Scenario-based Model Predictive Control for Path Planning and Obstacle Avoidance

Abstract

A basic problem in path planning is to regulate an appropriate path with the purpose of minimizing a cost function of interest under conditions of obstacle avoidance and model dynamics satisfaction. The cost function can be further minimized if some constraints are allowed to be violated with a guaranteed probability in some practical cases. However, very few results are reported about path planning with a preferred probability of constraints violation. In this paper, we investigate the scenario-based stochastic model predictive control (SCMPC) problem for path planning and obstacle avoidance. We find out the main reason that prevents the SCMPC approach to work for path planning is that the obstacles are commonly formulated as non-convex constraints, and a fundamental assumption in the field of SCMPC approach is the convexity of all the constraints. To address this problem, we propose a novel concept of candidate path, which is used to explicitly denote all the possible combinations of linear constraints. A conditional-scenario algorithm is accordingly developed that turns the original non-convex optimization problem to several convex subproblems. Simulation results verify the validity of the presented theories.