The Convex Feasible Set Algorithm for Real Time Optimization in Motion Planning
This addresses the need for faster motion planning in robotics, though it appears incremental as it builds on existing optimization methods for non-convex constraints.
The paper tackles the challenge of real-time motion planning in robotics by introducing the Convex Feasible Set (CFS) algorithm, which efficiently solves non-convex optimization problems with convex costs and non-convex constraints, and simulations demonstrate its effectiveness.
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.