Robot path planning and obstacle avoidance by means of potential function method

An important problem in robotics is to determine an obstacle avoidance control which transfers the system along a collision-free path among obstacles in the work space. Most algorithms which have been developed to solve this problem are based on a mapping of the given problem into a finite state space which always resulted in a problem which can be solved by a computer but have a high computational complexity. Certain previously developed algorithms worked directly with continuous problem space and are called continuum algorithms. These algorithms were relatively unsophisticated when compared to the continuous algorithms. This observation served as a motivation for the research reported here, in which it was sought to provide continuum algorithms with a more rigorous theoretical base. The main result of this work is the development of a real-valued function which is denoted by the symbol $\Omega$ and called Omega, which characterizes the proximal relationship of two non-point convex bodies. This function is different from similar functions reported previously in that it also provides useful information when the sets under consideration intersect. In this thesis, the need for such a function is established, and certain computationally useful properties of the developed function are proven. These result are subsequently used in a path-planning algorithm based on the use of the $\Omega$ function and the Potential Function approach. Results of this algorithm are presented and compared with those of previously developed algorithms.