Real-time velocity feedback obstacle avoidance via complex variables and conformal mapping

A method for mobile robot motion planning is presented for both two- and three-dimensional robots. For the two-dimensional case, the algorithm is based on complex variable theory and conformal mapping. The method gives the robot the capability of avoiding obstacles more efficiently, smoothly, and at a constant curvilinear velocity. In order to establish the structure of the proposed velocity feedback obstacle avoidance scheme, several issues are addressed and successfully resolved. First, an analytical solution is derived for the case of circular obstacles. Second, the algorithm uses conformal mapping to establish the solution for an arbitrarily shaped obstacle based on the derived solution for a circular obstacle. The use of complex variable methodology with the objectives of exploiting the powerful technique of uniformal mapping constitutes the fundamental characteristic of the proposed technique. Third, by analogy, a solution to 3-D space-flying and subsea robots is also derived