Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations, nonlinear dynamics, and non-convex constraints. In this work, we first introduce a continuous-time planning formulation with an average-value-at-risk constraint over the entire planning horizon. Then, we propose a sample-based approximation that unlocks an efficient and general-purpose algorithm for risk-averse trajectory optimization. We prove that the method is asymptotically optimal and derive finite-sample error bounds. Simulations demonstrate the high speed and reliability of the approach on problems with stochasticity in nonlinear dynamics, obstacle fields, interactions, and terrain parameters.

翻译：不确定性下的轨迹优化是机器人领域众多应用的基础。然而，现有方法在认知不确定性和偶然不确定性的来源分析、时空相关性、非线性动力学以及非凸约束的处理上存在局限。本文首先提出了一种连续时间规划框架，其中包含覆盖整个规划周期的平均风险价值约束。随后，我们提出了一种基于样本的近似方法，为风险规避轨迹优化提供了高效且通用的算法。我们证明了该方法的渐近最优性，并推导了有限样本误差界。仿真结果表明，该方法在处理非线性动力学、障碍场、交互作用及地形参数随机性问题时具有高速度和高可靠性。