Chance-Constrained Trajectory Optimization for Automatic Parking Based on Conservative Approximation

In this article, the optimal parking trajectory planning problem with chance constraints is considered. A conservative approximation-based method is presented to handle the chance constraints. Based on a designed parametric continuous function, the probabilistic constraints are replaced by the ones with explicit expression and the original chance-constrained optimization problem is approximated by a nonlinear programming problem. It is proved that the feasible set of this approximation problem is a subset of the original feasible set and converges to it. Moreover, the cluster point of the optimal solutions obtained by solving a sequence of approximation problems is shown to be the optimal solution of the original problem. Numerical results are presented to verify the effectiveness and conservatism of using the proposed approach to solve the chance-constrained optimal parking trajectory planning problem. Comparative simulations are also conducted, showing that the approximation problem is enough to reflect the actual situation in terms of the optimal maneuver time.