Branch-Stochastic Model Predictive Control for Motion Planning under Multi-Modal Uncertainty with Scenario Clustering
Authors: Zekun Xing, Ramkrishna Chaudhari, Marion Leibold, Dirk Wollherr, Martin Buss
Abstract
Motion planning for autonomous driving must account for multi-modal uncertainty in both the intentions and trajectories of surrounding vehicles. Handling uncertainty in a worst-case manner guarantees robustness but often leads to excessive conservatism. Stochastic Model Predictive Control (SMPC) reduces trajectory-level conservatism through chance constraints, yet remains conservative with respect to intention uncertainty since constraints must hold across all intentions. We present a novel combination of SMPC and the branching structure, enabling the planner to generate distinct trajectories for different possible intentions while maintaining safety under trajectory uncertainty. A novel scenario clustering is proposed to merge prediction scenarios based on high-level decision similarity, thereby ensuring real-time tractability. Furthermore, an adaptive branching-time computation postpones commitment to separate plans until intention uncertainty is sufficiently reduced. Simulation studies in challenging highway scenarios demonstrate that the proposed method improves safety, reduces conservatism, and achieves real-time computational performance.
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
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.
Autonomous vehicles must plan trajectories that satisfy a multitude of requirements on safety, passenger comfort, and compliance with traffic rules. However, in safety-critical scenarios, it is not always possible to satisfy all requirements simultaneously, necessitating their prioritization based on importance. At the same time, in these safety-critical scenarios, the uncertainty in trajectory predictions of the surrounding traffic, such as other vehicles and pedestrians, should be explicitly accounted for. In this work, we propose an uncertainty-aware trajectory planning framework that incorporates a predefined lexicographic ordering over Signal Temporal Logic (STL) specifications that stays valid under uncertainty. We implement this formulation with Model Predictive Path Integral (MPPI) control and we demonstrate the effectiveness of our method on simulation scenarios, showing that our framework efficiently handles conflicting objectives under realistic multi-modal uncertainty.