Dynamical feedback control of robotic manipulators with joint flexibility

Dynamic feedback control strategies are proposed for the asymptotic stabilization and asymptotic output tracking problems, associated with the operation of flexible joint manipulators. Smooth dynamical linearizing feedback controllers, as well as dynamical sliding mode regulators, are derived within the context of M. Fliess's (1989) generalized observability canonical form (GOCF). The GOCF is obtained by means of a state elimination procedure, carried out on the system of differential equations describing the manipulator dynamics. The remarkable feature of this new approach lies in the fact that a truly effective smoothing of the sliding mode controlled responses is possible while substantially reducing the chattering in the control input torque. Simulation examples are given that illustrate the performance of the proposed controllers. >

[1]  P. Lischinsky-Arenas,et al.  Differential algebraic approach in non-linear dynamical compensator design for d.c.-to-d.c. power converters , 1991 .

[2]  Michel Fliess,et al.  State-Variable Representation Revisited, Application to Some Control Problems , 1990 .

[3]  H. Sira-Ramirez.  The differential algebraic approach in nonlinear dynamical feedback controlled landing maneuvers , 1992 .

[4]  Alberto Isidori,et al.  An Application of Nonlinear Model Matching to the Dynamic Control of Robot Arm with Elastic Joints , 1985 .

[5]  Michel Fliess,et al.  Discontinuous predictive control, inversion and singularities. Application to a heat exchanger , 1990 .

[6]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

[7]  H. Sira-Ramirez,et al.  Nonlinear variable structure systems in sliding mode: the general case , 1989 .

[8]  M. Fliess,et al.  What the Kalman state variable representation is good for , 1990, 29th IEEE Conference on Decision and Control.

[9]  Mark W. Spong,et al.  Invariant manifolds and their application to robot manipulators with flexible joints , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[10]  M. Fliess,et al.  Généralisation non linéaire de la forme canonique de commande et linéarisation par bouclage , 1989 .

[11]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[12]  H. Sira-Ramírez.  Structure at infinity, zero dynamics and normal forms of systems undergoing sliding motions , 1990 .

[13]  S. Abu el Ata-Doss,et al.  Nonlinear Predictive Control by Inversion , 1989 .

[14]  P. Kokotovic,et al.  Feedback linearization of a flexible manipulator near its rigid body manifold , 1985 .

[15]  Riccardo Marino,et al.  Nonlinear control techniques for flexible joint manipulators: A single link case study , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[16]  A. Isidori,et al.  A frequency domain philosophy for nonlinear systems, with applications to stabilization and to adaptive control , 1984, The 23rd IEEE Conference on Decision and Control.

[17]  Jessy W. Grizzle,et al.  Rank invariants of nonlinear systems , 1989 .

[18]  Sette Diop,et al.  Elimination in control theory , 1991, Math. Control. Signals Syst..

[19]  Alessandro De Luca.  Dynamic control of robots with joint elasticity , 1988, ICRA.

[20]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[21]  Martin Hasler,et al.  Questioning the Classic State-Space Description Via Circuit Examples , 1990 .

[22]  Petar V. Kokotovic,et al.  An integral manifold approach to the feedback control of flexible joint robots , 1987, IEEE J. Robotics Autom..

[23]  S. Ahmad,et al.  Pulse width modulated control of robotic manipulators , 1990, 29th IEEE Conference on Decision and Control.

[24]  Michel Fliess,et al.  Generalized controller canonical form for linear and nonlinear dynamics , 1990 .

[25]  Michel Fliess,et al.  Nonlinear control theory and differential algebra , 1988 .

[26]  K. Khorasani.  Nonlinear feedback control of flexible joint manipulators: a single link case study , 1990 .

[27]  M. Fliess,et al.  Vers une stabilisation non linéaire discontinue , 1990 .

[28]  F. Mrad,et al.  Adaptive control of flexible joint robots with stability in the sense of Lyapunov , 1990, 29th IEEE Conference on Decision and Control.

[29]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[30]  M. Spong.  Modeling and Control of Elastic Joint Robots , 1987 .

[31]  Shaheen Ahmad,et al.  Control of industrial robots with flexible joints , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[32]  P. Kokotovic,et al.  Feedback linearization in the presence of uncertainties , 1988 .

[33]  Mark W. Spong,et al.  Control of Flexible Joint Robots: A Survey , 1990 .

[34]  Martin J. Corless,et al.  Control of uncertain systems with unmodeled actuator and sensor dynamics and incomplete state information , 1989, IEEE Trans. Syst. Man Cybern..