Probabilistic Recursively Feasible Motion Planning Under Uncertain Environments

2026-05-18

AI Summary

This work addresses the challenge of ensuring recursive feasibility in safe motion planning under uncertain and time-varying environments. The authors propose a Probabilistic Recursively Feasible Model Predictive Control (PRF-MPC) framework that, for the first time, provides rigorous probabilistic guarantees of recursive feasibility. The key innovation lies in introducing the notion of “distributional consistency,” which enables the construction of an ideal predictor and yields closed-form expressions for the mean and covariance of future trajectories. Building on this, the method designs probabilistic safety constraints that, with high probability, ensure the current safe set is contained within future safe sets. Simulations in a lane-changing scenario demonstrate that the approach significantly enhances recursive feasibility, validating its effectiveness and robustness in dynamic, uncertain environments.

Abstract

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.

Problem

• motion planning
• recursive feasibility
• uncertain environments
• probabilistic safety
• time-varying environments

Innovation

• Probabilistic Recursively Feasible MPC
• Recursive Feasibility
• Uncertain Environments
• Distributional Consistency
• Safety Constraints