of safety strategies at once, it is possible to compare the contribution of each safety strategy to the whole. We can similarly evaluate cases where a person approaches the robot or several people are in its vicinity (Figures 29 and 30). Next, we will devise and automate an operationoptimization method.
Dohi, T. 1996. Classification and safety of medical and human care robots. In Proceedings of JSME Annual Conference on Robotics and Mechatronics pp. 1181–1182 (in Japanese). Ikuta, K., Makita, S., and Arimoto, S. 1991. Non-contact magnetic gear for micro transmission mechanism. In Proceedings of International Workshop on Micro Electromechanical Systems (MEMS’91) pp. 125–130. Ikuta, K., Kawahara, A., and Yamazumi, S. 1991. Miniature cybernetic actuators using piezoelectric device. In
Downloaded from http://ijr.sagepub.com at PENNSYLVANIA STATE UNIV on February 8, 2008 © 2003 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.
Ikuta, Ishii and Nokata / Safety Evaluation Method Proceedings of International Workshop on Micro Electromechanical Systems (MEMS’91) pp. 131–135. International Organization for Standardization. 1990. Guidelines for the inclusion of safety aspects in standards, ISO/IEC GUIDE 51. Saito, Y., et al. 1996. Research on safety operating of the assisting robot. In Proceedings of JSME Annual Conference on Robotics and Mechatronics pp. 1177–1180 (in Japanese). Saito, T., and Sugimoto, N. 1997. A study on electrorheological motion control using an antagonistic rotary actuator. In Proceedings of the 6th International Conference on ER-Fluids, ERMR’97.
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Shannon, C.E. 1948. A mathematical theory of communication. Bell System Technology Journal 27:379–423, 623– 656. Suita, K., et al. 1995. A failure-to-safety “Kyozon” system with simple contact detection and stop capabilities for safe human-robot coexistence. In Proceedings of IEEE International Conference on Robotics and Automation Vol. 3, pp. 3089–3096. Uehara, Y., et al. 2002. A Handbook for Safety Engineering, Corona Publishing, Tokyo, pp. 1063 (in Japanese). Yoshikawa, T. 1985. Manipulability of robotic mechanisms. International Journal of Robotics Research 4(2):3–9.
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Safety Evaluation Method of Design and Control for Human-Care Robots Koji Ikuta, Hideki Ishii and Makoto Nokata The International Journal of Robotics Research 2003; 22; 281 DOI: 10.1177/0278364903022005001 The online version of this article can be found at: http://ijr.sagepub.com/cgi/content/abstract/22/5/281
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Koji Ikuta Hideki Ishii Department of Micro System Engineering School of Engineering Nagoya University Japan
Makoto Nokata
Safety Evaluation Method of Design and Control for Human-Care Robots
Department of Robotics Faculty of Science and Engineering Ritsumeikan University Japan
Abstract We propose the world’s first general method of evaluating safety for human-care robots. In the case of a careless collision between a robot and a human, impact force and impact stress are chosen as evaluation measures, and a danger-index is defined to quantitatively evaluate the effectiveness of each safety strategy used for design and control. As a result, this proposed method allows us to assess the contribution of each safety strategy to the overall safety performance of a human-care robot. In addition, a new type of three-dimensional robot simulation system for danger evaluation is constructed on a PC. The system simplifies the danger evaluation of both the design and control of various types of human-care robots to quantify the effectiveness of various safety strategies.
KEY WORDS—human-care robot, safety evaluation, danger index, safety design and control
ation measures which describe the degree of safety. Then, we apply our method to evaluate several safety design/control strategies, and we prove the viability of our safety evaluation method. Finally, we construct a new type of three-dimensional (3D) robot simulation system for danger evaluation on a PC, and we realize an easily designed robot, controlling safety.
2. Safety Strategy for Human-Care Robots 2.1. Injury to Humans from Human-Care Robots We have given thorough consideration to the possibility of injury to humans from human-care robots and machines. The causes of injury may be classified as follows: 1. mechanical injury • shock—internal bleeding, fracture of a bone; • scar—bleeding, contagion;
1. Introduction An aged society is not far in the future. Human-care robots must be realized to nurse aged and disabled people. Humancare robots will need to work around humans and to touch them. So, conventional safety strategies for industrial robots cannot be applied to human-care robots. It is now necessary to make a new study of safety in the areas where humans and machines will exist together. In this paper, we investigate human injury caused by robots and machines, and then we classify the safety design and control strategy for robots. Next, we propose a method for evaluating safety for human-care robots and we define evaluThe International Journal of Robotics Research Vol. 22, No. 5, May 2003, pp. 281-297, ©2003 Sage Publications
2. electric injury • electric shock—death from shock, burn; • electromagnetic wave—cancer, leukemia; 3. acoustic injury • boom—hardness of hearing; • low frequency sound—insomnia, neurosis. In this research, as the subject of our study we have chosen the safety strategy to prevent mechanical injury. Although protecting humans from electric and acoustic injury is possible by making use of insulators or soundproofing materials, it is very difficult to isolate the mechanical damage in the 281
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robot working space. In order to secure human-care robots which work around humans, many types of design and control strategies are indispensable. But many complex and difficult problems are conformed in the design of the robot. 2.2. Classification of Safety Strategies We classify safety strategies as follows: 1. pre-contact safety strategy; 2. post-contact safety strategy. Pre-contact safety strategies consider minimizing human injury before human–robot collision. Post-contact safety strategies aim to reduce potential injuries after collisions. In analogy to car safety strategy, the former strategy corresponds to avoiding a collision by means of an Antilock Brake System (ABS), the latter strategy to absorbing the shock by means of an air bag or side door beam. From the point of view of a human-care robot user or designer, this discussion can be classified as follows: 1. safety design strategy (minimizing injury by design); 2. safety control strategy (minimizing injury by control). Table 1 shows the classification of safety strategies, clearly showing the details. We have already developed cybernetic actuators (Ikuta et al. 1991) and non-contact magnetic gear (Ikuta, Makita, and Arimoto 1991), which have force limiting functions as safety designs. Other strategies have been devised, such as force limiting equipment using electrorheological fluid (Saito and Sugimoto 1997), force control, shock absorption cover (Suita et al. 1995), and chamfering, etc. Thus far, little research has been carried out on safety evaluation methods; some of the research to date measures the danger inherent in different actuator arrangements (Dohi 1996) and safety in human control (Saito et al. 1996).
