53.8 Summary

This chapter introduces robot control design methods using the Lyapunov based method. By utilizing the physical properties of the robot kinematics and dynamics, several set-point and adaptive tracking controllers have been presented in both the joint space and task space. A simple motion controller that is effective for set-point regulation is the PD controller with gravity compensation. For tracking control tasks, the adaptive controller has been presented for a robot manipulator with uncertain dynamics. Using sensory feedback of the robot end-effector position in the task space, approximate Jacobian set-point controllers and adaptive Jacobian tracking controllers have been presented for robot manipulators with uncertainties in both kinematics and dynamics.

References

Abdallah CT, Dawson D, Dorato P, Jamshidi M (1991) Survey of robust control for rigid robots. IEEE Trans Control Syst Mag 11(2):24–30

Arimoto S (1994) A class of quasi-natural potentials and hyper-stable PID servo-loops for nonlinear robotic systems. Trans Soc Instrum Control Eng 30(9):1005–1012

Arimoto S (1996) Control theory of non-linear mechanical systems: a passivity-based and circuittheoretic approach. Oxford University Press, New York

Arimoto S, Miyazaki F (1985)Asymptotic stability of feedback control for robot manipulators. In: Proceedings of IFAC symposium on robot control, Barcelona, pp 447–452

Arimoto S, Miyazaki F (1984)Stability and robustness of PID feedback control for robot manipulators of sensory capability. In: Proceedings of the 1st international symposium on robotics research, pp 783–799

Arimoto S, Kawamura S, Miyazaki F (1984) Bettering operation of robots by learning. J Robot Syst 1(2):123–140

Arimoto S, Naniwa T, Parra-Vega V, Whitcomb L (1994) A quasi-natural potential and its role in design of hyper-stable PID servo-loop for robotic systems. In: Proceedings of the CAI Pacific symposium control and industrial automation application, pp 110–117

Berghuis H, Ortega R, Nijmeijer H (1993) A robust adaptive robot controller. IEEE Trans Robot Autom 9(6):825–830

Braganza D, Dixon WE, Dawson DM, Xian B (2005)Tracking control for robot manipulators with kinematic and dynamic uncertainty. In: Proceedings of IEEE conference on decision and control, Seville, pp 5293–5297

Cheah CC (2003)Approximate Jacobian robot control with adaptive Jacobian matrix. In: Proceedings of IEEE international conference on decision and control, Hawaii, pp 5859–5864

Cheah CC, Liaw H (2005) Inverse Jacobian regulator with gravity compensation: stability and experiment. IEEE Trans Robot Autom 21(4):741–747

Cheah CC, Kawamura S, Arimoto S (1998) Feedback control for robotic manipulators with uncertain kinematics and dynamics. In: Proceedings of IEEE international conference on robotics and automation, Leuven, pp 3607–3612

Cheah CC, Kawamura S, Arimoto S (1999a) Feedback control for robotic manipulators with an uncertain Jacobian matrix. J Robot Syst 12(2):119–134

Cheah CC, Hirano M, Kawamura S, Arimoto S (2003) Approximate Jacobian control for robots with uncertain kinematics and dynamics. IEEE Trans Robot Autom 19(4):692–702

Cheah CC, Liu C, Slotine JJE (2004) Approximate Jacobian adaptive control for robot manipulators. In: Proceeding of IEEE international conference on robotics and automation, New Orleans, pp 3075–3080

Cheah CC, Liu C, Slotine JJE (2006a) Adaptive tracking control for robots with unknown kinematic and dynamic properties. Int J Robot Res 25(3):283–296

Chien-Chern Cheah, Chao Liu, Slotine J-JE (2006b) Adaptive Jacobian tracking control of robots with uncertainties in kinematic, dynamic and actuator models. IEEE Trans Automat Contr 51(6):1024–1029

Cheah CC, Liu C, Slotine JJE (2007) Adaptive vision based tracking control of robots with uncertainty in depth information. In: Proceedings of IEEE conference on roboties and automation, Roma, pp 2817–2822

Cheah CC, Liu C, Slotine JJE (2010) Adaptive Jacobian vision based control for robots with uncertain depth information. Automatica 46:1228–1233

