Robots will increasingly operate near humans that introduce uncertainties in the motion planning problem due to their complex nature. Typically, chance constraints are introduced in the planner to optimize performance while guaranteeing probabilistic safety. However, existing methods do not consider the actual probability of collision for the planned trajectory, but rather its marginalization, that is, the independent collision probabilities for each planning step and/or dynamic obstacle, resulting in conservative trajectories. To address this issue, we introduce a novel real-time capable method termed Safe Horizon MPC, that explicitly constrains the joint probability of collision with all obstacles over the duration of the motion plan. This is achieved by reformulating the chance-constrained planning problem using scenario optimization and predictive control. Our method is less conservative than state-of-the-art approaches, applicable to arbitrary probability distributions of the obstacles' trajectories, computationally tractable and scalable. We demonstrate our proposed approach using a mobile robot and an autonomous vehicle in an environment shared with humans.

翻译：机器人将越来越多地在人类附近运行，而人类因其复杂性质给运动规划问题引入了不确定性。通常，规划器中会引入机会约束，以在保证概率安全性的同时优化性能。然而，现有方法并未考虑规划轨迹的实际碰撞概率，而是考虑其边缘化，即每个规划步骤和/或动态障碍物的独立碰撞概率，从而导致轨迹过于保守。为解决这一问题，我们提出了一种新型实时方法，称为Safe Horizon MPC，该方法明确约束运动规划持续时间内与所有障碍物的联合碰撞概率。这是通过使用场景优化和预测控制重新表述机会约束规划问题来实现的。我们的方法相比现有技术更加宽松，适用于障碍物轨迹的任意概率分布，计算上易于处理且可扩展。我们使用移动机器人和自动驾驶车辆在与人类共享的环境中展示了所提出的方法。