Interactive Trajectory Planning with Learning-based Distributionally Robust Model Predictive Control and Markov Systems

2026-05-08

AI Summary

This work addresses the challenge of decision uncertainty among surrounding agents in interactive trajectory planning by proposing a Probably Approximately Correct (PAC) learning-based Distributionally Robust Model Predictive Control (DR-MPC) framework. The approach integrates Markovian system modeling with stochastic optimization, explicitly accounting for both the learned distribution of agent behaviors and the associated learning error to achieve robustness against uncertainty. By innovatively combining PAC learning theory with distributionally robust optimization, the planner adaptively balances conservatism and performance based on the available sample size. Experimental results demonstrate that, under limited data, the proposed framework achieves a superior trade-off between robustness and performance, significantly outperforming conventional stochastic MPC and purely robust MPC methods.

Abstract

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.

Problem

• Interactive Trajectory Planning
• Decision Uncertainty
• Distributionally Robust Optimization
• Stochastic Model Predictive Control
• PAC Learning

Innovation

• Distributionally Robust Optimization
• PAC Learning
• Stochastic Model Predictive Control
• Interactive Trajectory Planning
• Markov Systems