Cheah CC, Kawamura S, Arimoto S, Lee K (1999) PID control for robotic manipulator with uncertain jacobian matrix. In: Proceedings of IEEE international conference on robotics and automation, Detroit, pp 494–499

Craig JJ, Hsu P, Sastry SS (1987) Adaptive control of mechanical manipulators. Int J Robot Res 6(2):10–20

Dixon WE (2007) Adaptive regulation of amplitude limited robot manipulators with uncertain kinematics and dynamics. IEEE Trans Automat Control 52(3):488–493

Garcia-Rodriguez R, Parra-Vega V (2012) Cartesian sliding PID control schemes for tracking robots with uncertain Jacobian. Trans Inst Meas Control 34(4):448–462

Hutchinson S, Hager GD, Corke P (1996) A tutorial on visual servo control. IEEE Trans Autom Control 12(5):651–670

Ioannou P, Sun J (1996) Robust adaptive control. Prentice-Hall, Englewood Cliffs

Kelly R (1993) Comments on adaptive PD controller for robot manipulators. IEEE Trans Robot Autom 9:117–119

Kelly R (1997) PD control with desired gravity compensation of robotic manipulators: a review. Int J Robot Res 16(5):660–672

Kelly R (1998) Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions. IEEE Trans Autom Control 43(7):934–938

Kelly R, Santibanez V, Loria A (2005) Control of robot manipulators in joint space. Springer–Verlag, London

Koditschek DE (1987)Adaptive techniques for mechanical systems. In: 5th Yale workshop on applications of adaptive systems theory, New Haven, pp 259–265

Lee KW, Khalil H (1997) Adaptive output feedback control of robot manipulators using high gain observer. Int J Control 67(6):869–886

Lewis FL (1996) Neural network control of robot manipulators. Intell Syst Appl 11(3):64–75

Liang X, Huang X, Wang M, Zeng X (2010) Adaptive task-space tracking control of robots without task-space- and joint-space-velocity measurements. IEEE Trans Robot 26(4):733–742

Middleton RH, Goodwin GC (1988) Adaptive computed torque control for rigid link manipulators. Syst Control Lett 10:9–16

Niemeyer G, Slotine JJE (1991) Performance in adaptive manipulator control. Int J Robot Res 10(2):149–161

Ortega R, Spong MW (1989) Adaptive motion control of rigid robots: a tutorial. Automatica 25(6):877–888

Ortega R, Loria A, Kelly R (1995) A semi-globally stable output feedback PI2D regulator for robot manipulators. IEEE Trans Autom Control 40(8):1432–1436

Paden B, Panja R (1988) A globally asymptotically stable PD+ controller for robot manipulator. Int J Control 47(6):1697–1712

Sadegh N, Horowitz R (1990) Stability and robustness analysis of a class of adaptive controllers for robotic manipulators. Int J Robot Res 9(3):74–92

Slotine JJE (1985) The robust control of robot manipulators. Int J Robot Res 4(2):49–61

Slotine JJE, Li W (1987) On the adaptive control of robot manipulators. Int J Robot Res 6(3):49–59

Slotine JJE, Li W (1991) Applied nonlinear control. Prentice Hall, Englewood Cliffs

Spong MW (1992) On the robust control of robot manipulators. IEEE Trans Autom Control 37(11):1782–1786

Spong MW, Hutchinson S, Vidyasagar M (2006) Robot modeling and control. Wiley, New York

Takegaki M, Arimoto S (1981) A new feedback method for dynamic control of manipulators. ASME J Dyn Syst Meas Control 103:119–125

Tomei P (1991) Adaptive PD controller for robot manipulators. IEEE Trans Robot Autom 7:565–570

Wang H, Xie Y (2009) Prediction error based adaptive Jacobian tracking of robots with uncertain kinematics and dynamics. IEEE Trans Automat Control 54(12):2889–2894, art. no. 5332275

Wang H, Liu YH, Zhou D (2007) Dynamic visual tracking for manipulators using an uncalibrated fixed camera. IEEE Trans Robot 23(3):610–617

Wen JT, Bayard D (1988) New class of control laws for robotic manipulators Part 2. Adaptive case. Int J Control 47(5):1387–1406

Ziegler JG, Nichols NB (1942) Optimum settings for automatic controllers. ASME Trans 64:759–768