Fazal-ur-Rehman

Systems without drift, nonholonomic systems, controllability, Lie algebra, Lyapunov function

This paper presents a simple method for the construction of statedependent steering control law for nonholonomic control systems. The effectiveness of the method is tested on a fire truck model. The feedback controls are piece-wise constant and states dependent and the method is based on the construction of a cost function V which is the sum of two semi-positive definite functions V1 and V2, where V1 is the function of the first m state variables that can be steered along the given vector fields and V2 is the function of the remaining n − m state variables that can be steered along the missing Lie brackets. The values of the functions V1 and V2 allow the determination of a desired direction of system motion and permit to construct a sequence of control laws such that the sum of these functions decreases in an average sense. The individual functions are hence not restricted to decrease monotonically, but their oscillations are limited and coordinated in a way that guarantees convergence. The task of the control is to decay the nondifferentiable cost function along the controlled system trajectories only asymptotically. This approach does not necessitate the conversion of the system model into a “chained form, and thus does not rely on any special transformation techniques. The approach presented is general and can be employed to control a variety of mechanical systems with velocity constraints.

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