Nonlinear control of a class of underactuated systems

A theoretical framework is established for the dynamics and control of underactuated systems, defined as systems which have fewer inputs than degrees of freedom. Control system formulation of underactuated systems is addressed and the class of second-order nonholonomic systems is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results.

[1]  H. Sussmann.  Subanalytic sets and feedback control , 1979 .

[2]  Ilya Kolmanovsky,et al.  Hybrid feedback stabilization of rotational–translational actuator (RTAC) system , 1998 .

[3]  N. H. McClamroch,et al.  A hybrid switched mode control approach for V/STOL flight control problems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[4]  Mark W. Spong,et al.  The swing up control problem for the Acrobot , 1995 .

[5]  J. Baillieul.  Kinematically redundant robots with flexible components , 1993, IEEE Control Systems.

[6]  H. Sussmann.  A general theorem on local controllability , 1987 .

[7]  K. Y. Wichlund,et al.  Control of Vehicles with Second-Order , 1995 .

[8]  Giuseppe Oriolo,et al.  Dynamic mobility of redundant robots using end-effector commands , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[9]  Giuseppe Oriolo,et al.  Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[10]  M. Reyhanoglu.  Control and stabilization of an underactuated surface vessel , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[11]  Mark W. Spong,et al.  Energy Based Control of a Class of Underactuated Mechanical Systems , 1996 .

[12]  S. Shankar Sastry,et al.  Nonlinear control design for slightly non-minimum phase systems: Application to V/STOL aircraft , 1992, Autom..

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

[14]  A. Bloch,et al.  Control and stabilization of nonholonomic dynamic systems , 1992 .

[15]  Dennis S. Bernstein,et al.  Design of a rotational actuator for global stabilization of translational motion , 1994 .

[16]  R. W. Brockett,et al.  Asymptotic stability and feed back stabilization , 1983 .

[17]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .