Real-time obstacle avoidance using harmonic potential functions

The paper presents a solution of motion planning and control of mobile robot in a two-dimensional environment with elliptical static obstacle based on hydrodynamics description. Theoretical background refers to solution of Laplace equation using complex algebra. The method of designing complex potential with respect to stationary elliptical obstacle and stationary goal is formally shown. Next, the planning motion problem is extended assuming that the goal is moving. Then results of motion planning is used in order to design closed-loop control algorithms which is based on decoupling technique. Theoretical considerations are supported by numerical simulations illustrating example results of motion planning and control.