Distribution-Transfer Safe-Horizon MPC under Mode Uncertainty

Stephen Crawford; Nora Ayanian

cs.ROOct 5, 2026

Distribution-Transfer Safe-Horizon MPC under Mode Uncertainty

Authors: Stephen Crawford, Nora Ayanian

Organizations: Department of Computer Science, Brown University, Providence, RI, USA.

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

Figures & tables

Sampling law	$\zeta/\underline{\zeta}$	$\zeta$	Required $S$	$\Delta r$	$\Delta q_{\rm dang}$
Envelope optimum $q^{\rm env}$	1.000	1.573	1931	0.0149	-0.0356
Wasserstein min- $\zeta$ $q^{W}$	1.000	1.573	1931	0.0149	-0.0356
Nominal $\widehat{p}$	1.420	2.225	2901	0	0
Risk-aware $q^{\star}$	1.420	2.225	2901	0.0458	+0.0624

TABLE I : Sampling-law ablation for

M=5

g=100

, over 100 independent calibration instances. Here

\underline{\zeta}=\sum_{m}u_{m}

is the minimum attainable domination factor,

\Delta r=\langle q,r\rangle-\langle\widehat{p},r\rangle

, and

\Delta q_{\rm dang}

is the change in total probability assigned to dangerous modes relative to nominal sampling.

Fig. 1 : Held-out true-law validation. Solid curves show equal-seed-weighted mean violation estimates over 30 paired seeds; dotted curves show median pointwise 95% Clopper–Pearson upper endpoints from 1000 independent held-mode validation trajectories per returned decision.

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Safe motion planning in uncertain, time-varying environments is challenging because the safe region can change unpredictably across planning steps, often causing a loss of recursive feasibility. In this work, we present a Probabilistic Recursively Feasible Model Predictive Control (PRF-MPC) framework that guarantees recursive feasibility with a specified probability. We introduce properties that an ideal predictor should satisfy to ensure distributional consistency, and use these properties to derive closed-form expressions for the means and covariances of trajectories predicted at future time steps. Building on this analysis, we construct safety constraints that ensure, with high probability, that the current safe set is contained within the safe sets at future time steps, thereby probabilistically guaranteeing recursive feasibility. Simulation results on a lane-change scenario demonstrate that the proposed method significantly improves recursive feasibility.

Abstract

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