Tracking control design for underactuated constrained systems

Abstract

An extension of a model-based tracking control strategy to underactuated systems is presented. Originally, it is designed for actuated systems that can perform tasks specified by equations of algebraic or differential constraints referred to as programmed, which may be nonintegrable. It is demonstrated that for both actuated and underactuated nonholonomically constrained systems one tracking control strategy can be designed. Systems we consider are nonholonomic because of constraints put on their motions as well as unactuated degrees of freedom. We detail an example, which illustrates the theory and demonstrates advantages of application of one tracking control strategy for actuated and underactuated constrained systems.

Quasi-coordinates based dynamics modeling and control design for nonholonomic systems

“…Transition from the Cartesian to joint coordinates requires the substitution of x = l 1 cos Θ 1 + l 2 cos(Θ 1 + Θ 2 ) and y = l 1 sin Θ 1 + l 2 sin(Θ 1 + Θ 2 ) [5].…”

“…Simulation is faster and no numerical stabilization of the constraint equations is needed. This reference model and the controller design may be compared to the analogous design done with the use of generalized coordinates in [5].…”

“…From the control theory perspective, a constraint concept, constraint sources and their classification are viewed in a different way than in analytical mechanics [4][5][6][7]. The reasons are as follows.…”

“…For wheeled robots other constraints, like the one that specifies an allowable value of the acceleration that prevents a robot wheel from slippage and mechanical shock during motion, have to be taken into account when a control strategy is designed [8]. A new group of constraints, which are tasks that can be specified by equations may be distinguished [4][5][6][7]. The source of these constraints is not in other bodies.…”

“…The above modeling procedure and control design are typical ways in which tasks are executed within nonlinear control theory framework. In [4][5][6][7] the programmed and dynamic constraints are included in the generalized programmed motion equations (GPME) derived in generalized coordinates.…”