  Safe corridor-based Trajectory Optimization (TO) presents an appealing
approach for collision-free path planning of autonomous robots, offering global
optimality through its convex formulation. The safe corridor is constructed
based on the perceived map, however, the non-ideal perception induces
uncertainty, which is rarely considered in trajectory generation. In this
paper, we propose Distributionally Robust Safe Corridor Constraints (DRSCCs) to
consider the uncertainty of the safe corridor. Then, we integrate DRSCCs into
the trajectory optimization framework using Bernstein basis polynomials.
Theoretically, we rigorously prove that the trajectory optimization problem
incorporating DRSCCs is equivalent to a computationally efficient, convex
quadratic program. Compared to the nominal TO, our method enhances navigation
safety by significantly reducing the infeasible motions in presence of
uncertainty. Moreover, the proposed approach is validated through two robotic
applications, a micro Unmanned Aerial Vehicle (UAV) and a quadruped robot
Unitree A1.
