Viability control for a class of underactuated systems

This paper addresses the feedback control design for a class of nonholonomic systems which are subject to inequality state constraints defining a constrained (viability) set K. Based on concepts from viability theory, the necessary conditions for selecting viable controls for a nonholonomic system are given, so that system trajectories starting in K always remain in K. Furthermore, a class of state feedback control solutions for nonholonomic systems are redesigned by means of switching control, so that system trajectories starting in K converge to a goal set G in K, without ever leaving K. The proposed approach can be applied in various problems, whose objective can be recast as controlling a nonholonomic system so that the resulting trajectories remain forever in a subset K of the state space, until they converge into a goal (target) set G in K. The motion control for an underactuated marine vehicle in a constrained configuration set K is treated as a case study; the set K essentially describes the limited sensing area of a vision-based sensor system, and viable control laws which establish convergence to a goal set G in K are constructed. The robustness of the proposed control approach under a class of bounded external perturbations is also considered. The efficacy of the methodology is demonstrated through simulation results.