In this paper, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method for limiting the risk of unsafety even when the true distribution of the obstacles' movements deviates, within an ambiguity set, from the empirical distribution obtained using a limited amount of sample data. By choosing the ambiguity set as a statistical ball with its radius measured by the Wasserstein metric, we achieve a probabilistic guarantee of the out-of-sample risk, evaluated using new sample data generated independently of the training data. To resolve the infinite-dimensionality issue inherent in the distributionally robust MPC problem, we reformulate it as a finite-dimensional nonlinear program using modern distributionally robust optimization techniques based on the Kantorovich duality principle. To find a globally optimal solution in the case of affine dynamics and output equations, a spatial branch-and-bound algorithm is designed using McCormick relaxation. The performance of the proposed method is demonstrated and analyzed through simulation studies using a nonlinear car-like vehicle model and a linearized quadrotor model.

中文翻译：

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Wasserstein 分布式鲁棒运动控制使用条件风险值避免碰撞

在本文中，当不确定性的真实概率分布未知时，为移动机器人考虑风险感知运动控制方案以避开随机移动的障碍物。我们提出了一种新的模型预测控制 (MPC) 方法，用于限制不安全风险，即使障碍物运动的真实分布在模糊集内偏离使用有限数量的样本数据获得的经验分布。通过选择模糊集作为一个统计球，其半径由 Wasserstein 度量测量，我们实现了样本外风险的概率保证，使用独立于训练数据生成的新样本数据进行评估。为了解决分布鲁棒 MPC 问题中固有的无限维问题，我们使用基于 Kantorovich 对偶原理的现代分布鲁棒优化技术将其重新表述为有限维非线性程序。为了在仿射动力学和输出方程的情况下找到全局最优解，使用 McCormick 松弛设计了空间分支定界算法。通过使用非线性汽车类车辆模型和线性化四旋翼模型的仿真研究，证明和分析了所提出方法的性能。