发表机构
Brown University（布朗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对基于场景的MPC在分布失配下的问题，提出一种安全时域MPC方法，通过构建置信集和乘法支配界转移碰撞风险证书，并利用Wasserstein几何和碰撞风险替代函数优化采样，量化额外收紧并揭示组合保守性。
AI 中文摘要
基于场景的模型预测控制（MPC）是一种有吸引力的机会约束运动规划策略，它通过有限集的采样场景来近似不确定性。作为一种基于采样的方法，基于场景的MPC对分布失配敏感。我们在安全时域模型预测控制（SH-MPC）的背景下解决这个问题，其中障碍物由切换动态模式控制。从有限的模式观测中，我们为未知的分类模式分布构建一个置信集，并推导出一个乘法支配界，该界将安全时域碰撞风险证书从选定的场景采样分布转移到置信集中的每个分布。使用Wasserstein几何根据模式诱导轨迹预测的相似性来正则化模式间的概率重新分配，而碰撞风险替代函数则使采样偏向危险模式。所得的证书明确量化了分布失配下所需的额外收紧，并揭示了当多个障碍物的转移因子组合时产生的乘法保守性。
英文摘要
Scenario-based MPC is an attractive strategy for chance-constrained motion planning that approximates uncertainty via a finite set of sampled scenarios. As a sampling-based method, scenario-based MPC is sensitive to distribution mismatch. We address this problem in the context of Safe-Horizon Model Predictive Control (SH-MPC) with obstacles governed by switching dynamic modes. From finite mode observations, we construct a confidence set for the unknown categorical mode law and derive a multiplicative domination bound that transfers a Safe-Horizon collision-risk certificate from a selected scenario-sampling distribution to every law in the confidence set. Wasserstein geometry is used to regularize probability reallocation among modes according to the similarity of their induced trajectory predictions, while a collision-risk surrogate biases sampling toward dangerous modes. The resulting certificate explicitly quantifies the additional tightening required under distribution mismatch and exposes the multiplicative conservatism that arises when several obstacle-wise transfer factors are combined
