Experimental Study on Advanced Underwater Robot Control
IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 4, AUGUST 2005
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Experimental Study on Advanced Underwater Robot Control Side Zhao, Member, IEEE, and Junku Yuh, Fellow, IEEE
Abstract—The control issue of underwater robots is very challenging due to the nonlinearity, time variance, unpredictable external disturbances, such as the sea current fluctuation, and the difficulty in accurately modeling the hydrodynamic effect. Conventional linear controllers may fail in satisfying performance requirements, especially when changes in the system and environment occur during the operation since it is almost impossible to manually retune the control parameters in water. Therefore, it is highly desirable to have an underwater robot controller capable of self-adjusting control parameters when the overall performance degrades. This paper presents the theory and experimental work of the adaptive plus disturbance observer (ADOB) controller for underwater robots, which is robust with respect to external disturbance and uncertainties in the system. This control scheme consists of disturbance observer (DOB) as the inner-loop controller and a nonregressor based adaptive controller as the outer-loop controller. The effectiveness of the ADOB was experimentally investigated by implementing three controllers: PID, PID plus DOB, and ADOB on an autonomous underwater robot, ODIN III. Index Terms—Adaptive control, disturbance observer (DOB), underwater robots.
I. INTRODUCTION
O
CEANS are the main resource of the energy and chemical balance that sustains mankind whose future is very much dependent on the living and nonliving resources in the oceans [1]. Oceans’ activities are also critically relevant to climate changes. Therefore, various studies have been conducted for ocean exploration and intervention. Underwater vehicles have been a popular and effective means for ocean exploration and intervention as they make it possible to go far beneath the ocean surface, collect first-hand information about how the oceans work, and furthermore perform intervention tasks. There are three types of underwater vehicles. 1) Manned submersible vehicles: They can carry out complicated tasks because of human intelligence. However, they have short endurance due to human physical and psychological limitations, and are costly to operate because of the endeavor done to ensure
Manuscript received June 3, 2004; revised August 8, 2004. This paper was recommended by Associate Editor W. K. Chung and Editor I. Walker upon the evaluation of the reviewers’ comments. This work was sponsored in part by the National Science Foundation under Grant BES97-01614, in part by the Office of Naval Research under Grants N00014-97-1-0961 and N00014-00-1-0629, and in part by KRISO/KORDI via MASE. Any opinions, findings and conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies. S. Zhao is with Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, HI 96822 USA (e-mail: [email protected]). J. Yuh is with National Science Foundation, Arlington, VA 22230 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TRO.2005.844682
human safety. Alvin at the Woods Hole Oceanographic Institute and Pisces V at the NOAA Hawaii’s Undersea Research Laboratory are examples of manned submersible vehicles. 2) Remotely operated vehicles (ROV): They are unmanned, tethered vehicles with umbilical cables to transfer power, sensor data and control commands between the operators on the surface and the ROV. They are usually launched from surface ships. They can also carry out complicated tasks via tele-operation by human pilots on the surface ships. Even though their operations are often limited by operator fatigue, they are free from the safety concern of on-board human operators and have almost unlimited endurance in the ocean, compared to manned submersibles. However, the dragging force on the tether, time delay, and operator fatigue make ROV difficult to operate and . the daily operating cost is still very expensive KAIKO from the Japanese Marine–Earth Science and Technology Center (JAMSTEC) was the most advanced ROV ever operated at a 11 000-m depth. Unfortunately, KAIKO was lost during the operation in 2003 as the tether was snapped due to bad weather. 3) Autonomous underwater vehicles (AUVs) or underwater robots: They are unmanned, tether-free, powered by onboard energy sources, equipped with various navigation sensors such as inertial measurement unit (IMU), sonar sensor, laser ranger, and pressure sensor, and controlled by onboard computers for given missions. They are more mobile and could have much wider reachable scope than ROV. On-board power and intelligence could help AUV self-react properly to changes in the system and its environment, avoiding any disastrous situation like the KAIKO case. With the continuous advance in control, navigation, artificial intelligence, material science, computer, sensor, and communication, AUVs have become a very attractive platform in exploring the oceans, and numerous AUV prototypes have been proposed, such as ODIN [2], REMUS [3], and ODYSSEY [4]. While most of the currently available AUV are for noncontact tasks such as mapping, monitoring or sampling in the water column, research on AUV with robotic manipulators has recently been underway [5]. Various underwater robotic technologies were surveyed by Yuh and West [6]. The control issue of AUV is very challenging due to the nonlinearity, time-variance, unpredictable external disturbances, such as the environmental force generated by the sea current fluctuation, and the difficulty in accurately modeling the hydrodynamic effect. The well-developed linear controllers may fail in satisfying performance requirements especially when changes in the system and environment occur during the AUV operation since it is almost impossible to manually retune the control parameters in water. Therefore, it is highly desirable
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to have an AUV controller capable of self-adjusting control parameters when the overall performance degrades. Various advanced control schemes for underwater robots have been proposed in the literature as some of them are summarized below. Sliding mode control (SMC): SMC restricts the system states inside a certain subspace of the whole state space and makes them asymptotically converge to their equilibrium point. It requires a raw estimation of the system parameters and an estimation of the system uncertainty for the switching surface design and variable-structure control law design. Even though SMC has been well known for its robustness to parameter variations, it has the inherent problem of chattering phenomenon. Yoerger and Newman [7] and Yoerger and Slotine [8] introduced the basic methodology of using sliding mode control for AUV application, and later Yoerger and Slotine [9] developed an adaptive sliding mode control scheme, in which a nonlinear system model was used. When the generalized disturbance makes the system state exceed the sliding mode tolerance layer, the exceeding value is used to update the nonlinear model parameters and furthermore update the control input. Song and Smith [10] introduced a sliding mode fuzzy controller that uses Pontryagin’s maximum principle for time-optimal switching surface design, and uses fuzzy logic to form this surface. Robust/optimal control: The principles of the robust/optimal control are calculus of variations, Pontryagin maximum principle, and Bellman dynamic programming. However, due to the difficulty of deriving an accurate model of AUV system, it is difficult to apply optimal control directly. Therefore, generally optimal control combined with system identification or robust control is used in AUV control. Kim et al. [11] proposed an control scheme, in which the robust stability problem against time delays and parameter uncertainties is transformed into control problem, and performance problem is transformed into problem. Riedel and Healey [12] proposed an optimal control (LQR) scheme that uses an auto-regression (AR) model to predict the wave-induced hydrodynamic disturbance. Adaptive control: Adaptive control modifies control gains according to the changes in the process dynamics and the disturbances. Since there are parameter uncertainties and unknown disturbances in the underwater vehicle’s hydrodynamics, many researchers studied adaptive control to address the AUV control issues. However, adaptive control may fail when the dynamics changing speed is beyond its adapting capability, and the model-based adaptive control may be calculation burdensome because of the excessive endeavor in system identification. Cristi and Healey [13] proposed a model-based adaptive controller. Assuming that the vehicle dynamics are nearly linear within the range of its operating conditions, the controller uses the RLS method for system parameter estimation and, futhermore, uses the pole placement technique for control gain desgin. Yuh [14] proposed a discrete-time adaptive controller using a parameter adaptation algorithm. Yuh [15], and Yuh and Nie [16] proposed a nonregressor-based adaptive control scheme that uses parametric bound estimation, instead of system parameter estimation, to tune the control gains. Neural network (NN) control: Neural networks attracted many researchers because they can achieve nonlinear mapping.
IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 4, AUGUST 2005
Using NN in constructing controllers has the advantage that the dynamics of the controlled system need not be completely known. This makes NN suitable for underwater vehicle control. However, NN-based controllers have the disadvantage that no formal mathematical characterization exists for the closed-loop system behavior. The validation of the final design can only be demonstrated experimentally. There are mainly two approaches in using NN for control purpose: learning with a forward model and direct learning. In the former approach, generally, the forward model is trained by the output error or state error and then used for gain derivation, while in the latter approach, the state or output error is used directly to map the desired control input [17]. Yuh [18] described a multiplayer feedforward network. Each layer has 13 neurons, except the last layer that has six neurons. The input signals are six position errors, six velocity errors and a constant. The output signals are the six control forces. The back-propagation (BP) algorithm is used for training the network. Ishii et al. [19] proposed a neural network system that is based on self-organizing neural-net control system (SONCS) that executes identification of robot dynamics and controller adaptation in parallel with robot control and adjusts the controller network based on the results of virtual operation of the control calculation and the actual control operation. Fuzzy logic control: The theoretical basis of fuzzy logic control is that any real continuous function over a compact set can be approximated to any degree of accuracy by the fuzzy inference system. For control engineering applications, researchers use fuzzy logic to form a smooth approximation of a nonlinear mapping from system input space to system output space. This makes it suitable for nonlinear system control. However, determining the linguistic rules and the membership functions requires experimental data and, therefore, very time-consuming, and the rule-based structure of fuzzy logic control makes it difficult to characterize the behavior of the closed-loop system in order to determine response time and stability. Kato et al. [20] used a very basic fuzzy controller in AQUA EXPLORER 1000 cable inspection. Lee et al. [21] proposed a self-adaptive neurofuzzy inference system (SANFIS) that uses a five-layer-structured NN to achieve better function approximation: a recursive least squares algorithm and a modified Levenberg–Marquardt algorithm with limited memory are used in extracting fuzzy rules and tuning the membership functions. Kim and Yuh [22] proposed a fuzzy membership function-based neural networks (FMFNNs) that uses a BP network for fuzzy control’s membership function derivation. This paper describes an adaptive plus DOB (ADOB) controller for underwater robots as an extension of the second author’s previous study on a nonregressor based adaptive controller [16], [23]. The nonregressor based adaptive controller does not require any physical information about the robot model except the number of inputs and the number of outputs. As demonstrated by experimental investigation in [16], [23], the nonregressor based adaptive controller is very effective for autonomous underwater vehicles whose hydrodynamics cannot be accurately modeled or may vary while in operation as changes in the system and environment occur. However, the adaptive controller does not address robustness with respect to external
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Fig. 1. Diagram of the ADOB controller.
disturbances while DOB is very robust with respect to external disturbances. While more details about DOB can be found in [24]–[26], it can be briefly described as follows. The DOB basically removes the effect of external disturbances and modeling errors, and makes the system behave close to a nominal model that was prechosen by the user. Then the user designs an outer-loop controller, such as PID that controls the overall system. However, the DOB controllers require using a low-pass filter affected by the nominal model, and, therefore, the performance of the DOB controller such as PID plus DOB varies depending on the nominal model or the low-pass filter. As shown in Fig. 1, this paper presents an ADOB controller using DOB as an inner-loop compensator, taking advantage of its robustness with respect to disturbances, and using the nonregress based adaptive controller as an outer-loop controller, taking advantage of its robustness with respect to model uncertainties due to the nominal model or the low-pass filter. The effectiveness of the control system was experimentally investigated by implementing three controllers: PID, PID plus DOB, and ADOB on an autonomous underwater robot, ODIN III. The PID controller gains were manually tuned for satisfactory performance and its result was used as the baseline performance in this study. The paper is organized as follows. Section II describes the ADOB controller and Section III presents experimental results before conclusions in Section IV. II. CONTROLLER DESIGN There are two coordinate systems that are commonly used to describe the AUV kinematics: the earth-fixed frame (E-frame) and the body-fixed frame (B-frame). The position and orientation of the vehicle are described in the E-frame, while the linear and angular velocity and the control forces/moments are described in the B-frame: position and orientation vector in E-frame; velocity vector in force/moment B-frame; and vector in B-frame. The velocity vectors in E-frame and in B-frame have the following relationship: (1) is the transformation matrix between the B-frame where and the E-frame.
The dynamics of AUV in the B-frame can be represented by a six-degree-of-freedom (DOF) nonlinear dynamic equation shown as follows: (2) is the inertial matrix including added mass; is where the matrix of Coriolis and centripetal terms, and velocity-depenis the damping matrix indent terms due to added mass; is the gravitational cluding terms representing drag forces; force and buoyant force; is the control input; is the external disturbance. Detailed description of (1) and (2) can be found in Fossen [27]. is The overall control system as shown in Fig. 1, where the desired system output, is the system output, is the external disturbance, is the output measurement noise, and is the nominal model that can be chosen by the user. It has the inner loop compensator of DOB inside the dotted line and the outer loop of the adaptive controller. It can be easily seen that the system compensated by DOB becomes the nominal model assuming no measurement noise) if the (i.e., . It would be straightforward to design low-pass filter the outer-loop controller to control the nominal model that is known. However, the low-pass filter is needed since the inverse of the nominal model cannot be realized. First proposed in [24] and later refined in [25] and [26], DOB can remove the effect of the external disturbance and the modeling error, which can be referred as the generalized disturbance, in the bandwidth of the low-pass filter . However, because of the phase delay and bandwidth restriction of the low-pass filter , there is always an estimation error of the generalized disturbance, and, therefore, the overall performance with a simple outer-loop controller, such as PID, may vary depending on affected by the nominal model. Therefore, the system compensated by DOB with could be seen as a nominal model with disturbance estimation error that would be handled by the adaptive controller. in the bodyConsider the following nominal model for fixed frame in designing DOB (3) After applying DOB, the system dynamics becomes (4) (5)
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IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 4, AUGUST 2005
where represents the estimation error, and is in Fig. 1. shown as The DOB compensated system shown in (4) could be rewritten in the E-frame using as follows [27]: (6) where
, , , and class of estimation errors which are bounded by
, represents a
will also asymptotically zero and the parameter estimations . converge to It is noted that the direct use of the controller shown in (12) would generate large control input signals and chattering phenomenon when the value of the denominator is close to zero. To avoid this problem, the following modified controller is used: for (15) for
(7) where , is a desired value of , and , , and are positive constants. Since the system matrices are based on the nominal model (3) chosen by the user, they are known and can be bounded as
(8) where , , and are positive constants. Instead of mathematically proving (7) and (8), this paper describes how to estimate (9) , is a positive constant, and when . Consider the following control law:
where
(10) where
, which is the desired acceleration, , which is a positive constant, , are the control gain matrices. The error equation can be obtained by combing (6) and (10) as
(11) , , , . where The adaptive controller defines the gain matrices and the esas follows: timations of the (12) (13) where
are positive constants,
are estimates of
, and (14)
where is a positive constant satisfying . It is proven in Appendix A that using the controller described in (10), (12)–(14), the tracking error will asymptotically go to
where and are positive constants. The modified controller (15) may not guarantee the asymptotic stability but tracking errors are bounded by small numbers depending on . There are three parameters that affect the performance of , sigma , and the adaptive controller: adaptation gain . One can note the following: affects the time threshold affects constant of the overall system; the adaptation gain the adaptation period; and appropriate values of the threshold would keep the denominator in (15) from becoming the near zero value that may cause high gain values and large control signals beyond saturation limits. More details about the adaptive control part and discussion about influence of the adaptive control parameters could be found in [16] and [23] with experimental results. III. EXPERIMENTAL RESULTS The experimental work of the proposed controller was carried out on ODIN III [28], which is shown in Fig. 2. It is a six-DOF autonomous underwater robot developed by the Autonomous Systems Laboratory of the University of Hawaii. ODIN III is and Windows 2000 with the Real Time eXbased on tension (RTX) embedded real-time system. It is a close-framed sphere-shaped vehicle that makes its dynamics in each direction nearly identical. It has eight thrusters: four horizontal and four vertical, which make ODIN III capable of six-DOF maneuvering and also have thrust redundancy for fault tolerance purpose. It also has various navigation sensors including eight sonar sensors, a pressure sensor and an Inertial Measurement Unit (IMU). The eight sonar sensors are used to measure the displacements in the horizontal plane, the pressure sensor is used to measure the depth of the vehicle, and the IMU is used to measure the angular displacements. A Kalman filter is used to suppress the sensor noise and to estimate the translational and angular velocities. ODIN III has a multisampling-rate system with the sampling rate of the sonar sensors at 3 Hz and the sampling rate of the pressure sensors and the IMU at 30 Hz. The controller sampling rates are selected same as those of the sensors: 3 Hz for surge and sway and 30 Hz for roll, pitch, yaw, and depth. All the tests were done in the diving pool of Kahanamoku Pool at the University of Hawaii. Three different controllers (PID controller, PID plus DOB controller, and ADOB controller) were implemented on ODIN and the results are shown in this section. The vehicle was tested for a six-DOF desired motion shown as a solid line in Fig. 3(a) and (b) tracking in , , and in sequence . The controller settings used in while regulating in the experiment are listed as follows.
