A fuzzy approach to discrete and continuous optimizations in path planning

This paper outlines a fuzzy formulation and its solutions for a path-planning problem. In this fuzzy approach, a workspace can be either a finite or infinite collection of discrete points with each representing a fuzzy set. The path-planning problem is formulated as a fuzzy optimization problem where the cost to be minimize representing the length of the path connecting two fuzzy sets representing the source and destination. There are two approaches to treating obstacles: formulating the fuzzy membership function of the fuzzy sets representing the area occupied by obstacles into the constraints, and formulating the fuzzy cost function with stiff penalty in using these fuzzy sets representing the area occupied by obstacles. Solutions are derived and numerical simulations are presented to verify the theoretical results.