Chance Constrained Mobile Robot Trajectory Optimization in Partially Known Environments

This paper studies a mobile robot trajectory optimization problem where the control path constraints are affected by stochastic parameters and the obstacle information is limited. Based on online measured data, an upper confidence bound (UCB) is designed such that the estimated obstacle regions are guaranteed to cover the real obstacles with a predefined probability, thus avoiding collisions. Using the proposed approach, the control path constraints are transformed into deterministic constraints using analytic approximations. By adjusting the parameters in the proposed approximation function, the feasible set of the approximate optimization problem converges to the real feasible set conservatively. Such a property leads to both feasibility and sub-optimality of the solution obtained by solving a deterministic optimization problem. Numerical results demonstrate that the designed UCB and approximation function are effective for trajectory optimization problems with control bounds and obstacle avoidance chance constraints. Comparative studies verified that the approximation function ensures the feasibility of the original chance constrained problem and reduces conservatism.