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
ζ/ζ
ζ
Required S
Δr
Δqdang
Envelope optimum qenv
1.000
1.573
1931
0.0149
-0.0356
Wasserstein min- ζqW
1.000
1.573
1931
0.0149
-0.0356
Nominal p
1.420
2.225
2901
0
0
Risk-aware q⋆
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 ζ=∑mum is the minimum attainable domination factor, Δr=⟨q,r⟩−⟨p,r⟩ , and Δqdang 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.
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.
Hyeontae Sung, Hyeongchan Ham, Junyoung Park +2
School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea · The SYCAMORE Lab, ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Switzerland
Sampling-Based Model-Predictive Control (MPC) algorithms are a flexible class of controllers used for navigation on a wide range of robotic systems. Historically, such approaches have lacked hard safety guarantees, a shortcoming which we remedy in this work by computing guaranteed reachable-set overapproximations online with a fast, interval-based pipeline. We show that our method achieves similar performance to a state-of-the-art reachability-based planner without the need for the expensive pre-computation step, and can be scaled to systems that are infeasible using existing approaches. Finally, we demonstrate that our technique reduces safety violations by over 99% in a racing simulation and successfully controls a model racecar on real hardware experiments without crashes.
We investigate interactive trajectory planning subject to uncertainty in the decisions of surrounding agents. To control the ego-agent, we aim to first learn the decision distribution and solve a Stochastic Model Predictive Control (SMPC) problem. To account for errors in the learned distribution, we show that it is possible to utilize Probably Approximately Correct (PAC) learning in combination with Distributionally Robust (DR) optimization to obtain a solution which accounts for the errors induced by the learning model. The results indicate that our PAC learning-based DR-MPC framework provides a method to interpolate between a robust MPC and an omnipotent SMPC, based on the available number of samples.
Erik Börve, Nikolce Murgovski, Morteza Haghir Chehreghani +1
Chalmers University of Technology, Chalmersgatan 4, 412 96 Göteborg, Sweden · Volvo Group Trucks Technology, Gropegårdsgatan 2, 417 15 Göteborg, Sweden