Distribution-Transfer Safe-Horizon MPC under Mode Uncertainty

2026-10-05

AI Summary

This study addresses the vulnerability of scenario model predictive control (MPC) to mode uncertainty under distribution mismatch, which invalidates safety certificates. To handle switching dynamic obstacles, this work constructs confidence sets for mode laws and derives multiplicative dominance bounds. It proposes a Safe-Horizon MPC framework incorporating Wasserstein geometry-based regularized probability redistribution and danger-biased sampling strategies. The primary contributions include explicitly quantifying the additional conservatism cost incurred by distributional shifts, establishing robustly safe collision risk certificates, and revealing the multiplicative conservatism characteristics of transfer factors in multi-obstacle scenarios.

Abstract

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

Problem

• Scenario-based MPC
• distribution mismatch
• mode uncertainty
• chance-constrained motion planning
• Safe-Horizon MPC

Innovation

• Scenario-based MPC
• Distribution mismatch
• Wasserstein geometry
• Collision-risk certificate
• Mode uncertainty