The Secant Method: Global Trajectory Planning With Variable Radius, Solid Obstacles

Artificial Potential Field (APF) theory is a unique branch of robotic path planning, which could be capable of handling the need for high dimensional robotic obstacle avoidance. However, APF theories have general performance issues which often make them undesirable in application. This research analyzes the Secant Approach; an algorithm developed to follow the APF style of path planning, but which has guaranteed convergence and obstacle avoidance properties in n-dimensional space. Using a unique potential function, the Secant Approach can guarantee a global minimum at the target while provably eliminating local minimums at other locations. Also, a control scheme has been developed which has guaranteed convergence properties. The Secant Approach is therefore capable of guiding various forms of robotic applications to target positions in n-dimensional space, making the theory a powerful path planning tool. This analysis examines the structure of the Secant Approach and extends the theory to include variable radius, solid obstacles.