We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by incorporating chance constraints into the planning problem. This problem is not suitable for online optimization outright for arbitrary probability distributions. Hence, we sample from these chance constraints using an uncertainty model, to generate "scenarios", which translate the probabilistic constraints into deterministic ones. In practice, each scenario represents the collision constraint for a dynamic obstacle at the location of the sample. The number of theoretically required scenarios can be very large. Nevertheless, by exploiting the geometry of the workspace, we show how to prune most scenarios before optimization and we demonstrate how the reduced scenarios can still provide probabilistic guarantees on the safety of the motion plan. Since our approach is scenario based, we are able to handle arbitrary uncertainty distributions. We apply our method in a Model Predictive Contouring Control framework and demonstrate its benefits in simulations and experiments with a moving robot platform navigating among pedestrians, running in real-time.
翻译:我们提出一种基于优化的方法,在动态障碍(例如人类)的不确定因素下规划自主机器人的运动。我们的方法通过将机会限制纳入规划问题,在每一个时间点将碰撞的边际风险捆绑在每一个时间点上。这个问题不适合于在任意概率分布上直接进行在线优化。因此,我们用一种不确定模式对这些机会限制进行抽样抽样,将概率限制转化为确定因素。在实践中,每一种情景都代表着在抽样地点对动态障碍的碰撞限制。理论上需要的情景数量可能非常大。然而,通过利用工作空间的几何方法,我们展示如何在优化之前利用大多数情景,我们展示如何在缩小情景时仍能为运动计划的安全提供概率性保障。由于我们的方法是基于一种假设,我们能够处理任意不确定性分布。我们在模型预测性调控框架中运用了我们的方法,并展示了在行人之间实时移动机器人平台的模拟和实验中的好处。