A new generic representation of the gravity vector in the rigid link robot dynamic model is proposed. We use this representation to design a linear state feedback regulator and show that the closed loop nonlinear system is globally asymptotically stable and exponentially stable in any closed ball. We exploit the fact that the gravity vector is the gradient of the potential function. We also consider robustness of the linear state feedback regulator to parameter uncertainty.
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Troch, I., Kopcek, P., and Desoyer, K.: Simplified models for robot control, in L. L. Basanez, G. Ferrate, and G. Siridis (eds),IFAC Robot Control (Syroco'85), 1985, pp. 31–35.
Neuman, C. and Murry, J.J.: Linearization and sensitivity functions of dynamic robot models,IEEE SMC 14(6) (Nov./Dec. 1984), 805–818.
Lin, C.-F.: Advanced controller design for robot arms,IEEE AC 29(4) (April 1984), 350–353.
Arimoto, S. and Miyazaki, F.: Asymptotic stability of feedback control laws for robot manipulators, in L. L. Basanez, G. Ferrate, and G. Siridis (eds),IFAC Robot Control (Syroco'85), 1985, pp. 221–226.
Lim, K. Y. and Eslami, M.: Adaptive controller designs for robot manipulator system using Lyapunov direct method,IEEE AC 30(12), (Dec. 1985), 1229–1233.
Lim, K. Y. and Eslami, M.: Robust adaptive controller designs for robot manipulator systems,IEEE J. Robotics and Automation 3(1) (1987), 54–66.
Lim, K. Y. and Eslami, M.: Adaptive controller designs for robot manipulator systems yielding reduced cartisian error,IEEE AC 32(2) (Feb. 1987), 184–187.
Hollerbach, J. M.: A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complixity,IEEE SMC 28 (Nov. 1980), 730–736.
Marino, R. and Nicosia, S.: Hamiltonian-Type Lyapunov functions,IEEE AC 28 (Nov. 1983), 1050–1056.
Fu, K. S., Gonzalez, R. C., and Lee, C. S. G.:Robotics Control Sensing, Vision and Intelligence, McGraw-Hill, New York, 1987.
Khalil, H. K.:Nonlinear Systems, Macmillan, 1992.
Rudin, W.:Principles of Mathematical Analysis, McGraw-Hill, New York, 1976.
Walcott, B. L. and Zak, S. H.: Combined observer-controller synthesis for uncertain dynamical systems with applications,IEEE SMC 18(1) (Jan./Feb. 1988), 88–104.
Denavit, J. and Hartenberg, R. S.: A kinematic notation for lowe pair mechanisms,J. Appl. Mech. 22 (1955), 215–221.
Spong, M. W. and Vidyasagar, M. V.:Robot Dynamics and Control, Wiley, New York, 1989.
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Abouelsoud, A.A., Sultan, M.A. & Hassan, M.F. Linear state feedback regulator for rigid link manipulators. J Intell Robot Syst 15, 291–305 (1996). https://doi.org/10.1007/BF00572264
- Rigid link manipulators
- state feedback
- point-to-point control
- exponential stability