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, general-purpose, and time-consistent 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技术中众多应用的基础。然而，现有方法在认知不确定性和偶然不确定性来源、时空相关性、非线性动力学以及非凸约束的推理方面存在局限。本研究首先引入了一种连续时间规划框架，在整个规划周期内施加了平均风险值约束。随后，我们提出了一种基于样本的近似方法，实现了高效、通用且时间一致的风险规避轨迹优化算法。我们证明了该方法具有渐近最优性，并推导出有限样本误差界。仿真结果验证了该方法在处理非线性动力学随机性、障碍场、交互作用及地形参数等问题时的高速性与可靠性。