Obstacle avoidance in Rn based on artificial harmonic potential fields

The artificial potential field method is frequently employed for obstacle avoidance both of mobile robots and of manipulator arms. This paper extends previous results for planar problems to the general n-dimensional case. The complexity is reduced by projecting the n-dimensional workspace onto a 2D subspace called operation plane. Furthermore, only the closest obstacles are taken into account when designing the artificial potential field. Still, global convergence is achieved. The methodology is illustrated with several numerical examples