ZHAO AND YUH: EXPERIMENTAL STUDY ON ADVANCED UNDERWATER ROBOT CONTROL
Fig. 2.
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Omni-Directional intelligent navigator (ODIN III). (a) View in water. (b) Inside view. (c) Hardware diagram.
PID controller: The system was decoupled into six SISO subsystems and a separate PID controller was designed for each DOF not only because ODIN III is a nearly decoupled system but also because it would be easier to manually tune gains. After a lengthy gain-tuning process, the following numerical values for proportional, derivative and integral gains in each DOF ; ; were used: ; ; ; . PID plus DOB controller: In constructing DOB, the , low-pass filters are all set as and the nominal model is set as a pure inertia where system, is the rigid body inertia paramand . However, eters with and because the sampling frequencies in are different, different are used in parameterizing : for ; for . the The following numerical values were used for PID control ; ; gains: ; ; ; . ADOB controller: The DOB part is the same as that of the PID plus DOB controller. The adaptive controller part parameters ; , , are: , ; , , , . The initial values of all control gain in (10) were zero by setting initial values of in (12) to zero. It does not require manually tuning gain values un-
like PID since it is capable of self tuning. Before the vehicle began trajectory tracking, ODIN III was let to have a short initial adaptation period when the vehicle adaptive control self-adjusted control gains from zero initial values. To show the experimental results more effectively, two performance indices named generalized position error (GPE) and generalized orientation error (GOE) are defined in (16) and (17), respectively, where are errors in
(16) (17)
A. Effect of External Disturbance The effect of external disturbance was considered during the experiment. In addition to a strong water circulation in the pool, a disturbance in the horizontal plane was applied to ODIN III between the fiftieth and the one-hundredth seconds by mechanically holding the vehicle at the current position for the same duration and releasing it. Fig. 3 shows results of the PID controller. Since the PID gains were manually tuned for satisfactory performance, results shown in Fig. 3 are used as the baseline performance in this study. Fig. 3(a) shows tracking performance in , , and while Fig. 3(b) shows regulation performance of roll, pitch, and yaw. Fig. 3(c) and (d) show GPE and GOE, respectively. They show large errors around the eightieth second when the additional disturbance was applied. It is noted that performance of the sonar sensor degrades as it gets close to its range
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Fig. 3. PID control with external disturbance (a) tracking performance ], (c) generalized in [ x y z ], (b) regulation performance in [ position error, and (d) generalized orientation error.
Fig. 4. PID plus DOB control with external disturbance (a) tracking performance in [ x y z ], (b) regulation performance in [ ], (c) generalized position error, and (d) generalized orientation error.
limits. GPE and GOP were computed using sensor outputs including unfiltered sonar measurements and Fig. 3(c) shows a large noise level around the 320th second as the vehicle sensors are away from the wall. It is also observed in Fig. 3(a) and
(b) that GPE and GOE of the baseline performance are approximately bounded by 0.3 m and 0.06 rad, respectively. Fig. 4(c) and (d) show GPE and GOE of the PID plus DOB controller, respectively. It is observed that the DOB is effective
ZHAO AND YUH: EXPERIMENTAL STUDY ON ADVANCED UNDERWATER ROBOT CONTROL
Fig. 5. ADOB control with external disturbance (a) tracking performance in [x y z ], (b) regulation performance in [ ], (c) generalized position error, and (d) generalized orientation error.
in reducing the effect of the external disturbance as expected. Fig. 5(c) and (d) show GPE and GOE of the ADOB controller, respectively. Compared to the results of PID and PID plus DOB, it is also observed in Fig. 5 that satisfactory performance can be
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Fig. 6. PID plus DOB control with 2.0 times nominal model parameter change (a) tracking performance in [ x y z ], (b) regulation performance in [ ], (c) generalized position error, and (d) generalized orientation error.
obtained by the ADOB controller whose gains were initially set to zero and then self tuned during the operation.
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PID plus DOB with the larger nominal model. It is observed in Figs. 4 and 6 that the choice of the nominal model affects the overall performance of PID plus DOB. Fig. 7 shows results of ADOB with the larger nominal model. It is observed in Figs. 5 and 7 that the choice of the nominal model does not affect the overall performance of ADOB as much as that of PID plus DOB. IV. CONCLUSION The effectiveness of a new control system, ADOB was experimentally investigated on an underwater robot, ODIN III using PID as a baseline performance. The ADOB consists of the regressor-free adaptive control and DOB, taking advantages of DOB robustness with respect to external disturbances and modeling errors, and the regressor-free adaptive controller’s robustness with respect to uncertainties in the system model. The ADOB controller has the capability of self-tuning control gains and adapting to changes in the system and environment while PID requires a lengthy pretuning process for satisfactory performance. The PID would need retuning control gains when the performance degrades due to changes in the system and environment. However, it is almost impossible to retune control gains of underwater robots until they are brought up to the surface where hydrodynamics would change again. Therefore, as shown in the experimental result, the ADOB controller is promising for underwater robots, especially when the robot performance degrades or fails by PID type controllers. Fault-tolerant control for underwater robots including ADOB is currently considered for future study. APPENDIX Proof: Construct the Lyapunov function as follows: (A1) Differentiating (A1) along (11) with respect to time yields
(A2) With the adaptive control law (12), (13) and tion in the first bracket of (A2) becomes
, the equa-
Fig. 7. ADOB control with 2.0 times nominal model parameter change (a) ], tracking performance in [ x y z ], (b) regulation performance in [ (c) generalized position error, and (d) generalized orientation error.
