Bio-Inspired Actuation and Sensing - Springer Link
Autonomous Robots 11, 267–272, 2001 c 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
Bio-Inspired Actuation and Sensing BLAKE HANNAFORD, KRISTEN JAAX AND GLENN KLUTE Biorobotics Lab, Departments of Electrical Engineering and Bioengineering, University of Washington, Seattle, WA, USA
Abstract. The superb ability of animals to negotiate rough terrain has caused engineers to focus on mechanical properties of muscle and other unique features in order to design improved robots for exploration. This paper reviews recent work in artificial muscle actuators, as well as a new sensor based on a robotic model of the muscle spindle cell. The actuator contains a pneumatic force generator in parallel with a non-linear damping element and in series with a non-linear elastic “tendon”. Work loop experiments were performed to characterize this actuator under conditions similar to real locomotion at different speeds. The robotic muscle spindle is an 8 × 1 cm device which simulates the response of the physiological muscle spindle to stretch. Its non-linear properties are thought to contribute to stable accurate control over a wide range of motion. Keywords: biorobotics, muscle spindle, artificial muscle, pneumatic muscle, sensors
1.
Introduction
One approach for developing such advanced robots for planetary exploration involves emulating human and animal models since both regularly interact an unstructured environment in a robust manner. Researchers in many labs worldwide have contributed to this technical evolution. Our actuation and sensing technologies build on much previous research and illustrate some salient features of biological transducers: exploitation of useful non-linear properties, small size (high volumetric efficiency), and, in the case of the muscle length transducer, the muscle spindle, an actuation component embedded in the sensor.1 2.
Artificial Muscle and Tendon
Our design of an artificial muscle-tendon actuator is based on known static and dynamic properties of vertebrate skeletal muscle and tendon that were extracted from the literature. These properties were used to mathematically describe the unique force, length, velocity, and activation relationships and specify the performance requirements for an artificial triceps surae and Achilles tendon (see Klute et al., 2001 for details).
Briefly, skeletal muscle can be modeled as an actuator whose output force is a function of length, velocity, and level of activation. At maximal activation, this relationship can be described by a parabolic, dimensionless equation: FL/FL 0 = c1 (L/L 0 )2 + c2 (L/L 0 ) + c3
(1)
where FL is the isometric force at muscle length L and FL 0 is the isometric force at the muscle’s “resting” length L 0 . In addition to the force-length relationship of skeletal muscle, it is also well known that the output force drops significantly as the contraction velocity increases. Numerous whole muscle models of this phenomenon have been proposed, but the most enduring has been that of Hill (1938). The Hill muscle model captures perhaps 90 percent of what is relevant for organism level biomechanics with a simple, hyperbolic equation. The general form of the Hill model is: [Fm + a][V + b] = [FL + a]b
(2)
where Fm is the instantaneous muscle force, V is the instantaneous muscle velocity, and FL is the isometric muscle force at muscle length L.
268
Hannaford, Jaax and Klute
To connect tissue the artificial muscle and the skeleton of a biomorphic robot, we also examined the properties of tendons for the purposes of designing an artificial tendon. The properties of weight-bearing tendons, which store of energy during locomotion, have been extracted from the literature and used to develop a mathematical model for an energy-storing tendon. We then used these mathematical models to construct an artificial muscle-tendon system consisting of two flexible pneumatic actuators in parallel with a hydraulic damper, in series with a bi-linear, two-spring implementation of an artificial tendon. To verify the system’s performance, we experimentally measured the output force for various constant velocity and activation profiles enveloped by the maximum conditions expected in the human triceps surae muscle during locomotion and plotted the force-length-velocity relationships for various activation levels (Klute et al., 2001). While these force-length-velocity relationships can be used to predict the maximum work and instantaneous power output of biological muscle, but they are not a good measure of the sustainable performance produced during periodic or stretch-shortening cycles typical of locomotion. Gitter et al. (1991) reported the ankle musculature contributed 36 J of energy to locomotion for each step in the gait cycle. 2.1.