Table 1. Classification of Safety Strategies
International safety standards have defined safety as “freedom from unacceptable risk of harm”, and thus estimate only the risk of harm (International Organization for Standardization 1990). This estimation method lacks a quantitative basis because it relies on the use of insufficiently provable data. Furthermore, the estimation methods of safety vary with the researchers. As a result, we cannot compare the various strategies. So we have carried out only one separate case study from beginning to end. The reasons for this are attributable to the vagueness of the concept of safety. Everyone thinks that it is difficult to calculate the degree of safety or dangerousness and the contribution of each safety design and control strategy to the overall safety performance of robots. So nobody tries to do it. As a result, the aim of this study is to propose a method to evaluate safety for various robots on the same scale in order to compare and investigate them quantitatively. A detailed or complicated method limits the evaluated objects and contents. In order to evaluate various types of robot, the method should be simple and must use the simplified model, calculating general physical quantity.
3. Proposal of Evaluation Measures 3.1. Necessity for Quantitative Evaluation of Safety It is necessary to define “evaluation measures” for devising various safety strategies of human-care robots. Evaluation measures enable us to compare the effect of each safety strategy on the same scale and to optimize the design and control of human-care robots. In the field of information science, Shannon (1948) has defined information as the degree of entropy, thereby advancing information theory remarkably. In the robotics field, Yoshikawa (1985) and Uchiyama defined the measure of manipulability, which has enabled us to compare the manipulation performance of various kinds of robot uniformly. The former definition does not express enough about the quality of the information; the latter does not express various kinds of control performance completely. But we cannot deny their contribution to science and engineering. If we overcome some different opinions and define the general evaluation measures of human-care robots, we will be able to achieve similar effects. 3.2. Selection of Evaluation Measures In the event of careless collision between robots and humans, the degree of dangerousness can be expressed as eq. (2) by using only main factors such as design and control: Dangerousness
=
{f (design) · g(control)} (1) ×(a rate of accident incidence).
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Ikuta, Ishii and Nokata / Safety Evaluation Method In the International Organization for Standardization (ISO), this has been analyzed by the risk management of the rate of accident incidence caused by human error, manipulation and so on. Their main aim is how to reduce the probability of accident and how to estimate it. Little attention has been paid to the relation between the design or control of humancare robots and the danger of injury. In this research, we aim to study “what design or control can minimize human injury” at the occurrence of an accident. In other words, our aim is to make a quantitative evaluation of the effectiveness of safety design or control strategies, and to minimize the dangerousness on the condition that the rate of accident incidence is 1. So what should the evaluation measures be? A human-care robot works around humans who move irregularly. We consider an appropriate safety strategy while adapting the classified design/control safety strategy mentioned previously. A safety design strategy is a means for reducing the injury to a human after an irregular collision. A safety control strategy is a means for minimizing the injury before a human–robot collision. Therefore, it is important to estimate not the occurrence rate but the injury due to collision. No matter what the cause of collision accident may be, the shock of mechanical injury depends on the impact force, and the scar depends on impact stress. Namely, we consider impact force and stress as evaluation measures.
4. Safety Evaluation Method Using Evaluation Measures In this section, we propose a safety evaluation method using evaluation measures for human-care robots. 4.1. Safety Evaluation of Safety Design Strategy First, we define the critical impact force Fc as a minimal impact force that causes injury to humans. Next, we define the danger-index α as the producible impact force F against Fc in eq. (2): α=
F Fc
(α ≥ 0).
injury to a human is output. The index is dependent on the transfer function. In this system, several factors are connected with each other in series. The characteristic of the whole system can be expressed as the multiplication of each transfer function. So the total danger-index of the whole robot αall is expressed by the multiplication shown in eq. (3), a calculation which is made possible by quantifying the effect of safety strategies on the same scale: αall =
n
αi .
(3)
i=1
Here, n is the total number of safety strategies and i is the number of safety strategies. As an example, we consider the case of reducing impact force using a perfect shock absorption material. Even if a robot which has a dangerous shape or other factors collides with a human, the impact force to the human is qualitatively zero because it is isolated by the material. The danger-index αj (1, 2, . . . j . . . , n) about the shock absorption material is expressed as zero by using the proposed evaluation method of safety. The total danger-index multiplied by each index results in zero, so it is obvious to agree the usual. But too many safety strategies will cause a lowering of the ability of robot work or operation. This problem can be solved by devising a safety strategy on condition that required working ability is satisfied, or calculating the optimum solution between eq. (3) and efficiency of robot working. This is an advantage produced by a quantitative evaluation of dangerousness. The improvement rate η can be calculated as follows, by using impact force and the danger-index before improvement as F0 and α0 respectively: η=
α0 F0 Fc F0 = = , α Fc F F
ηall =
n α0 i=1
(2)
Strictly speaking, the value of force Fc varies according to age, sex and body part. But we use one representative value for realizing the generality of safety evaluation. In exceptional cases such as body parts where Fc is very low, such as eyes, these cases are treated as a singular point. Another evaluation is needed for such points. Next, we consider the overall danger-index provided by several safety strategies. We express the characteristic of safety strategies for minimizing the impact force by using a block chart, which is popular in the control field. For example, producible impact force is input, a safety strategy is a factor, its danger-index is transfer function, and
283
αi
.
