Title: The Convex Feasible Set Algorithm for Real Time Optimization in Motion Planning,
Abstract: With the development of robotics, there are growing needs for real time
motion planning. However, due to obstacles in the environment, the planning
problem is highly non-convex, which makes it difficult to achieve real time
computation using existing non-convex optimization algorithms. This paper
introduces the convex feasible set algorithm (CFS) which is a fast algorithm
for non-convex optimization problems that have convex costs and non-convex
constraints. The idea is to find a convex feasible set for the original problem
and iteratively solve a sequence of subproblems using the convex constraints.
The feasibility and the convergence of the proposed algorithm are proved in the
paper. The application of this method on motion planning for mobile robots is
discussed. The simulations demonstrate the effectiveness of the proposed
algorithm.