Work Loop Technique
In an effort to determine the sustainable performance produced in-vivo during the stretch-shortening cycles of locomotion, a number of investigators have been involved with the development and refinement of the work loop technique (e.g., Machin and Pringle, 1960; Josephson, 1993; James et al., 1995; Ettema, 1996; Full et al., 1998). The technique involves subjecting a muscle to a cyclic length change during appropriate stimulation (see Fig. 1). The work loop begins with an eccentric contraction where the muscle is stretched
Figure 1. A work loop is formed during the stretch-shortening cycle of muscle and tendon.
from its shortest to longest length. The work done by the environment, or antagonistic muscles, is simply the area under this curve. The cycle continues with a subsequent concentric contraction where the muscle actively contracts from its longest to shortest length. The work done by the muscle is the area under the curve, and for many cases, is greater than the work required to stretch the muscle. The loop area, and hence the net work done over the complete cycle, is the difference between the work done by the muscle during the concentric phase and the work done by the environment (or antagonistic muscles) during the eccentric phase. 2.2.
Artificial Musculo-Tendon Work Loop Measurements
Using the artificial musculo-tendon system, we conducted experiments using the work loop technique and the axial-torsional BionixTM (MTS Systems Corp., Minnesota, U.S.A.) tensile testing instrument. The test set-up is reported elsewhere (Klute et al., 2001). The artificial muscle-tendon system consisted of two McKibben/Gaylord pneumatic braided actuators (3/4 in. nominal braid diameter with a resting length of 250 mm) placed parallel to the hydraulic damper. The actuators were then placed in series with the two-spring artificial tendon. A pneumatic servo-regulator (Festo Corporation, Germany, model number MP3-1/8) was used to apply and release pressure upon command at 2, 3, 4, and 5 bar. A square velocity trajectory was selected as the input activation profile using either concentric activation (pressure applied to the artificial muscle only during the concentric phase of the stretchshortening cycle and allowing it to relax during the eccentric phase). Tested velocities included: 1, 10, 25, 50, 100, 150, 200, 250, and 300 mm/s. 2.3.
Concentric Activation Results
The results of the concentric activation tests are shown in Fig. 2. The plot in the upper left is for a stretchshortening cycle with a square velocity trajectory of 1 mm/sec. As the muscle was passively stretched during the eccentric phase, near zero force was recorded. Upon reaching its maximum length, the artificial muscle was activated to the specified pressure (2, 3, 4, or 5 bar). The force rapidly increased and the muscle began to actively contract. As the muscle shortened, the force decreased until the end of its contraction range was reached. The direction of this counter-clockwise work loop cycle is shown with arrows (Fig. 2).
Bio-Inspired Actuation and Sensing
269
Figure 2. Concentric activation work loops for stretch-shortening cycles. Velocity profiles shown are step inputs at 1 mm/sec (upper left), 50 mm/sec (upper right), 100 mm/sec (lower left), and 200 (lower right). Activation pressures of 2 and 5 bar labeled in the upper left with proportional pressures of 3 and 4 bar in-between but unlabeled.
The plot at 50 mm/sec (Fig. 2, upper right) follows a similar loop, but at a faster velocity. At the beginning of the eccentric phase, the muscle takes some time to completely relax and achieve near zero force. Similarly, at the beginning of the concentric phase, the muscle takes some time to reach its maximum force. For the faster velocity of 100 mm/sec (Fig. 2, lower left) the actuator force takes a significant amount of time to relax at the beginning of the eccentric phase and does not achieve zero force for the highest pressure of 5 bar. Lower pressures do achieve complete relaxation, but only for a short period of time. However, the work loop cycle now forms a “figure eight” and indicates the concentric activation profile does both positive and negative work. At 200 mm/sec, shown in the lower right of Fig. 2, the actuator never completely relaxes and the work loop (shown with arrows) forms a clockwise loop in which no positive work is done. The maximum positive net work of 43.7 J was at the highest activation pressure (5 bar) and the lowest velocity (1 mm/sec). The net work was positive for each work loop until 100 mm/sec. At higher velocities, the negative work that was required to passively stretch the artificial musculo-tendon was greater than the positive work performed during the active concentric contraction.
2.4.
Concentric Activation Discussion
Positive work is done by the artificial musculo-tendon system at velocities less than 100 mm/sec for all pressure activation conditions tested. At velocities of 150 mm/sec and higher, the work required to stretch the system was greater than that done by the actuator, resulting in a negative net work for all pressure conditions. This result occurs because the actuator is being lengthened while some residual pressure remains and because of the system’s damping.