(4)
(5)
In eq. (4) Fc is canceled. So we can simply compare before and after safety strategies. The algorithm of our proposed evaluation method is as follows: 1. investigating the factor of damage to a human as evaluation measures; 2. calculating the impact force F of each safety strategy; 3. calculating the danger-index α from eq. (2); 4. executing the safety evaluation by using the total danger-index;
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5. discussing the review of the safety strategy or not from the result. This method enables us to evaluate the effect of each or all safety strategies. 4.2. Expansion into Safety Control Strategy For safety control strategies, it is possible to employ impact force as an evaluation measure. So each danger-index can be calculated in the same way as the safety design strategy (Section 4.1). The premises are as follows: 1. robots are always controlled without collision with a human; 2. robots can be controlled just before collision even if the collision is unexpected.
4.3. Expansion for Evaluating Various Types of Danger In order to discuss the safety of the many types of humancare robots or equipment, various types of danger must be considered and examined. Most have a tendency to be independent. So it is difficult to measure them on the same scale even if they can be quantified. Thus, we propose the evaluation method of safety strategy for human-care equipment in general by expanding the method described above. First, a suitable evaluation measure S is defined for each safety strategy the same as impact force. If critical impact values of damage to human Sc is given, the danger-index is as follows: α=
S Sc
(α ≥ 0).
When we evaluate several strategies together which have the same evaluation measures, the total danger-index can be calculated by multiplying eq. (13)
The following equations are derived similar to eqs. (2)–(5): F∗ α∗ = Fc
(α ∗ ≥ 0)
n
∗ αall =
αi∗
(6)
(7)
i=1
η∗ =
α0 F0 = ∗ ∗ α F
∗ ηall =
n
ηi∗ .
(8)
(9)
i=1
We use “*” in these equations in order to distinguish them from the safety design strategy. When safety design and control strategy are carried out at the same time, the total dangerindex of the whole robot can be expressed in multiplication equations the same as eqs.(7) and (9): αall =
i=1
ηall
αall =
αi
αj∗
(10)
j =1
m n α0 α0 = . αi j =1 αj∗ i=1
(11)
By using these equations, it is possible to optimize both safety design and safety control and to evaluate them at the same time. In the case of treating scar, impact force is replaced with impact stress.
n
αi ,
(13)
i=1
where N is the total number of safe strategies and i is the number of the safety strategy. The general danger-index Gα , which considers several evaluation measures, is obtained by additional equations because these values are independent of each other. Gα =
ci α(Si )all .
(14)
i
The weight coefficient ci is defined by measuring individual properties of humans. For an example of another safety strategy, if the dangerous factor is an electric shock, the evaluation measure is determined as a current I (A) because the damage to humans is dependent on it. If the minimal current value which produces the damage to humans is defined as the critical current value Ic , the danger-index becomes the same as eq. (12): α(I ) =
n
m
(12)
I . Ic
(15)
The improvement rate can be calculated in the same way as impact force. The total danger-index can be calculated by multiplying eq. (15): α(I )all =
n
α(I )i .
(16)
i=1
In addition, it is possible to quantify burn (temperature, T (K), e.g., radio knife), fall (moment, M (N m−1 ), e.g., wheel chair), pressing (pressure, P (Pa), e.g., holding in robot arms) and noise (decibel (dB)) in spite of I (A) by the general
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danger-index of these evaluation measures, which are independent of each other, by summation of eq. (14): Gα = c1 α(I )all + c2 α(T )all + c3 α(M)all + · · · .
(17)
There are several ways to decide ci ; one is by using a medical benefit or medical insurance. For example, critical impact force Fc causes injury which will take four weeks to heal completely; critical current Ic causes injury which will take two weeks to heal completely. We can fix on a cforce value which is twice as large as ccurrent . By using this method, not only impact force F but also many types of safety or dangerousness can be evaluated quantitatively. It is possible to realize the correlation between safety and practical use, such as function, workspace, work efficiency, and so on, using simultaneous equations with their estimated equations and eq. (17). Fig. 1. Manipulator covered with soft material.
