Probabilistic Recursively Feasible Motion Planning Under Uncertain Environments

TL;DR

This paper introduces a probabilistic model predictive control framework that guarantees recursive feasibility in uncertain, dynamic environments by ensuring safety constraints hold with high probability.

Contribution

It develops a novel PRF-MPC method with closed-form trajectory predictions and probabilistic safety constraints to maintain recursive feasibility under uncertainty.

Findings

Significantly improves recursive feasibility in simulations.

Provides closed-form expressions for trajectory means and covariances.

Ensures safety constraints hold with high probability.

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.