3.
The Robotic Muscle Spindle
The Robotic Muscle Spindle is a biomimetic replica of the mammalian muscle spindle, an actuated length sensor that transduces skeletal muscle displacement for kinesthetic awareness and control. Extending earlier work by Marbot et al. (1995), the robotic sensor implements in precision hardware a three element abstraction of muscle spindle physiology: mechanical filtering, transduction and encoding. The performance of the sensor is assessed according to its accuracy as a model, i.e., its ability to replicate the behavior of the biological sensor.
270
Hannaford, Jaax and Klute
Figure 3. The biological muscle spindle (a) anatomy and (b) conceptual diagram. The differing mechanical properties of the contractile and sensory region result in unequal strain distribution which mechanically filters inputs before they reach the sensory region.
3.1.
The Biological Muscle Spindle
The 1 cm long biological muscle spindle (Fig. 3) lies embedded in muscle tissue with its long axis parallel to the muscle fibers. Its core feature is a linearly elastic sensory region that transduces strain into an analog potential. Nerve endings called type Ia fibers encode this analog potential into a frequency modulated signal, the Ia output. Lying at either end of the sensory region are contractile regions, the tiny intrafusal muscles, which mechanically filter strain applied across the muscle spindle before it reaches the sensory region. The central nervous system (CNS) controls the contraction of the intrafusal muscles via the gamma motorneuron, γ mn. Using this dedicated signal, the CNS can modulate the sensor’s transduction, tuning it to change its response from absolute position to perturbations from a desired position. The CNS is able to
selectively extract length or velocity information from muscle spindles by stimulating either static or dynamic γ mn, respectively. The static γ mns primarily innervate the length sensitive muscle spindle fiber types, nuclear bag2 and nuclear chain, while dynamic γ mns primarily innervate the velocity sensitive fiber type, nuclear bag1. For further details, see Kandel et al. (1991) or Gladden (1986). 3.2.
Design of the Robotic Muscle Spindle
In replicating the biological muscle spindle, we sought to reproduce the behavior of each of the abstracted subsystems, mechanical filtering, transduction and encoding, directly in the mechatronics of the hardware design (Fig. 4). Biological data from the literature describing the muscle spindle’s kinematics, receptor potential and Ia output were used to formulate performance
Figure 4. Robotic muscle spindle (8 cm × 1 cm). Length and velocity inputs applied through cable, C. Strain gauged cantilevers on nut, B, transduce inputs to voltage. A VCO on printed circuit board encodes voltage as frequency modulated spike train. Lead screw actuator, A, replicates intrafusal muscle behavior, mechanically filtering inputs.
Bio-Inspired Actuation and Sensing
271
Figure 5. Control algorithm. Software muscle model calculates desired muscle force, Fd , based on length, velocity and γ mn input. Force control loop uses Fd to control linear actuator. Transducer and encoder convert sensory region strain to Ia output.
specifications (Gladden, 1986; Dickson et al., 1989). Aspects of the muscle spindle’s behavior not captured in the mechanical and electrical properties of the hardware were added in control software using an adaptation of the Schaafsma muscle spindle model (Schaafsma et al., 1991). The transduction function of the sensory subsystem is implemented with two, strain gauged, stainless steel cantilevers 51 microns thick lying perpendicular to the axis of sensing. The encoder subsystem behavior is reproduced with a voltage controlled oscillator. The circuitry necessary to convert the sensory region’s strain into a frequency modulated square wave is implemented with surface mount components on a printed circuit board (PCB) mounted directly to the nut to minimize distortion of the transducer’s millivolt signal. This subsystem maps the sensory region’s deflection to a frequency range of 1 kHz–13 kHz. The mechanical filtering function of the contractile element was implemented with a combination of a linear actuator and a biologically-based control algorithm. To meet the engineering specifications for a fast, precise linear actuator, we designed a precision lead screw system. A miniature motor directly coupled to a lead screw drives the threaded nut, B, forwards and backwards. Cylindrical housings encasing the robotic spindle form linear bushings around the nut, converting rotary motion to linear motion. Constant tension applied across the spindle during normal function minimizes backlash in the lead screw. Using a PID position controller, the actuator met the performance specifications with a 1mm step response rise time
Bio-Inspired Actuation and Sensing BLAKE HANNAFORD, KRISTEN JAAX AND GLENN KLUTE Biorobotics Lab, Departments of Electrical Engineering and Bioengineering, University of Washington, Seattle, WA, USA
Abstract. The superb ability of animals to negotiate rough terrain has caused engineers to focus on mechanical properties of muscle and other unique features in order to design improved robots for exploration. This paper reviews recent work in artificial muscle actuators, as well as a new sensor based on a robotic model of the muscle spindle cell. The actuator contains a pneumatic force generator in parallel with a non-linear damping element and in series with a non-linear elastic “tendon”. Work loop experiments were performed to characterize this actuator under conditions similar to real locomotion at different speeds. The robotic muscle spindle is an 8 × 1 cm device which simulates the response of the physiological muscle spindle to stretch. Its non-linear properties are thought to contribute to stable accurate control over a wide range of motion. Keywords: biorobotics, muscle spindle, artificial muscle, pneumatic muscle, sensors
1.