5. Deriving Danger-Indices of Robot Design Methods In this section, we give examples of safety design strategy to show the practical derivation of a danger-index. We propose a linear approximate model of each safety strategy and solve it individually. The aim of the approximation is to extract only the effect of a safety factor and to remove the effects of other factors, as much as possible. Usually, we make models and equations which satisfy all effects of boundary conditions at the same time. But this requires reconsideration of the model or the equation when the conditions are changed. If many phenomena are considered, it makes the equation complicated and increases unknown variables. To execute the evaluation and the comparison of safety strategies, it is necessary not only to consider all phenomena strictly but also to quantify the safety with the aim of wide use. As a result, we work out the danger-index of the safety strategy by using a linear approximate model individually. This research supposes a sudden collision between human and robot, so we discuss each safety strategy for reducing the damage from the collision. 5.1. Effect of Reducing the Weight We consider a strategy of reducing a robot weight in order to minimize the impact force. Impact force F is derived as eq. (18) by Newton’s equation of motion. This impact force F of the robot against the critical force yields the danger-index α, eq. (19): F = ma
(18)
ma . Fc
(19)
α=
As an example, a danger-index is shown when robot material is changed. For a robot whose main material is steel (density, 7.86 × 103 kg m−3 ) and whose weight is 20 kg moving at 1 m s−2 , if the material is replaced with aluminum (density, 2.69 × 103 kg m−3 ), the robot weight becomes 6.7 kg and its danger-index α is 0.34. Or, if replaced with a plastic (density, 1.40 × 103 kg m−3 ), the weight becomes 3.5 kg and its index α is 0.18. In short, if the weight is reduced by half, α is also halved. 5.2. Effect of Absorbing Impact Force We consider a strategy of absorbing impact force by soft material as shown in Figure 1. Generally speaking, several humanrelated parameters need to be set in the case of working out the time response of material deformation. But we employ the same boundary conditions in order to purpose the safety evaluation method and calculate the maximum impact force in a collision. If the approach speed of the robot is reduced from v to v , the impact force F is derived from momentum as in eq. (20): F =
mv − mv
. dt
(20)
The collision between human and robot can be expressed by a linear approximate model (Figure 2), and the following equation of motion is obtained: mx¨ + cx˙ + kx = 0
(x = xrg − xrs ).
(21)
This model shows damped oscillation, so the solution of eq. (21) is as follows:
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Fig. 2. Model of the collision between human and robot. Fig. 3. Manipulator with compliant joints.
x = e−ζ ωn t C cos(ωd t − β) where
(22)
5.3. Effect of Joint Compliance It is an effective strategy to have compliance in each joint as in Figure 3. Rotational motion around the joint is produced by collision, and impact force F can be calculated using
ωn = k/m, ωd = ωn 1 − ζ 2
F3 =
√ ζ = c/2 mk and
C=
a02 +
(x = a0 , x˙ = v0 at t = 0). Equation (23) is obtained by differentiating eq. (22): x˙ = Ce−ζ ωn t (−ζ ωn cos(ωd t − β) − ωd sin(ωd t − β)) . (23) When the speed after collision v is 0, the impact force becomes maximum. So the collision time dt is obtained as −1
I θ¨ + C θ˙ + Kθ = 0
(27)
tan−1 (−ζ ωn /ωd ) + π/2 , (28) ωd √ √ √ where ωn is K/I , ωd = ωn 1 − ζ 2 , ζ is C/2 I K, and dt =
α=
(24)
As a result, the danger-index α is derived as mv . α= Fc dt
(26)
where I is the moment of inertia and l is the distance from joint to contact point. The collision time can be obtained in the same manner as in Section 5.2. So eqs. (28) and (29) are derived by replacing eq. (21) with
v0 + a 0 ζ ωn v 0 + a 0 ζ ωn , β = tan−1 ωd a0 ωd
tan (−ζ ωn /ωd ) + π/2 dt = . ωd
I ω − I ω
l dt
I θ˙ . Fc dt
(29)
5.4. Minimizing Impact Stress Caused by Shape (25)
In this equation, the time response is not considered. But the most dangerous situation is considered because maximum value is obtained. For example, the danger-index of a robot, which moves at α = 1.0, is reduced to 0.05 by covering it with rubber (thickness 10 mm, Young’s modulus 5.0 Mpa).
This strategy is to design robot shape for minimizing impact stress. Impact stress σ is calculated by σ =
F A
(30)
where A is contact area. Strictly, contact area A is dependent not only on the shape but also on the material specification.
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Table 2. Safety Design Strategies and Danger-Indices
Fig. 4. Deformation area under the collision between human and robot. So we calculate the danger-index α by using the rate of deformation λ (eq. (31)) which considers the possession space of human A1 (outline, y = human(x)) and deformation space A2 (outline, y = robot (x)) in order to extract the effect of shape (Figure 3): 2l −l (human(x) − robot (x)) dx A2 λ= . (31) = 2 l l A1 2 ( − human(x)) dx l 2 − 2
As a result, the danger-index is as follows: λ (32) λc where λc is the critical rate of deformation. As an example, we consider a collision with a human head (φ = 0.2 m) and other things, such as (1) a kitchen knife (width 50 mm, thickness 2 mm), (2) a bat (φ = 0.1 m) and (3) a curved surface (y = −0.5x 2 ). Each danger-index α is (1) 24.08, (2) 4.8 and (3) 0.92 as compared with a flat surface. So it is possible to evaluate the dangerousness of shapes. α=
5.5. Effect of Reducing Surface Friction It is possible to release impact force by slipping on the surface with less friction: F = µN
(33)
µN (34) Fc where µ is the coefficient of friction, and N is the vertical force. As an example, we compare robots which are covered with iron, nylon and Teflon. If the robot’s surface material, iron (µ = 0.5), is replaced with nylon (µ = 0.2) or Teflon (µ = 0.04), each danger-index α is 0.4 and 0.08. Danger-indices of the above safety design strategies are integrated in Table 2. Those indices can be calculated by inputting each design parameter to the equations in it. α=
6. Examples of Evaluating Practical Robot Design We now explain how to apply safety strategies to the practical design of robots. 6.1. Case 1 The following safety designs are executed in the case of a conventional robot (Figure 5(1), arm length 0.25 m, weight 1.8 kg):
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Fig. 5. Safety design of manipulator and the danger-indices (case 1).
1. shape—not sharp to humans;
Fig. 6. Safety design of manipulators and the danger-indices (case 2).
