Guaranteeing persistent feasibility of model predictive motion planning for autonomous vehicles

Model predictive control (MFC) approach is prone to loss of feasibility due to the limited prediction horizon for decision making. For autonomous vehicle motion planning, many of detected obstacles, which are beyond the prediction horizon, cannot be considered in the instantaneous decisions, and late consideration of them may cause infeasibility. The conditions that guarantee persistent feasibility of a model predictive motion planning scheme are studied in this paper. Maintaining the system's states in a control invariant set of the system guarantees the persistent feasibility of the corresponding MPC scheme. Therefore, the persistent feasibility concern can be expressed as the problem of computing an effective control invariant set of the system and maintaining the system states inside it. In this paper, two approaches are presented to compute control invariant sets for the motion planning problem, the linearization-convexification approach and the brute-force search approach. The control invariant sets calculated via these two approaches are numerically analyzed and compared.