Introduction
One approach for developing such advanced robots for planetary exploration involves emulating human and animal models since both regularly interact an unstructured environment in a robust manner. Researchers in many labs worldwide have contributed to this technical evolution. Our actuation and sensing technologies build on much previous research and illustrate some salient features of biological transducers: exploitation of useful non-linear properties, small size (high volumetric efficiency), and, in the case of the muscle length transducer, the muscle spindle, an actuation component embedded in the sensor.1 2.
Artificial Muscle and Tendon
Our design of an artificial muscle-tendon actuator is based on known static and dynamic properties of vertebrate skeletal muscle and tendon that were extracted from the literature. These properties were used to mathematically describe the unique force, length, velocity, and activation relationships and specify the performance requirements for an artificial triceps surae and Achilles tendon (see Klute et al., 2001 for details).
Briefly, skeletal muscle can be modeled as an actuator whose output force is a function of length, velocity, and level of activation. At maximal activation, this relationship can be described by a parabolic, dimensionless equation: FL/FL 0 = c1 (L/L 0 )2 + c2 (L/L 0 ) + c3
(1)
where FL is the isometric force at muscle length L and FL 0 is the isometric force at the muscle’s “resting” length L 0 . In addition to the force-length relationship of skeletal muscle, it is also well known that the output force drops significantly as the contraction velocity increases. Numerous whole muscle models of this phenomenon have been proposed, but the most enduring has been that of Hill (1938). The Hill muscle model captures perhaps 90 percent of what is relevant for organism level biomechanics with a simple, hyperbolic equation. The general form of the Hill model is: [Fm + a][V + b] = [FL + a]b
(2)
where Fm is the instantaneous muscle force, V is the instantaneous muscle velocity, and FL is the isometric muscle force at muscle length L.
268
Hannaford, Jaax and Klute
To connect tissue the artificial muscle and the skeleton of a biomorphic robot, we also examined the properties of tendons for the purposes of designing an artificial tendon. The properties of weight-bearing tendons, which store of energy during locomotion, have been extracted from the literature and used to develop a mathematical model for an energy-storing tendon. We then used these mathematical models to construct an artificial muscle-tendon system consisting of two flexible pneumatic actuators in parallel with a hydraulic damper, in series with a bi-linear, two-spring implementation of an artificial tendon. To verify the system’s performance, we experimentally measured the output force for various constant velocity and activation profiles enveloped by the maximum conditions expected in the human triceps surae muscle during locomotion and plotted the force-length-velocity relationships for various activation levels (Klute et al., 2001). While these force-length-velocity relationships can be used to predict the maximum work and instantaneous power output of biological muscle, but they are not a good measure of the sustainable performance produced during periodic or stretch-shortening cycles typical of locomotion. Gitter et al. (1991) reported the ankle musculature contributed 36 J of energy to locomotion for each step in the gait cycle. 2.1.