2. weight—light weight material; 3. cover—soft material such as rubber. As a result, a new robot (Figure 5(2)) is obtained. Its roundish shape can be seen: weight, 0.9 kg; shape, y = 0.25x 2 ; surface, rubber (E = 0.5 MPa, thickness 0.1 m). We evaluate the effect of the weight, the shape and the surface of these robots by the evaluation method proposed in the previous section. In the case of collision between a human and a central part of the robot at angular velocity 1.57 rad s−1 , each danger-index of weight, surface material and shape is calculated by eqs. (19), (25) and (32), respectively. The result of such a calculation is shown in Figure 5. We employed the producible impact force of a conventional robot as the critical impact force. The danger-index of the whole robot αall is 0.031. This result reveals that the redesigned robot is 32.78 times as safe as a conventional robot. 6.2. Case 2 As the next example, we evaluate the three types of robot that are shown in Figure 6. Each design specification is as follows: 1. one-joint manipulator robot (material, steel; 3 = 200.0 GPa);
2. one-joint manipulator robot, covered with rubber on the surface (thickness, 0.1 m); 3. ten-joint manipulator robot, with flexible joint covered with rubber. (The full length and the cross-section of the robot are 1 m and 0.1 × 0.1 m2 . The Young’s modulus of rubber is 0.5 MPa.) The calculation results are also shown in Figure 6. When robots 2 and 3 take the same motion of robot 1, the total danger-indices are αall2 = 0.1 and αall3 = 0.024, and the total safe indices are ηall2 = 10.0 and ηall3 = 41.7. As shown by the above, we have been able to quantify the safety of the practically designed robot by using the method of safety evaluation which we have proposed. The subject of the next study will be to verify these findings experimentally.
7. Deriving Danger-Indices of Robot Control Methods In this section, we give examples of safety control strategies to show the practical derivation of a danger-index. We make each danger-index equation kinematically on some assumption to make the effect of it clear as a first trial. If dynamical analysis
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Ikuta, Ishii and Nokata / Safety Evaluation Method or consideration of extra parameters are needed, the safety is evaluated by replacing just the equation of impact force F in eq. (2).
289
and α ∗ are 0.59 s, 24.15 N and 0.049, respectively. The improvement rate η∗ , obtained from eq. (9), is 3.01. The result revealed quantitatively that the danger was decreased almost to 30%.
7.1. Effect of Keeping Distance Sufficient distance produces enough time to reduce impact force by braking, actions to avert collision, and so on. We discuss the effect of keeping distance when the approaching speed of a robot (mass m) is reduced at acceleration a from distance l. The time until collision 4t is obtained by eq. (35), when v > 0 and a > 0: a4t 2 2
(35)
v 2 2l − . a a
(36)
l = v4t − v 4t = − a
The collision speed becomes v −a4t, and the impact force F ∗ and the danger-index α ∗ are expressed as in eqs. (37) and (38). We assume that the impact force does not become a negative value: F∗ = m
(v − a4t) − v
dt
F∗ (v − a4t) − v
α = =m . Fc Fc dt ∗
(37)
7.2. The Effect of Approaching Velocity Human damage caused by approaching velocity is expressed as a time change of the momentum. Therefore, the impact force and danger-index are shown in the following equation: F∗ =
mv − mv
dt
α∗ =
mv − mv
. Fc dt
(39)
Velocity after collision v and contact time dt are determined by shape, material, and so on. For the purpose of picking up the effect of velocity and generally evaluating the danger of the robot, velocity after collision v and contact time dt are substituted by 0 m s−1 and 1 s obtained from the normalization technique of impact force. When a robot (mass 10 kg) comes close to a human at a velocity of 5 m s−1 , the impact force F0 , calculated from eq. (39), is 50 N. Thus, the danger-index α0 is 0.102. If the velocity is reduced from 5 to 1 m s−1 , F ∗ becomes 10 N, and α ∗ becomes 0.020. Thus, a high improvement rate, η∗ = 5, can be obtained. 7.3. The Effect of Posture
(38)
Here, we examine nursing work by a multi-joint manipulator. First, the “normalization technique of impact force” is introduced in order to pick up the effect of distance. In eqs. (35)–(38), acceleration a has no influence on the effect of distance and differs between every robot. Velocity after collision v cannot be specifically determined before the collision. The normalization technique determines these parameters. They are provided by the assumption that impact force is 1 N (normalized impact force). Therefore, unknown parameters in these equations, obtained from this technique, should be a = 1 m s−2 , v = 0 m s−1 , dt = 1.0 s. We consider a concrete example of a robot (mass, 10 kg) approaching a human from a distance of 0.5 m at a velocity of 2 m s−1 . The time until collision 4t, calculated from eq. (36), is 0.27 s. The impact force F0 , obtained from eq. (37), is 64.65 N. The critical impact force Fc is 490 N, i.e., 10% of the force which the human head can withstand without injury (Uehara et al. 2002). A safety factor of 10 on Fc is introduced on our own terms. Strictly speaking, the value of Fc changes according to age, sex and body part. But we use 490 N as one representative value for realizing the generality of danger evaluation. If another value of Fc is needed, the safety is evaluated by replacing just the equation of impact force F in eq. (2). The danger-index α0 calculated from eq. (38) is 0.13. When the robot is set up 1.0 m away from a human, 4t, F ∗
Postures with a minimum momentum of inertia and minimum stiffness improve safety against collisions between humans and robots. 7.3.1. Posture of Minimum Momentum of Inertia Impact force differs according to the posture of a manipulator, namely the momentum of inertia. When the robot (with momentum of inertia I ) works at angular acceleration θ¨ and collides with a human at the point of length r from the base, the impact force and danger-index are expressed as follows: F∗ =
I θ¨ r
α∗ =
F∗ I θ¨ = . Fc Fc r
(40)
In this paper, I is not a 3×3 matrix but a simple value because motions of the robot are limited on single plane. To provide examples with a multi-joint manipulator, we calculate the danger-indices of the three postures shown in Figure 7 using the above equations and the normalization technique of impact force. We decide that θ¨ is 2 rad s−1 because the arm (6 = 1 m, m = 1 kg), which collides at the point r = 0.5 m, produces an impact force of 1 N. The momenta of inertia are (a) 8.75, (b) 6.57 and (c) 2.75, so the impact forces, calculated from eq. (40), are (a) 35 N, (b) 26.3 N and (c) 11 N. The danger-indices are (a) 0.071, (b) 0.053 and (c) 0.022. The improvement rates for (b) and (c) are 1.33 and 3.18, respectively.
