Nonholonomic Path Planning Using Harmonic Functions
Christopher I. Connolly, Roderic A. Grupen · 1994
A method is presented for planning obstacle-avoiding paths for a system which exhibits nonholonomic constraints. The method is based on the use of harmonic functions. Linear constraints on the velocity of a nonholonomic system can be directly expressed as Neumann boundary conditions for a harmonic function. Such boundary conditions are easily represented in a resistive network. The resulting potential represents an integration of nonholonomic constraints over an admissible subset of configuration space. The method is applied to path planning for simple wheeled vehicles. 1 Introduction This paper draws on the relationship between harmonic functions and resistive networks to propose a new method for planning the motion of nonholonomic systems. Simple nonholonomic constraints [1] restrict the velocity of mechanical systems to a linear subspace of their configuration space. These constraints bear a resemblance to the Neumann boundary condition for harmonic functions. Although nonho...