Work Loop Technique
In an effort to determine the sustainable performance produced in-vivo during the stretch-shortening cycles of locomotion, a number of investigators have been involved with the development and refinement of the work loop technique (e.g., Machin and Pringle, 1960; Josephson, 1993; James et al., 1995; Ettema, 1996; Full et al., 1998). The technique involves subjecting a muscle to a cyclic length change during appropriate stimulation (see Fig. 1). The work loop begins with an eccentric contraction where the muscle is stretched
Figure 1. A work loop is formed during the stretch-shortening cycle of muscle and tendon.
from its shortest to longest length. The work done by the environment, or antagonistic muscles, is simply the area under this curve. The cycle continues with a subsequent concentric contraction where the muscle actively contracts from its longest to shortest length. The work done by the muscle is the area under the curve, and for many cases, is greater than the work required to stretch the muscle. The loop area, and hence the net work done over the complete cycle, is the difference between the work done by the muscle during the concentric phase and the work done by the environment (or antagonistic muscles) during the eccentric phase. 2.2.
Artificial Musculo-Tendon Work Loop Measurements
Using the artificial musculo-tendon system, we conducted experiments using the work loop technique and the axial-torsional BionixTM (MTS Systems Corp., Minnesota, U.S.A.) tensile testing instrument. The test set-up is reported elsewhere (Klute et al., 2001). The artificial muscle-tendon system consisted of two McKibben/Gaylord pneumatic braided actuators (3/4 in. nominal braid diameter with a resting length of 250 mm) placed parallel to the hydraulic damper. The actuators were then placed in series with the two-spring artificial tendon. A pneumatic servo-regulator (Festo Corporation, Germany, model number MP3-1/8) was used to apply and release pressure upon command at 2, 3, 4, and 5 bar. A square velocity trajectory was selected as the input activation profile using either concentric activation (pressure applied to the artificial muscle only during the concentric phase of the stretchshortening cycle and allowing it to relax during the eccentric phase). Tested velocities included: 1, 10, 25, 50, 100, 150, 200, 250, and 300 mm/s. 2.3.
Concentric Activation Results
The results of the concentric activation tests are shown in Fig. 2. The plot in the upper left is for a stretchshortening cycle with a square velocity trajectory of 1 mm/sec. As the muscle was passively stretched during the eccentric phase, near zero force was recorded. Upon reaching its maximum length, the artificial muscle was activated to the specified pressure (2, 3, 4, or 5 bar). The force rapidly increased and the muscle began to actively contract. As the muscle shortened, the force decreased until the end of its contraction range was reached. The direction of this counter-clockwise work loop cycle is shown with arrows (Fig. 2).
Bio-Inspired Actuation and Sensing
269
Figure 2. Concentric activation work loops for stretch-shortening cycles. Velocity profiles shown are step inputs at 1 mm/sec (upper left), 50 mm/sec (upper right), 100 mm/sec (lower left), and 200 (lower right). Activation pressures of 2 and 5 bar labeled in the upper left with proportional pressures of 3 and 4 bar in-between but unlabeled.
The plot at 50 mm/sec (Fig. 2, upper right) follows a similar loop, but at a faster velocity. At the beginning of the eccentric phase, the muscle takes some time to completely relax and achieve near zero force. Similarly, at the beginning of the concentric phase, the muscle takes some time to reach its maximum force. For the faster velocity of 100 mm/sec (Fig. 2, lower left) the actuator force takes a significant amount of time to relax at the beginning of the eccentric phase and does not achieve zero force for the highest pressure of 5 bar. Lower pressures do achieve complete relaxation, but only for a short period of time. However, the work loop cycle now forms a “figure eight” and indicates the concentric activation profile does both positive and negative work. At 200 mm/sec, shown in the lower right of Fig. 2, the actuator never completely relaxes and the work loop (shown with arrows) forms a clockwise loop in which no positive work is done. The maximum positive net work of 43.7 J was at the highest activation pressure (5 bar) and the lowest velocity (1 mm/sec). The net work was positive for each work loop until 100 mm/sec. At higher velocities, the negative work that was required to passively stretch the artificial musculo-tendon was greater than the positive work performed during the active concentric contraction.
2.4.
Concentric Activation Discussion
Positive work is done by the artificial musculo-tendon system at velocities less than 100 mm/sec for all pressure activation conditions tested. At velocities of 150 mm/sec and higher, the work required to stretch the system was greater than that done by the actuator, resulting in a negative net work for all pressure conditions. This result occurs because the actuator is being lengthened while some residual pressure remains and because of the system’s damping.
