Viability control for a class of underactuated systems

• Published in: Automatica (Oxford) Vol. 49; no. 1; pp. 17 - 29
• Main Authors: Panagou, Dimitra, Kyriakopoulos, Kostas J.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.01.2013; Elsevier
• Subjects: Adaptative systems; Applied sciences; Automation; Computer science; control theory; systems; Constrained control; Constraint satisfaction problems; Constraints; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Convergent control; Disturbance rejection; Effectiveness; Exact sciences and technology; Feedback control; Invariance; Laws; Nonholonomic control; Robot control; Robotics; Robust control; Trajectories; Underactuated robots; Viability; Robust control; Underactuated robots; Disturbance rejection; Convergent control; Robot control; Constrained control; Constraint satisfaction problems; Invariance; Nonholonomic control; State feedback; Control program; Feedback regulation; Constraint satisfaction; Control synthesis; State space; Robotics; Control constraint; Inequality constraint; Robustness; Bounded perturbation; State constraint; Multimodel control; Computer vision; Non holonomic system; State space method; Constrained optimization; Closed feedback; Underactuation; Motion control
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2012.09.002

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.