B. Effect of the Nominal Model in DOB The effect of the nominal model in DOB was also considered by using a nominal model whose parameters are two times larger than the nominal model used in Fig. 4. Fig. 6 shows results of
(A3)
ZHAO AND YUH: EXPERIMENTAL STUDY ON ADVANCED UNDERWATER ROBOT CONTROL
and the second bracket becomes
(A4) From (A2)–(A4),
is reduced to (A5)
Therefore, the tracking error will asymptotically go to zero will also asymptotically conand the parameter estimations verge to . ACKNOWLEDGMENT The authors would like to thank staff of the Autonomous Systems Laboratory and MASE, Inc., for their assistance in testing ODIN III, and the reviewers for their useful suggestions. REFERENCES [1] “Underwater Vehicles and National Needs,” National Academy Press, National Research Council, Washington, DC, 1996. [2] S. Choi, J. Yuh, and G. Takashige, “Development of the omni directional intelligent navigator,” IEEE Robot. Automat. Mag., vol. 2, no. 3, pp. 44–53, Mar. 1995. [3] C. Alt, B. Allen, T. Austin, N. Forrester, R. Goldsborough, M. Purcell, and R. Stokey, “Hunting for mines with REMUS: A High performance, affordable, free swimming underwater robot,” in Proc. MTS/IEEE Conf. Exhibition on OCEANS, Honolulu, HI, Nov. 2001, pp. 117–122. [4] J. Bellingham, C. Goudey, T. Consi, J. Bales, D. Atwood, J. Leonard, and C. Chryssostomidis, “A second generation survey AUV,” in Proc. Symp. Autonomous Underwater Vehicle Technol., Cambridge, MA, Jul. 1994, pp. 148–155. [5] J. Yuh, S. Choi, C. Ikehara, G. McMurtry, M. Nejhad, N. Sarkar, and K. Sugihara, “Design of a semi-autonomous underwater vehicle for intervention missions (SAUVIM),” in Proc. Int. Symp. Underwater Technology, Tokyo, Japan, Apr. 1998, pp. 15–17. [6] J. Yuh and M. West, “Underwater robotics,” Int. J. Adv. Robot., vol. 15, no. 5, pp. 609–639, 2001. [7] D. Yoerger and J. Newman, “Demonstration of closed-loop trajectory control of an underwater vehicle,” in Proc. IEEE Conf. Exhibition on OCEANS, vol. 17, San Diego, CA, Nov. 1985, pp. 1028–1033. [8] D. Yoerger and J. Slotine, “Robust trajectory control of underwater vehicles,” IEEE J. Ocean. Eng., vol. 10, no. 4, pp. 462–470, Oct. 1985. , “Adaptive sliding control of an experimental underwater vehicle,” [9] in Proc. IEEE Int. Conf. Robotics and Automation, Sacramento, CA, Apr. 1991, pp. 2746–2751. [10] F. Song and S. Smith, “Design of sliding mode fuzzy controllers for an autonomous underwater vehicle without system model,” in Proc. IEEE Conf. OCEANS, Providence, RI, Sep. 2000, pp. 835–840. [11] J. Kim, K. Lee, Y. Cho, H. Lee, and H. Park, “Mixed H =H control with regional pole placements for underwater vehicle systems,” in Proc. American Control Conf., Chicago, IL, Jun. 2000, pp. 80–84. [12] J. Riedel and A. Healey, “Model based predictive control of AUV’s for station keeping in a shallow water wave environment,” in Proc. Int. Advanced Robotics Program, New Orleans, LA, Feb. 1998, pp. 77–102. [13] R. Cristi and A. Healey, “Adaptive identification and control of an autonomous underwater vehicle,” in Proc. 6th Int. Symp. Unmanned Untethered Submersible Technology, Durham, NC, Jun. 1989, pp. 563–572. [14] J. Yuh, “Modeling and control of underwater robotic vehicles,” IEEE Trans. Syst., Man, Cybern., vol. 20, no. 6, pp. 1476–1483, Dec. 1990. , “A learning control system for unmanned underwater vehicles,” [15] in Proc. 1995 MTS/IEEE Conf. OCEANS, San Diego, CA, Oct. 1995, pp. 1029–1032. [16] J. Yuh and J. Nie, “Application of nonregressor-based adaptive control to underwater robots: Experiment,” Int. J. Comput. Elect. Eng., vol. 26, pp. 169–179, 2000.
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[17] T. Fujii, “Neural networks for ocean engineering,” in Proc. IEEE Int. Conf. Neural Networks, Perth Western, Nov. 1995, pp. 216–219. [18] J. Yuh, “Learning control for underwater robotic vehicles,” IEEE Control Syst. Mag., vol. 14, no. 2, pp. 39–46, Apr. 1994. [19] K. Ishii, T. Fujii, and T. Ura, “Neural network system for on-line controller adaptation and its application to underwater robot,” in Proc. IEEE Int. Conf. Robotics and Automation, Leuven, Belgium, May 1998, pp. 756–761. [20] N. Kato, Y. Ito, J. Kojima, K. Asakawa, and Y. Shirasaki, “Control performance of autonomous underwater vehicle ’AQUA explorer 1000’ for inspection of underwater cables,” in Proc. IEEE Conf. OCEANS, Brest, France, Nov. 1994, pp. 135–140. [21] C. S. G. Lee, J. Wang, and J. Yuh, “Self-Adaptive neuro-fuzzy sitemaps with fast parameter learning for autonomous underwater vehicle control,” Int. J. Adv. Robot., vol. 15, no. 5, pp. 589–608, 2001. [22] T. Kim and J. Yuh, “A novel neuro-fuzzy controller for autonomous underwater vehicle,” in Proc. IEEE Int. Conf. Robotics and Automation, Seoul, Korea, May 2001, pp. 2350–2355. [23] J. Nie, J. Yuh, E. Kardash, and T. I. Fossen, “On-Board sensor-based adaptive control of small UUV’s in very shallow water,” Int. J. Adaptive Control Signal Process., vol. 13, pp. 441–451, 2000. [24] T. Murakami and K. Ohnishi, “Advanced motion control in mechatronics—A tutorial,” in Proc. IEEE Int. Workshop Intelligent Motion Control, Istanbul, Turkey, Aug. 1990, pp. SI13–SI17. [25] T. Umeno, T. Kaneko, and Y. Hori, “Robust servosystem design with two degrees of freedom and its application to novel motion control of robot manipulators,” IEEE Trans. Ind. Electron., vol. 40, no. 5, pp. 473–485, Oct. 1993. [26] H. Lee and M. Tomizuka, “Robust motion controller design for highaccuracy positioning systems,” IEEE Trans. Ind. Electron., vol. 43, no. 2, pp. 48–55, Feb. 1996. [27] T. Fossen, Guidance and Control of Ocean Vehicles. New York: Wiley, 1994. [28] H. Choi, A. Hanai, S. Choi, and J. Yuh, “Development of an underwater robot, ODIN-III,” in Proc. IEEE/RSJ IROS, Las Vegas, NV, Oct. 2003, pp. 536–541. Side Zhao (M’00) was born in Hebei, China, in 1971. He received his B.S. degree in automotive engineering from Hebei University of Technology, Hebei, in 1993, the M.S. degree in automotive engineering from Jilin University of Technology, Jilin, China, in 1996, and the Ph.D. degree in mechanical engineering from the University of Hawaii, Honolulu, in 2004. His current research focus is on underwater robotic vehicle control. Mr. Zhao is an active member of the Association for Computing Machinery. Junku Yuh (F’05) received the B.S. degree from Seoul National University, Seoul, Korea, in 1981 and the M.S. and Ph.D. degrees from Oregon State University, Corvallis, in 1983 and 1986, respectively. He joined the U.S. National Science Foundation (NSF) in 2001 and serves as Program Director of the Robotics Program and Computer Vision Program, Division of Information and Intelligent Systems, after 17 years as a Professor of mechanical engineering with the Graduate Faculty of Information and Computer Science, University of Hawaii. His main research interests include intelligent navigation and guidance and underwater robotics. He has published over 120 technical articles and edited/co-edited ten books in the area of robotics, including Underwater Robots (Norwell, MA: Kluwer, 1996) and Underwater Robotic Vehicles: Design and Control (Albuquerque, NM: TSI, 1995). He serves as an Associate Editor for the International Journal of Engineering Design and Automation and International Journal of Intelligent Automation & Soft Computing. He also serves on the Editorial Board of the Journal of Autonomous Robots and the International Journal of Intelligent Automation & Soft Computing. Dr. Yuh received a 1991 Presidential Young Investigator Award from U.S. President George Bush from the NSF and a 2004 Lifetime Achievement Award from World Automation Congress. He has served as an Associate Editor for the IEEE TRANSACTION ON ROBOTICS AND AUTOMATION. He has chaired several conference, including Program Chair of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) and Program Co-Chair of the 2006 IEEE International Conference on Robotics and Automation. He founded and chairs the technical committee on Underwater Robotics of the IEEE Robotics and Automation Society.
