Posture Stabilization of a Unicycle Mobile Robot — Two Control Approaches

Abstract

State feedback control issues for nonholonomic systems are still very challenging for control researchers. Among the group of nonholonomic systems one can number wheeled mobile vehicles, manipulators with nonholonomic gears, free-floating robots, underwater vessels, nonholonomic manipulator’s grippers, dynamically balanced hopping robots and others [4, 10, 15]. Difficulties in designing effective stabilizers arise from nonintegrable kinematic constraints imposed on system evolution. These constraints impose restriction on admissible velocities of controlled dynamic systems, preserving however their controllability. Moreover, lower dimensionality of the control space U ⊂ ℝ^m in comparison to the configuration space Q ⊂ ℝⁿ (n > m) causes difficulties in control design, especially for stabilization task problems [5]. Despite the problems mentioned, many different feedback control strategies for nonholonomic kinematics in automatics and robotics literature have been proposed - see for example [7], [18] or [8]. Still, some important problems, like robustness to control signals limitations existance, intuitive contoller parameter tunning and good control quality during transient stage seem to remain open issues and involve further research. In this paper two different stabilization approaches to the mentioned problems, with alternative solution in comparison to existing strategies, are described. The presented approaches are applied to derive two stabilizers to solve the stabilization task for a unicycle mobile robot, taking into account control limitations.