On motion planning and feedback control of nonholonomic dynamic systems with applications to attitude control of multibody spacecraft.

Abstract

The dissertation contributes new results in three related areas: motion planning for noncatastatic nonholonomic control systems, feedback stabilization of nonholonomic control systems and attitude control of multibody spacecraft by joint actuators. Nonholonomic noncatastatic control systems model controlled mechanical systems with affine velocity constraints, including a drift term, that cannot be reduced to equivalent purely geometric constraints. This class of inherently nonlinear control systems can also arise in modelling mechanical systems with symmetries that result in conservation laws, e.g. for multibody spacecraft for which the angular momentum is a conserved quantity and is nonzero. In the dissertation, motion planning strategies for noncatastatic nonholonomic control systems are developed. These strategies rely on the use of high frequency periodic inputs and the theory of averaging to reduce the problem to a finite-dimensional root-finding problem. Two new techniques for stabilization of nonholonomic control systems are developed. The first technique provides switched mode time-invariant feedback controllers which combine a discrete-event supervisor and low-level continuous-time feedback controllers. The supervisor accomplishes switchings between the low level feedback controllers to achieve global finite-time convergence of the states to the origin. The second technique provides hybrid time-varying controllers which combine continuous-time and discrete-time features. These controllers operate by switching at discrete time instants between time-periodic functions to achieve stabilization of equilibria or trajectories of nonholonomic control systems. These motion planning and stabilization results are instrumental for attitude control of multibody spacecraft by joint internal actuators, which are capable of changing the shape of the spacecraft but do not change the spacecraft's angular momentum. It is demonstrated that the effect of high frequency small amplitude periodic joint motions can be made equivalent to that of an "external" torque acting on the multibody spacecraft in the locked rigid body shape. Based on this conclusion, joint actuation strategies for reconfiguring and performing various exact tracking and pointing maneuvers for multibody spacecraft are developed. Feedback laws which achieve stabilization of desired equilibria or asymptotic tracking of desired trajectories for multibody spacecraft are developed.