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Experimental Study on Advanced Underwater Robot Control Side Zhao, Member, IEEE, and Junku Yuh, Fellow, IEEE
Abstract—The control issue of underwater robots is very challenging due to the nonlinearity, time variance, unpredictable external disturbances, such as the sea current fluctuation, and the difficulty in accurately modeling the hydrodynamic effect. Conventional linear controllers may fail in satisfying performance requirements, especially when changes in the system and environment occur during the operation since it is almost impossible to manually retune the control parameters in water. Therefore, it is highly desirable to have an underwater robot controller capable of self-adjusting control parameters when the overall performance degrades. This paper presents the theory and experimental work of the adaptive plus disturbance observer (ADOB) controller for underwater robots, which is robust with respect to external disturbance and uncertainties in the system. This control scheme consists of disturbance observer (DOB) as the inner-loop controller and a nonregressor based adaptive controller as the outer-loop controller. The effectiveness of the ADOB was experimentally investigated by implementing three controllers: PID, PID plus DOB, and ADOB on an autonomous underwater robot, ODIN III. Index Terms—Adaptive control, disturbance observer (DOB), underwater robots.
I. INTRODUCTION
O
CEANS are the main resource of the energy and chemical balance that sustains mankind whose future is very much dependent on the living and nonliving resources in the oceans [1]. Oceans’ activities are also critically relevant to climate changes. Therefore, various studies have been conducted for ocean exploration and intervention. Underwater vehicles have been a popular and effective means for ocean exploration and intervention as they make it possible to go far beneath the ocean surface, collect first-hand information about how the oceans work, and furthermore perform intervention tasks. There are three types of underwater vehicles. 1) Manned submersible vehicles: They can carry out complicated tasks because of human intelligence. However, they have short endurance due to human physical and psychological limitations, and are costly to operate because of the endeavor done to ensure
Manuscript received June 3, 2004; revised August 8, 2004. This paper was recommended by Associate Editor W. K. Chung and Editor I. Walker upon the evaluation of the reviewers’ comments. This work was sponsored in part by the National Science Foundation under Grant BES97-01614, in part by the Office of Naval Research under Grants N00014-97-1-0961 and N00014-00-1-0629, and in part by KRISO/KORDI via MASE. Any opinions, findings and conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies. S. Zhao is with Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, HI 96822 USA (e-mail: [email protected]). J. Yuh is with National Science Foundation, Arlington, VA 22230 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TRO.2005.844682
human safety. Alvin at the Woods Hole Oceanographic Institute and Pisces V at the NOAA Hawaii’s Undersea Research Laboratory are examples of manned submersible vehicles. 2) Remotely operated vehicles (ROV): They are unmanned, tethered vehicles with umbilical cables to transfer power, sensor data and control commands between the operators on the surface and the ROV. They are usually launched from surface ships. They can also carry out complicated tasks via tele-operation by human pilots on the surface ships. Even though their operations are often limited by operator fatigue, they are free from the safety concern of on-board human operators and have almost unlimited endurance in the ocean, compared to manned submersibles. However, the dragging force on the tether, time delay, and operator fatigue make ROV difficult to operate and . the daily operating cost is still very expensive KAIKO from the Japanese Marine–Earth Science and Technology Center (JAMSTEC) was the most advanced ROV ever operated at a 11 000-m depth. Unfortunately, KAIKO was lost during the operation in 2003 as the tether was snapped due to bad weather. 3) Autonomous underwater vehicles (AUVs) or underwater robots: They are unmanned, tether-free, powered by onboard energy sources, equipped with various navigation sensors such as inertial measurement unit (IMU), sonar sensor, laser ranger, and pressure sensor, and controlled by onboard computers for given missions. They are more mobile and could have much wider reachable scope than ROV. On-board power and intelligence could help AUV self-react properly to changes in the system and its environment, avoiding any disastrous situation like the KAIKO case. With the continuous advance in control, navigation, artificial intelligence, material science, computer, sensor, and communication, AUVs have become a very attractive platform in exploring the oceans, and numerous AUV prototypes have been proposed, such as ODIN [2], REMUS [3], and ODYSSEY [4]. While most of the currently available AUV are for noncontact tasks such as mapping, monitoring or sampling in the water column, research on AUV with robotic manipulators has recently been underway [5]. Various underwater robotic technologies were surveyed by Yuh and West [6]. The control issue of AUV is very challenging due to the nonlinearity, time-variance, unpredictable external disturbances, such as the environmental force generated by the sea current fluctuation, and the difficulty in accurately modeling the hydrodynamic effect. The well-developed linear controllers may fail in satisfying performance requirements especially when changes in the system and environment occur during the AUV operation since it is almost impossible to manually retune the control parameters in water. Therefore, it is highly desirable
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to have an AUV controller capable of self-adjusting control parameters when the overall performance degrades. Various advanced control schemes for underwater robots have been proposed in the literature as some of them are summarized below. Sliding mode control (SMC): SMC restricts the system states inside a certain subspace of the whole state space and makes them asymptotically converge to their equilibrium point. It requires a raw estimation of the system parameters and an estimation of the system uncertainty for the switching surface design and variable-structure control law design. Even though SMC has been well known for its robustness to parameter variations, it has the inherent problem of chattering phenomenon. Yoerger and Newman [7] and Yoerger and Slotine [8] introduced the basic methodology of using sliding mode control for AUV application, and later Yoerger and Slotine [9] developed an adaptive sliding mode control scheme, in which a nonlinear system model was used. When the generalized disturbance makes the system state exceed the sliding mode tolerance layer, the exceeding value is used to update the nonlinear model parameters and furthermore update the control input. Song and Smith [10] introduced a sliding mode fuzzy controller that uses Pontryagin’s maximum principle for time-optimal switching surface design, and uses fuzzy logic to form this surface. Robust/optimal control: The principles of the robust/optimal control are calculus of variations, Pontryagin maximum principle, and Bellman dynamic programming. However, due to the difficulty of deriving an accurate model of AUV system, it is difficult to apply optimal control directly. Therefore, generally optimal control combined with system identification or robust control is used in AUV control. Kim et al. [11] proposed an control scheme, in which the robust stability problem against time delays and parameter uncertainties is transformed into control problem, and performance problem is transformed into problem. Riedel and Healey [12] proposed an optimal control (LQR) scheme that uses an auto-regression (AR) model to predict the wave-induced hydrodynamic disturbance. Adaptive control: Adaptive control modifies control gains according to the changes in the process dynamics and the disturbances. Since there are parameter uncertainties and unknown disturbances in the underwater vehicle’s hydrodynamics, many researchers studied adaptive control to address the AUV control issues. However, adaptive control may fail when the dynamics changing speed is beyond its adapting capability, and the model-based adaptive control may be calculation burdensome because of the excessive endeavor in system identification. Cristi and Healey [13] proposed a model-based adaptive controller. Assuming that the vehicle dynamics are nearly linear within the range of its operating conditions, the controller uses the RLS method for system parameter estimation and, futhermore, uses the pole placement technique for control gain desgin. Yuh [14] proposed a discrete-time adaptive controller using a parameter adaptation algorithm. Yuh [15], and Yuh and Nie [16] proposed a nonregressor-based adaptive control scheme that uses parametric bound estimation, instead of system parameter estimation, to tune the control gains. Neural network (NN) control: Neural networks attracted many researchers because they can achieve nonlinear mapping.
