无需分布假设，实现非高斯系统的安全轨迹优化与控制。
Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems
- 用共形推断构建动态置信集，结合收缩条件与扰动影响。
- 有限样本下获得非发散的统计保证，可处理任意参考轨迹。
- 适合用于神经网络等学习型控制器的安全验证场景。
本文提出一种针对离散时间、非线性、非高斯随机系统的分布无关鲁棒轨迹优化与控制新方法，可对闭环系统满足机会约束提供闭环保证。该框架利用共形推断生成围绕任意参考轨迹的闭环动态覆盖置信集，通过构造联合非一致性评分，量化收缩（即增量稳定性）条件的有效性以及外部随机扰动对闭环动态的影响，且无需任何分布假设。通过适当的约束收紧，机会约束可转化为对参考轨迹的可计算、统计有效的确定性约束。这为基于学习的运动规划器和控制器（如采用神经收缩度量者）在安全关键实际应用中的使用与验证提供了正式路径。值得注意的是，我们的统计保证是非发散的，仅需有限样本即可计算，无需过度保守的结构先验。我们在数值仿真与硬件实验中验证了该方法在设计安全且动态可行轨迹方面的有效性。
原文摘要 · Abstract (English)
This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework employs conformal inference to generate coverage-based confidence sets for the closed-loop dynamics around arbitrary reference trajectories, by constructing a joint nonconformity score to quantify both the validity of contraction (i.e., incremental stability) conditions and the impact of external stochastic disturbance on the closed-loop dynamics, without any distributional assumptions. Via appropriate constraint tightening, chance constraints can be reformulated into tractable, statistically valid deterministic constraints on the reference trajectories. This enables a formal pathway to leverage and validate learning-based motion planners and controllers, such as those with neural contraction metrics, in safety-critical real-world applications. Notably, our statistical guarantees are non-diverging and can be computed with finite samples of the underlying uncertainty, without overly conservative structural priors. We demonstrate our approach in motion planning problems for designing safe, dynamically feasible trajectories in both numerical simulation and hardware experiments.
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