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Fig. 7. Safety effect on the posture with inertial moment.
The above calculations are shown in Table 3. The dangerindex can be easily calculated merely by substituting each control parameter.
Fig. 8. Safety effect on the posture with joint compliance.
8. Examples of Evaluating Practical Robot Control
7.3.2. Posture of Minimum Stiffness
We apply our danger-evaluation method to a multi-articular manipulator. The danger-index for each strategy is calculated and evaluated when a manipulator comes close to a human, as shown in Figure 9.
When each joint has some compliance, the whole stiffness differs according to the posture of the manipulator. When a robot with a whole stiffness of k collides against a human and pushes into him δr, the impact force and danger-index are expressed as follows: F ∗ = kδr
kδr α∗ = . Fc
(41)
δr differs according to several robot and human parameters. We use δr = 0.01 m (k = 1.0 × 102 N m−1 ) obtained from the normalization technique of impact force. We calculate the danger-indexes of the three postures shown in Figure 8. The stiffness of ky at (a), which collides directly above, is infinity, so the impact force Fy is maximum. The stiffness of the side is kx = 0.2 × 102 N m−1 when the joint stiffness k is 1.0 × 102 N m−1 and the length of the arm 6 is 1 m. Impact force, calculated from eq. (41), is 0.2 N. The danger-indices should be 0.4 × 10−3 , 0.59 × 10−3 and 2.0 × 10−3 , respectively. These results mean that the upright posture (a) is the softest and minimizes the impact force of collisions from the side.
8.1. Indication of Danger-Index The robot moves around the human. A new method is required to indicate the danger-index because the index of control strategies is dependent on direction and time. The circle shown in Figure 9 plots the danger-index of each direction from the human. The circle line indicates α ∗ = F ∗ /Fc = 1. When the danger-index crosses over the line, it means that the robot will always injure the human. We call this the “danger-index chart”. This chart can clarify the danger of every direction at all times. The safety of control can be quantitatively improved by decreasing the danger of the direction. Figure 10 shows the danger-chart in the world of space and time, with the danger-index charted at all times on the time axis. As the chart expresses, the danger-index in time and space increases as the area of the danger-index (black area) grows larger. We call this index calculated from eqs. (42) and (43), the ‘time–space danger-chart”:
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Fig. 9. Indication of danger-index under each posture.
291
Fig. 11. Danger-index chart (the human is at point B).
Fig. 10. Schematic diagram of danger-chart in the world of space and time. Fig. 12. Danger-index chart (the human is at point C).
A=
t2 2π
α ∗ (t, θ )δθ δt
(42)
α ∗ (t, θ ) dθ dt.
(43)
t=t1 θ=0
t2 2π → t=t1 θ=0
The features are shown as follows: 1. easy understanding the danger of every direction at all times; 2. evaluation overall danger using the shape and volume; 3. useful for optimizing safety control. The maximum impact force produced in Figure 9 is applied as the critical impact force Fc in order to calculate the danger-index. We did this so that we could compare it with the following similar control strategies. If it becomes necessary to evaluate a concrete example, the same result can be obtained by replacing Fc with the actual value.
8.2. Relationship of the Position Between the Human and the Robot The danger-indices of human positions B, C and D shown are calculated from eq. (38). Each result is shown in Figures 11, 12 and 13. When the robot arrives at posture 4, the danger-index of human position C reaches its maximum, α ∗ (C) = 2.44. The index passes over the circular line of α ∗ = 1, which means that the situation is extremely dangerous. The dangerindices of human positions B and D are α ∗ (B) = 0.57 and α ∗ (D) = 0.45, respectively. This means that the danger is only slight since the index is inside the circle. 8.3. Relationship Between the Approaching Velocity and Danger-Index When a human is at position A in Figure 9, the danger-indices of approaching velocities 2v and v/2 are calculated from eq. (39). Each result is shown in Figure 14. The maximum danger-indices are α ∗ (2v) = 2.68 and α ∗ (0.5v) = 0.42, respectively. In the case where a robot approaches at twice the initial velocity, the index already reaches 1 when the robot approaches at posture 2. Here, there is a clear need for some kind of control, for example, a reduction in velocity.
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Fig. 16. Speed curve of the robot tip (cases A and B). Fig. 13. Danger-index chart (the human is at point D). 8.4. Relationship Between the Momentum of Inertia and Danger-Index Equation (40) is used to calculate the danger-indices when the inertia of the robot is 2I and 0.5I , respectively. We changed the mass of each robot to 2 and 0.5 m in order to fix other parameters. The results are shown in Figure 15. The maximum values of each danger-index are α ∗ (2I ) = 1.67 and α ∗ (0.5I ) = 0.67. As a result, it is easy for us to judge whether or not the robot’s posture is safe. This assists us in the discussion of safety posture. 8.5. Controlling Approaching Velocity and Time–Space Danger-Chart
Fig. 14. Danger-index chart (approaching speeds are 2v and 0.5v).