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Using NN in constructing controllers has the advantage that the dynamics of the controlled system need not be completely known. This makes NN suitable for underwater vehicle control. However, NN-based controllers have the disadvantage that no formal mathematical characterization exists for the closed-loop system behavior. The validation of the final design can only be demonstrated experimentally. There are mainly two approaches in using NN for control purpose: learning with a forward model and direct learning. In the former approach, generally, the forward model is trained by the output error or state error and then used for gain derivation, while in the latter approach, the state or output error is used directly to map the desired control input [17]. Yuh [18] described a multiplayer feedforward network. Each layer has 13 neurons, except the last layer that has six neurons. The input signals are six position errors, six velocity errors and a constant. The output signals are the six control forces. The back-propagation (BP) algorithm is used for training the network. Ishii et al. [19] proposed a neural network system that is based on self-organizing neural-net control system (SONCS) that executes identification of robot dynamics and controller adaptation in parallel with robot control and adjusts the controller network based on the results of virtual operation of the control calculation and the actual control operation. Fuzzy logic control: The theoretical basis of fuzzy logic control is that any real continuous function over a compact set can be approximated to any degree of accuracy by the fuzzy inference system. For control engineering applications, researchers use fuzzy logic to form a smooth approximation of a nonlinear mapping from system input space to system output space. This makes it suitable for nonlinear system control. However, determining the linguistic rules and the membership functions requires experimental data and, therefore, very time-consuming, and the rule-based structure of fuzzy logic control makes it difficult to characterize the behavior of the closed-loop system in order to determine response time and stability. Kato et al. [20] used a very basic fuzzy controller in AQUA EXPLORER 1000 cable inspection. Lee et al. [21] proposed a self-adaptive neurofuzzy inference system (SANFIS) that uses a five-layer-structured NN to achieve better function approximation: a recursive least squares algorithm and a modified Levenberg–Marquardt algorithm with limited memory are used in extracting fuzzy rules and tuning the membership functions. Kim and Yuh [22] proposed a fuzzy membership function-based neural networks (FMFNNs) that uses a BP network for fuzzy control’s membership function derivation. This paper describes an adaptive plus DOB (ADOB) controller for underwater robots as an extension of the second author’s previous study on a nonregressor based adaptive controller [16], [23]. The nonregressor based adaptive controller does not require any physical information about the robot model except the number of inputs and the number of outputs. As demonstrated by experimental investigation in [16], [23], the nonregressor based adaptive controller is very effective for autonomous underwater vehicles whose hydrodynamics cannot be accurately modeled or may vary while in operation as changes in the system and environment occur. However, the adaptive controller does not address robustness with respect to external
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Fig. 1. Diagram of the ADOB controller.
disturbances while DOB is very robust with respect to external disturbances. While more details about DOB can be found in [24]–[26], it can be briefly described as follows. The DOB basically removes the effect of external disturbances and modeling errors, and makes the system behave close to a nominal model that was prechosen by the user. Then the user designs an outer-loop controller, such as PID that controls the overall system. However, the DOB controllers require using a low-pass filter affected by the nominal model, and, therefore, the performance of the DOB controller such as PID plus DOB varies depending on the nominal model or the low-pass filter. As shown in Fig. 1, this paper presents an ADOB controller using DOB as an inner-loop compensator, taking advantage of its robustness with respect to disturbances, and using the nonregress based adaptive controller as an outer-loop controller, taking advantage of its robustness with respect to model uncertainties due to the nominal model or the low-pass filter. The effectiveness of the control system was experimentally investigated by implementing three controllers: PID, PID plus DOB, and ADOB on an autonomous underwater robot, ODIN III. The PID controller gains were manually tuned for satisfactory performance and its result was used as the baseline performance in this study. The paper is organized as follows. Section II describes the ADOB controller and Section III presents experimental results before conclusions in Section IV. II. CONTROLLER DESIGN There are two coordinate systems that are commonly used to describe the AUV kinematics: the earth-fixed frame (E-frame) and the body-fixed frame (B-frame). The position and orientation of the vehicle are described in the E-frame, while the linear and angular velocity and the control forces/moments are described in the B-frame: position and orientation vector in E-frame; velocity vector in force/moment B-frame; and vector in B-frame. The velocity vectors in E-frame and in B-frame have the following relationship: (1) is the transformation matrix between the B-frame where and the E-frame.
The dynamics of AUV in the B-frame can be represented by a six-degree-of-freedom (DOF) nonlinear dynamic equation shown as follows: (2) is the inertial matrix including added mass; is where the matrix of Coriolis and centripetal terms, and velocity-depenis the damping matrix indent terms due to added mass; is the gravitational cluding terms representing drag forces; force and buoyant force; is the control input; is the external disturbance. Detailed description of (1) and (2) can be found in Fossen [27]. is The overall control system as shown in Fig. 1, where the desired system output, is the system output, is the external disturbance, is the output measurement noise, and is the nominal model that can be chosen by the user. It has the inner loop compensator of DOB inside the dotted line and the outer loop of the adaptive controller. It can be easily seen that the system compensated by DOB becomes the nominal model assuming no measurement noise) if the (i.e., . It would be straightforward to design low-pass filter the outer-loop controller to control the nominal model that is known. However, the low-pass filter is needed since the inverse of the nominal model cannot be realized. First proposed in [24] and later refined in [25] and [26], DOB can remove the effect of the external disturbance and the modeling error, which can be referred as the generalized disturbance, in the bandwidth of the low-pass filter . However, because of the phase delay and bandwidth restriction of the low-pass filter , there is always an estimation error of the generalized disturbance, and, therefore, the overall performance with a simple outer-loop controller, such as PID, may vary depending on affected by the nominal model. Therefore, the system compensated by DOB with could be seen as a nominal model with disturbance estimation error that would be handled by the adaptive controller. in the bodyConsider the following nominal model for fixed frame in designing DOB (3) After applying DOB, the system dynamics becomes (4) (5)
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where represents the estimation error, and is in Fig. 1. shown as The DOB compensated system shown in (4) could be rewritten in the E-frame using as follows [27]: (6) where
, , , and class of estimation errors which are bounded by
, represents a
will also asymptotically zero and the parameter estimations . converge to It is noted that the direct use of the controller shown in (12) would generate large control input signals and chattering phenomenon when the value of the denominator is close to zero. To avoid this problem, the following modified controller is used: for (15) for
(7) where , is a desired value of , and , , and are positive constants. Since the system matrices are based on the nominal model (3) chosen by the user, they are known and can be bounded as
(8) where , , and are positive constants. Instead of mathematically proving (7) and (8), this paper describes how to estimate (9) , is a positive constant, and when . Consider the following control law:
where
(10) where
, which is the desired acceleration, , which is a positive constant, , are the control gain matrices. The error equation can be obtained by combing (6) and (10) as
(11) , , , . where The adaptive controller defines the gain matrices and the esas follows: timations of the (12) (13) where
are positive constants,
are estimates of
, and (14)
where is a positive constant satisfying . It is proven in Appendix A that using the controller described in (10), (12)–(14), the tracking error will asymptotically go to
where and are positive constants. The modified controller (15) may not guarantee the asymptotic stability but tracking errors are bounded by small numbers depending on . There are three parameters that affect the performance of , sigma , and the adaptive controller: adaptation gain . One can note the following: affects the time threshold affects constant of the overall system; the adaptation gain the adaptation period; and appropriate values of the threshold would keep the denominator in (15) from becoming the near zero value that may cause high gain values and large control signals beyond saturation limits. More details about the adaptive control part and discussion about influence of the adaptive control parameters could be found in [16] and [23] with experimental results. III. EXPERIMENTAL RESULTS The experimental work of the proposed controller was carried out on ODIN III [28], which is shown in Fig. 2. It is a six-DOF autonomous underwater robot developed by the Autonomous Systems Laboratory of the University of Hawaii. ODIN III is and Windows 2000 with the Real Time eXbased on tension (RTX) embedded real-time system. It is a close-framed sphere-shaped vehicle that makes its dynamics in each direction nearly identical. It has eight thrusters: four horizontal and four vertical, which make ODIN III capable of six-DOF maneuvering and also have thrust redundancy for fault tolerance purpose. It also has various navigation sensors including eight sonar sensors, a pressure sensor and an Inertial Measurement Unit (IMU). The eight sonar sensors are used to measure the displacements in the horizontal plane, the pressure sensor is used to measure the depth of the vehicle, and the IMU is used to measure the angular displacements. A Kalman filter is used to suppress the sensor noise and to estimate the translational and angular velocities. ODIN III has a multisampling-rate system with the sampling rate of the sonar sensors at 3 Hz and the sampling rate of the pressure sensors and the IMU at 30 Hz. The controller sampling rates are selected same as those of the sensors: 3 Hz for surge and sway and 30 Hz for roll, pitch, yaw, and depth. All the tests were done in the diving pool of Kahanamoku Pool at the University of Hawaii. Three different controllers (PID controller, PID plus DOB controller, and ADOB controller) were implemented on ODIN and the results are shown in this section. The vehicle was tested for a six-DOF desired motion shown as a solid line in Fig. 3(a) and (b) tracking in , , and in sequence . The controller settings used in while regulating in the experiment are listed as follows.
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Fig. 2.
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Omni-Directional intelligent navigator (ODIN III). (a) View in water. (b) Inside view. (c) Hardware diagram.
PID controller: The system was decoupled into six SISO subsystems and a separate PID controller was designed for each DOF not only because ODIN III is a nearly decoupled system but also because it would be easier to manually tune gains. After a lengthy gain-tuning process, the following numerical values for proportional, derivative and integral gains in each DOF ; ; were used: ; ; ; . PID plus DOB controller: In constructing DOB, the , low-pass filters are all set as and the nominal model is set as a pure inertia where system, is the rigid body inertia paramand . However, eters with and because the sampling frequencies in are different, different are used in parameterizing : for ; for . the The following numerical values were used for PID control ; ; gains: ; ; ; . ADOB controller: The DOB part is the same as that of the PID plus DOB controller. The adaptive controller part parameters ; , , are: , ; , , , . The initial values of all control gain in (10) were zero by setting initial values of in (12) to zero. It does not require manually tuning gain values un-
like PID since it is capable of self tuning. Before the vehicle began trajectory tracking, ODIN III was let to have a short initial adaptation period when the vehicle adaptive control self-adjusted control gains from zero initial values. To show the experimental results more effectively, two performance indices named generalized position error (GPE) and generalized orientation error (GOE) are defined in (16) and (17), respectively, where are errors in
(16) (17)
A. Effect of External Disturbance The effect of external disturbance was considered during the experiment. In addition to a strong water circulation in the pool, a disturbance in the horizontal plane was applied to ODIN III between the fiftieth and the one-hundredth seconds by mechanically holding the vehicle at the current position for the same duration and releasing it. Fig. 3 shows results of the PID controller. Since the PID gains were manually tuned for satisfactory performance, results shown in Fig. 3 are used as the baseline performance in this study. Fig. 3(a) shows tracking performance in , , and while Fig. 3(b) shows regulation performance of roll, pitch, and yaw. Fig. 3(c) and (d) show GPE and GOE, respectively. They show large errors around the eightieth second when the additional disturbance was applied. It is noted that performance of the sonar sensor degrades as it gets close to its range
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Fig. 3. PID control with external disturbance (a) tracking performance ], (c) generalized in [ x y z ], (b) regulation performance in [ position error, and (d) generalized orientation error.
Fig. 4. PID plus DOB control with external disturbance (a) tracking performance in [ x y z ], (b) regulation performance in [ ], (c) generalized position error, and (d) generalized orientation error.
limits. GPE and GOP were computed using sensor outputs including unfiltered sonar measurements and Fig. 3(c) shows a large noise level around the 320th second as the vehicle sensors are away from the wall. It is also observed in Fig. 3(a) and
(b) that GPE and GOE of the baseline performance are approximately bounded by 0.3 m and 0.06 rad, respectively. Fig. 4(c) and (d) show GPE and GOE of the PID plus DOB controller, respectively. It is observed that the DOB is effective
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Fig. 5. ADOB control with external disturbance (a) tracking performance in [x y z ], (b) regulation performance in [ ], (c) generalized position error, and (d) generalized orientation error.
in reducing the effect of the external disturbance as expected. Fig. 5(c) and (d) show GPE and GOE of the ADOB controller, respectively. Compared to the results of PID and PID plus DOB, it is also observed in Fig. 5 that satisfactory performance can be
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Fig. 6. PID plus DOB control with 2.0 times nominal model parameter change (a) tracking performance in [ x y z ], (b) regulation performance in [ ], (c) generalized position error, and (d) generalized orientation error.
obtained by the ADOB controller whose gains were initially set to zero and then self tuned during the operation.
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PID plus DOB with the larger nominal model. It is observed in Figs. 4 and 6 that the choice of the nominal model affects the overall performance of PID plus DOB. Fig. 7 shows results of ADOB with the larger nominal model. It is observed in Figs. 5 and 7 that the choice of the nominal model does not affect the overall performance of ADOB as much as that of PID plus DOB. IV. CONCLUSION The effectiveness of a new control system, ADOB was experimentally investigated on an underwater robot, ODIN III using PID as a baseline performance. The ADOB consists of the regressor-free adaptive control and DOB, taking advantages of DOB robustness with respect to external disturbances and modeling errors, and the regressor-free adaptive controller’s robustness with respect to uncertainties in the system model. The ADOB controller has the capability of self-tuning control gains and adapting to changes in the system and environment while PID requires a lengthy pretuning process for satisfactory performance. The PID would need retuning control gains when the performance degrades due to changes in the system and environment. However, it is almost impossible to retune control gains of underwater robots until they are brought up to the surface where hydrodynamics would change again. Therefore, as shown in the experimental result, the ADOB controller is promising for underwater robots, especially when the robot performance degrades or fails by PID type controllers. Fault-tolerant control for underwater robots including ADOB is currently considered for future study. APPENDIX Proof: Construct the Lyapunov function as follows: (A1) Differentiating (A1) along (11) with respect to time yields
(A2) With the adaptive control law (12), (13) and tion in the first bracket of (A2) becomes
, the equa-
Fig. 7. ADOB control with 2.0 times nominal model parameter change (a) ], tracking performance in [ x y z ], (b) regulation performance in [ (c) generalized position error, and (d) generalized orientation error.
