A hybrid design for robot path planning in the presence of obstacles

A method combining the tools of combinatorics and optimal control theory is presented to solve the path-planning problem. Initially, a combinatorial problem is solved to identify collision-free paths originally designed for a point object. Then the problem of moving the actual object through the safe paths for the point object is posed as an optimal control problem and is solved using a numerical technique involving finite-dimensional optimization. Some of the constraints to the optimization problem are in the form of inequalities, resulting in nondifferentiable expression when augmented with the performance index. Because of this, the R. Hooke and T.A. Jeeves method (1961), which is computationally quite prohibitive, has been adopted. To overcome this burden, at least partially, a method has been introduced whereby several variables appearing in the optimization are grouped into aggregate quantities, thus reducing the number of actual variables used in the iterations. 2-D and 3-D examples illustrate the applicability of the proposed hybrid design