Figure 17 shows the time–space danger-chart when the tip of a robot approaches with speed curves A and B shown in Figure 16. Even if a robot moves quickly, safety can be maintained by planning a suitable approaching velocity. As a result, optimized control becomes possible.
9. Development of Safe Human-Care Robots Using a Robot Simulator for Danger Evaluation
Fig. 15. Danger-index chart (inertial moments are 2I and 0.5I ).
When developing human-care robots, the effectiveness of necessary safety strategies has to be quantified and the safety of humans assured. Every time we modify an actual robot to enhance safety and evaluate the safety strategies used, great effort and cost go into the new development and construction. On the other hand, the use of a computerized robot model and simulation of danger evaluation make it easier to modify design, improve control strategies and evaluate the effectiveness of safety strategies applied. Less effort and cost will be required in the long run through such means. The features are shown as follows: 1. calculating danger-index of various robots; 2. easy modification of robot design and control; 3. less effort and cost.
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Fig. 18. Development process of human-care robots by using a danger-evaluation simulator.
Fig. 17. Results of the danger-chart in the world of space and time.
A robot simulator for danger evaluation must be capable of a number of functions including the ability to simulate a robot’s desired motions and to evaluate and indicate danger using a prescribed danger evaluation method. It should also serve to facilitate the design and easy modification of new robots. As shown in Figure 18, a robot simulator can make it possible to efficiently develop such robots with due consideration for the safety of humans. According to this concept, we have developed a robot simulator which assists us in the design and simulation of humancare robots, and calculates and shows the danger-index. 9.1. Robot Simulator for Danger-Evaluation This robot simulator works on a Windows PC and is capable of modeling and simulating robots, calculating the danger-index in the course of operations required of them, and indicating danger visually using danger and time–space danger-charts. The graphic user interface (GUI) of this simulator is shown in Figure 19. The main window, which is in the middle of the screen, performs the following functions, much as normal CAD/CAE systems do: 1. it helps us to design robots with friendly GUI; 2. it perceives and displays the motions of robots and other moving things. Danger-charts are shown at the right of the screen. They display quantified danger to multiple persons numerically or
Fig. 19. Graphic user interface of the robot simulator.
graphically. Danger in time and in space represented threedimensionally can be evaluated by observing the figure from various angles using a mouse. The sphere or cylinder is the limit of α = 1.0. Danger-index values shown outside this limit indicate that the person will suffer injury if the robot collides with him or her at that time. It is important therefore to devise safety strategies to ensure that the danger-index value remains within the sphere or cylinder. A simulation is practiced in the following way: 1. design the robots’ parts; 2. connect the parts using appropriate joints and give them motion; 3. select the subject’s or subjects’ motion, then execute a danger-evaluating simulation; 4. judge the result with graphs and numerical values;
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Fig. 22. Types of joints.
We then give motion to each joint by deciding its velocity pattern which fixes its displacement at a point of time by spline interpolation. The effectiveness of safety control strategies, such as reducing velocity in the direction of people or changing an approaching posture or course, is quantified by modifying motions of the joints.
Fig. 20. Shapes of parts.
9.4. Deciding a Person’s Motion and Calculating Danger-Indices
Fig. 21. Properties of a part (e.g., box).
5. if necessary, perform safety design/control strategies, and then carry out the simulation again. From here, procedures involved in the design of the simulator are explained in detail. 9.2. Modeling of the Robots’ Parts First of all, we create rough designs of the robot’s component parts. The shape of each can be chosen from among the five types shown in Figure 20. Its rough position and size are decided using a mouse. Then we decide the exact properties of each, such as position, size, mass, elasticity, and so on. The properties of a box are shown in Figure 21 as an example. The effectiveness of safety design strategies, such as reducing weight by using lightweight material or hollow structure and absorbing impact force with a soft substance, is quantified by calculating those properties exactly. 9.3. Connecting the Parts and Giving Motions The parts are connected using appropriate joints. Each joint is chosen from among three types shown in Figure 22.
This robot simulator treats a person as a moving point to which a critical force is applied, and is able to define multiple points. So it can evaluate danger toward each part of a person, or many people at once. In the dynamic coexistent space of the human and robot above-stated, the danger-index is calculated as eq. (38). The effectiveness of safety design strategies is evaluated by mass m and impact time dt computed from elasticity, and the effectiveness of safety control strategies is evaluated by relative velocity v and time to spare δt computed from distance. A constant a indicates the effect of time to spare. The dangerindex is calculated by dividing producible impact force computed as mentioned above by the critical impact force Fc . The whole danger can be evaluated by calculating the danger-index at all points of time and in all directions. 9.5. Indicating Danger-Index This robot simulator expands a danger-index chart to three dimensions, and is able to prepare multiple windows to show graphs and numerical values. The spherical danger-index chart shown in Figure 23(a) indicates danger toward a point on a person at a point in time synchronizing with its motion displayed in the main window. Now, we need to consider a time–space danger-chart. The sequence of spherical danger-index charts shown in Figure 23(b) makes the whole danger during the operation, but it is troublesome to judge the result without seeing all graphs. This robot simulator projects each spherical danger-index chart onto a plane and arranges all the projected danger-index charts along the time axis as shown in Figure 24. The danger during the
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Fig. 23. Indication of danger-index. Fig. 25. Simulation result of the initial state.
