Planning and control of a nonholonomic unicycle using ring shaped local potential fields

Abstract

Existing approaches for control of mobile robots using potential theory emphasize construction of local minimum free navigation functions in the configuration space. This is generally analytically complex and fails when nonholonomic constraints are introduced for a finite sized mobile robot. This paper approaches the issue by decoupling the problem into two parts: (1) generating a non-analytical local minimum free navigation function based on the workspace obstacles. (2) Trapping the nonholonomic unicycle in a local virtual potential field and then moving this local field along the path generated in the first step. This results in the trapped robot following the generated path. The emphasis here is on following a geometric path. No explicit parameterization of this path to a time-trajectory is done. Convergence and stability issues due to the presence of nonholonomic constraints are addressed. Simulation and experimental results are provided.