3.
The Robotic Muscle Spindle
The Robotic Muscle Spindle is a biomimetic replica of the mammalian muscle spindle, an actuated length sensor that transduces skeletal muscle displacement for kinesthetic awareness and control. Extending earlier work by Marbot et al. (1995), the robotic sensor implements in precision hardware a three element abstraction of muscle spindle physiology: mechanical filtering, transduction and encoding. The performance of the sensor is assessed according to its accuracy as a model, i.e., its ability to replicate the behavior of the biological sensor.
270
Hannaford, Jaax and Klute
Figure 3. The biological muscle spindle (a) anatomy and (b) conceptual diagram. The differing mechanical properties of the contractile and sensory region result in unequal strain distribution which mechanically filters inputs before they reach the sensory region.
3.1.
The Biological Muscle Spindle
The 1 cm long biological muscle spindle (Fig. 3) lies embedded in muscle tissue with its long axis parallel to the muscle fibers. Its core feature is a linearly elastic sensory region that transduces strain into an analog potential. Nerve endings called type Ia fibers encode this analog potential into a frequency modulated signal, the Ia output. Lying at either end of the sensory region are contractile regions, the tiny intrafusal muscles, which mechanically filter strain applied across the muscle spindle before it reaches the sensory region. The central nervous system (CNS) controls the contraction of the intrafusal muscles via the gamma motorneuron, γ mn. Using this dedicated signal, the CNS can modulate the sensor’s transduction, tuning it to change its response from absolute position to perturbations from a desired position. The CNS is able to
selectively extract length or velocity information from muscle spindles by stimulating either static or dynamic γ mn, respectively. The static γ mns primarily innervate the length sensitive muscle spindle fiber types, nuclear bag2 and nuclear chain, while dynamic γ mns primarily innervate the velocity sensitive fiber type, nuclear bag1. For further details, see Kandel et al. (1991) or Gladden (1986). 3.2.
Design of the Robotic Muscle Spindle
In replicating the biological muscle spindle, we sought to reproduce the behavior of each of the abstracted subsystems, mechanical filtering, transduction and encoding, directly in the mechatronics of the hardware design (Fig. 4). Biological data from the literature describing the muscle spindle’s kinematics, receptor potential and Ia output were used to formulate performance
Figure 4. Robotic muscle spindle (8 cm × 1 cm). Length and velocity inputs applied through cable, C. Strain gauged cantilevers on nut, B, transduce inputs to voltage. A VCO on printed circuit board encodes voltage as frequency modulated spike train. Lead screw actuator, A, replicates intrafusal muscle behavior, mechanically filtering inputs.
Bio-Inspired Actuation and Sensing
271
Figure 5. Control algorithm. Software muscle model calculates desired muscle force, Fd , based on length, velocity and γ mn input. Force control loop uses Fd to control linear actuator. Transducer and encoder convert sensory region strain to Ia output.
specifications (Gladden, 1986; Dickson et al., 1989). Aspects of the muscle spindle’s behavior not captured in the mechanical and electrical properties of the hardware were added in control software using an adaptation of the Schaafsma muscle spindle model (Schaafsma et al., 1991). The transduction function of the sensory subsystem is implemented with two, strain gauged, stainless steel cantilevers 51 microns thick lying perpendicular to the axis of sensing. The encoder subsystem behavior is reproduced with a voltage controlled oscillator. The circuitry necessary to convert the sensory region’s strain into a frequency modulated square wave is implemented with surface mount components on a printed circuit board (PCB) mounted directly to the nut to minimize distortion of the transducer’s millivolt signal. This subsystem maps the sensory region’s deflection to a frequency range of 1 kHz–13 kHz. The mechanical filtering function of the contractile element was implemented with a combination of a linear actuator and a biologically-based control algorithm. To meet the engineering specifications for a fast, precise linear actuator, we designed a precision lead screw system. A miniature motor directly coupled to a lead screw drives the threaded nut, B, forwards and backwards. Cylindrical housings encasing the robotic spindle form linear bushings around the nut, converting rotary motion to linear motion. Constant tension applied across the spindle during normal function minimizes backlash in the lead screw. Using a PID position controller, the actuator met the performance specifications with a 1mm step response rise time
