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.

翻译：基于安全走廊的轨迹优化（TO）为自主机器人无碰撞路径规划提供了一种有吸引力的方法，通过其凸优化公式实现全局最优性。安全走廊基于感知地图构建，然而非理想感知会引入不确定性，这在轨迹生成中很少被考虑。本文提出分布鲁棒安全走廊约束（DRSCCs）以考虑安全走廊的不确定性。随后，我们利用伯恩斯坦基多项式将DRSCCs集成到轨迹优化框架中。理论上，我们严格证明了包含DRSCCs的轨迹优化问题等价于一个计算高效的凸二次规划。与名义上的TO相比，我们的方法通过显著减少不确定性下的不可行运动来增强导航安全性。此外，所提方法通过两个机器人应用（微型无人机（UAV）和四足机器人Unitree A1）得到验证。