Fig. 24. Dimension contracted time–space danger-index.
Fig. 26. Time–space danger-index for increasing surface elasticity.
operation can be judged objectively by properly determining the plane. Repeating evaluation and modification in this way, the designer can optimize design and control of the human-care robot before building the actual machine.
9.6.1. Safety Design Strategy (Soft Material)
9.6. Examples of Danger Evaluation Simulations We carried out experiments to design a manipulator, to evaluate danger, to modify properties, and to improve safety, as described above. We modeled PA-10 by Mitsubishi. The manipulator was operated to approach a person with a load on a plane. Figure 25 shows the results obtained when we carried out this simulation. The dotted line is the course of the tip. During these simulations the critical impact force was 50 N, the impact time was 0.3 s, and the operation took 3 s. The time–space danger-chart shown on the right is the sequence of spherical danger-index charts projected from this side of the screen. The maximum danger-index value was 1.67, which was sharply over one. This means that the situation is extremely dangerous because a person will be injured if the manipulator collides with him. In the following, we show the results of the simulation with modified parameters as various safety design and control strategies were performed.
As an example of a safety design strategy, we carried out simulations increasing elasticity. Figure 26 shows the result obtained by increasing the impact time twice to 0.6 s as the manipulator was covered with soft material such as rubber. The danger was reduced by half while the maximum dangerindex value decreased to 0.84, which was less than 1. The cost of such a safety strategy is relatively high, but is sure to reduce danger. 9.6.2. Safety Control Strategy (Approaching Posture and Course) As an example of a safety control strategy, we changed the approaching posture and course. Figure 27 shows the result obtained when we modified the motion on the same plane as the initial simulation. Without delaying the operation, the maximum danger-index value was decreased to 0.93, which was less than 1. It seems that the posture of the bending manipulator cut down the velocity toward the person. Figure 28 shows the result obtained by rounding the approaching course to the side of the screen. The maximum danger-index value was decreased to 0.76, which was the smallest of all examples. Such safety control strategies are difficult to control properly, but need not be excessively costly and are very efficient.
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Fig. 27. Simulation result of improving to safe motion. Fig. 30. Simulation results under a dynamic environment.
10. Conclusions
Fig. 28. Simulation result of rounding frontward.
Fig. 29. The robot brings the tip part close to a cared person under a dynamic environment.
We have undertaken a new study of safety in the coexistent space of human and machine in order to realize a human-care robot for the nursing of the aged or disabled. First, the human injury from robot and machine was investigated thoroughly, and we found that it was important to treat safety strategies in the light of mechanical injury. Also, we grouped them as safety design and control strategy according to the difference in their contents. In order to take every safety strategy into consideration, impact force and stress were chosen as evaluation measures for quantifying safety. We proposed the evaluation method of safety and defined danger-index, improvement rate, and total evaluation index. Discussions of some safety strategies proved the viability of our safety evaluation method. In addition, we constructed a new type of 3D robot simulation system for danger evaluation on a PC. By simplifying the evaluation of danger in the stages of both design and control of human-care robots, the system makes it easy to quantify the effectiveness of various safety strategies. As a result, we were able to discuss the successful design and control optimization of robot safety. We believe that this method allows us to assess the contribution of each safety strategy to the overall safety performance of human-care robots.
References These experiments show that the effectiveness of various safety strategies can be easily evaluated quantitatively with our simulator. Furthermore, by calculating danger when performing several types of safety strategies at once, it is possible to compare the contribution of each safety strategy to the whole. We can similarly evaluate cases where a person approaches the robot or several people are in its vicinity (Figures 29 and 30). Next, we will devise and automate an operationoptimization method.
Dohi, T. 1996. Classification and safety of medical and human care robots. In Proceedings of JSME Annual Conference on Robotics and Mechatronics pp. 1181–1182 (in Japanese). Ikuta, K., Makita, S., and Arimoto, S. 1991. Non-contact magnetic gear for micro transmission mechanism. In Proceedings of International Workshop on Micro Electromechanical Systems (MEMS’91) pp. 125–130. Ikuta, K., Kawahara, A., and Yamazumi, S. 1991. Miniature cybernetic actuators using piezoelectric device. In
Downloaded from http://ijr.sagepub.com at PENNSYLVANIA STATE UNIV on February 8, 2008 © 2003 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.
Ikuta, Ishii and Nokata / Safety Evaluation Method Proceedings of International Workshop on Micro Electromechanical Systems (MEMS’91) pp. 131–135. International Organization for Standardization. 1990. Guidelines for the inclusion of safety aspects in standards, ISO/IEC GUIDE 51. Saito, Y., et al. 1996. Research on safety operating of the assisting robot. In Proceedings of JSME Annual Conference on Robotics and Mechatronics pp. 1177–1180 (in Japanese). Saito, T., and Sugimoto, N. 1997. A study on electrorheological motion control using an antagonistic rotary actuator. In Proceedings of the 6th International Conference on ER-Fluids, ERMR’97.
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Shannon, C.E. 1948. A mathematical theory of communication. Bell System Technology Journal 27:379–423, 623– 656. Suita, K., et al. 1995. A failure-to-safety “Kyozon” system with simple contact detection and stop capabilities for safe human-robot coexistence. In Proceedings of IEEE International Conference on Robotics and Automation Vol. 3, pp. 3089–3096. Uehara, Y., et al. 2002. A Handbook for Safety Engineering, Corona Publishing, Tokyo, pp. 1063 (in Japanese). Yoshikawa, T. 1985. Manipulability of robotic mechanisms. International Journal of Robotics Research 4(2):3–9.
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