B. Effect of the Nominal Model in DOB The effect of the nominal model in DOB was also considered by using a nominal model whose parameters are two times larger than the nominal model used in Fig. 4. Fig. 6 shows results of
(A3)
ZHAO AND YUH: EXPERIMENTAL STUDY ON ADVANCED UNDERWATER ROBOT CONTROL
and the second bracket becomes
(A4) From (A2)–(A4),
is reduced to (A5)
Therefore, the tracking error will asymptotically go to zero will also asymptotically conand the parameter estimations verge to . ACKNOWLEDGMENT The authors would like to thank staff of the Autonomous Systems Laboratory and MASE, Inc., for their assistance in testing ODIN III, and the reviewers for their useful suggestions. REFERENCES [1] “Underwater Vehicles and National Needs,” National Academy Press, National Research Council, Washington, DC, 1996. [2] S. Choi, J. Yuh, and G. Takashige, “Development of the omni directional intelligent navigator,” IEEE Robot. Automat. Mag., vol. 2, no. 3, pp. 44–53, Mar. 1995. [3] C. Alt, B. Allen, T. Austin, N. Forrester, R. Goldsborough, M. Purcell, and R. Stokey, “Hunting for mines with REMUS: A High performance, affordable, free swimming underwater robot,” in Proc. MTS/IEEE Conf. Exhibition on OCEANS, Honolulu, HI, Nov. 2001, pp. 117–122. [4] J. Bellingham, C. Goudey, T. Consi, J. Bales, D. Atwood, J. Leonard, and C. Chryssostomidis, “A second generation survey AUV,” in Proc. Symp. Autonomous Underwater Vehicle Technol., Cambridge, MA, Jul. 1994, pp. 148–155. [5] J. Yuh, S. Choi, C. Ikehara, G. McMurtry, M. Nejhad, N. Sarkar, and K. Sugihara, “Design of a semi-autonomous underwater vehicle for intervention missions (SAUVIM),” in Proc. Int. Symp. Underwater Technology, Tokyo, Japan, Apr. 1998, pp. 15–17. [6] J. Yuh and M. West, “Underwater robotics,” Int. J. Adv. Robot., vol. 15, no. 5, pp. 609–639, 2001. [7] D. Yoerger and J. Newman, “Demonstration of closed-loop trajectory control of an underwater vehicle,” in Proc. IEEE Conf. Exhibition on OCEANS, vol. 17, San Diego, CA, Nov. 1985, pp. 1028–1033. [8] D. Yoerger and J. Slotine, “Robust trajectory control of underwater vehicles,” IEEE J. Ocean. Eng., vol. 10, no. 4, pp. 462–470, Oct. 1985. , “Adaptive sliding control of an experimental underwater vehicle,” [9] in Proc. IEEE Int. Conf. Robotics and Automation, Sacramento, CA, Apr. 1991, pp. 2746–2751. [10] F. Song and S. Smith, “Design of sliding mode fuzzy controllers for an autonomous underwater vehicle without system model,” in Proc. IEEE Conf. OCEANS, Providence, RI, Sep. 2000, pp. 835–840. [11] J. Kim, K. Lee, Y. Cho, H. Lee, and H. Park, “Mixed H =H control with regional pole placements for underwater vehicle systems,” in Proc. American Control Conf., Chicago, IL, Jun. 2000, pp. 80–84. [12] J. Riedel and A. Healey, “Model based predictive control of AUV’s for station keeping in a shallow water wave environment,” in Proc. Int. Advanced Robotics Program, New Orleans, LA, Feb. 1998, pp. 77–102. [13] R. Cristi and A. Healey, “Adaptive identification and control of an autonomous underwater vehicle,” in Proc. 6th Int. Symp. Unmanned Untethered Submersible Technology, Durham, NC, Jun. 1989, pp. 563–572. [14] J. Yuh, “Modeling and control of underwater robotic vehicles,” IEEE Trans. Syst., Man, Cybern., vol. 20, no. 6, pp. 1476–1483, Dec. 1990. , “A learning control system for unmanned underwater vehicles,” [15] in Proc. 1995 MTS/IEEE Conf. OCEANS, San Diego, CA, Oct. 1995, pp. 1029–1032. [16] J. Yuh and J. Nie, “Application of nonregressor-based adaptive control to underwater robots: Experiment,” Int. J. Comput. Elect. Eng., vol. 26, pp. 169–179, 2000.
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[17] T. Fujii, “Neural networks for ocean engineering,” in Proc. IEEE Int. Conf. Neural Networks, Perth Western, Nov. 1995, pp. 216–219. [18] J. Yuh, “Learning control for underwater robotic vehicles,” IEEE Control Syst. Mag., vol. 14, no. 2, pp. 39–46, Apr. 1994. [19] K. Ishii, T. Fujii, and T. Ura, “Neural network system for on-line controller adaptation and its application to underwater robot,” in Proc. IEEE Int. Conf. Robotics and Automation, Leuven, Belgium, May 1998, pp. 756–761. [20] N. Kato, Y. Ito, J. Kojima, K. Asakawa, and Y. Shirasaki, “Control performance of autonomous underwater vehicle ’AQUA explorer 1000’ for inspection of underwater cables,” in Proc. IEEE Conf. OCEANS, Brest, France, Nov. 1994, pp. 135–140. [21] C. S. G. Lee, J. Wang, and J. Yuh, “Self-Adaptive neuro-fuzzy sitemaps with fast parameter learning for autonomous underwater vehicle control,” Int. J. Adv. Robot., vol. 15, no. 5, pp. 589–608, 2001. [22] T. Kim and J. Yuh, “A novel neuro-fuzzy controller for autonomous underwater vehicle,” in Proc. IEEE Int. Conf. Robotics and Automation, Seoul, Korea, May 2001, pp. 2350–2355. [23] J. Nie, J. Yuh, E. Kardash, and T. I. Fossen, “On-Board sensor-based adaptive control of small UUV’s in very shallow water,” Int. J. Adaptive Control Signal Process., vol. 13, pp. 441–451, 2000. [24] T. Murakami and K. Ohnishi, “Advanced motion control in mechatronics—A tutorial,” in Proc. IEEE Int. Workshop Intelligent Motion Control, Istanbul, Turkey, Aug. 1990, pp. SI13–SI17. [25] T. Umeno, T. Kaneko, and Y. Hori, “Robust servosystem design with two degrees of freedom and its application to novel motion control of robot manipulators,” IEEE Trans. Ind. Electron., vol. 40, no. 5, pp. 473–485, Oct. 1993. [26] H. Lee and M. Tomizuka, “Robust motion controller design for highaccuracy positioning systems,” IEEE Trans. Ind. Electron., vol. 43, no. 2, pp. 48–55, Feb. 1996. [27] T. Fossen, Guidance and Control of Ocean Vehicles. New York: Wiley, 1994. [28] H. Choi, A. Hanai, S. Choi, and J. Yuh, “Development of an underwater robot, ODIN-III,” in Proc. IEEE/RSJ IROS, Las Vegas, NV, Oct. 2003, pp. 536–541. Side Zhao (M’00) was born in Hebei, China, in 1971. He received his B.S. degree in automotive engineering from Hebei University of Technology, Hebei, in 1993, the M.S. degree in automotive engineering from Jilin University of Technology, Jilin, China, in 1996, and the Ph.D. degree in mechanical engineering from the University of Hawaii, Honolulu, in 2004. His current research focus is on underwater robotic vehicle control. Mr. Zhao is an active member of the Association for Computing Machinery. Junku Yuh (F’05) received the B.S. degree from Seoul National University, Seoul, Korea, in 1981 and the M.S. and Ph.D. degrees from Oregon State University, Corvallis, in 1983 and 1986, respectively. He joined the U.S. National Science Foundation (NSF) in 2001 and serves as Program Director of the Robotics Program and Computer Vision Program, Division of Information and Intelligent Systems, after 17 years as a Professor of mechanical engineering with the Graduate Faculty of Information and Computer Science, University of Hawaii. His main research interests include intelligent navigation and guidance and underwater robotics. He has published over 120 technical articles and edited/co-edited ten books in the area of robotics, including Underwater Robots (Norwell, MA: Kluwer, 1996) and Underwater Robotic Vehicles: Design and Control (Albuquerque, NM: TSI, 1995). He serves as an Associate Editor for the International Journal of Engineering Design and Automation and International Journal of Intelligent Automation & Soft Computing. He also serves on the Editorial Board of the Journal of Autonomous Robots and the International Journal of Intelligent Automation & Soft Computing. Dr. Yuh received a 1991 Presidential Young Investigator Award from U.S. President George Bush from the NSF and a 2004 Lifetime Achievement Award from World Automation Congress. He has served as an Associate Editor for the IEEE TRANSACTION ON ROBOTICS AND AUTOMATION. He has chaired several conference, including Program Chair of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) and Program Co-Chair of the 2006 IEEE International Conference on Robotics and Automation. He founded and chairs the technical committee on Underwater Robotics of the IEEE Robotics and Automation Society.
