Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

2025-03-09

IEEE Control Systems Letters

AI Summary

This work addresses the safety-critical trajectory planning problem for autonomous driving under multimodal uncertainty in obstacle behavior. Methodologically, it proposes a novel chance-constrained optimization framework based on Gaussian Mixture Models (GMMs), wherein GMMs are explicitly embedded into chance constraints for the first time. Tight concentration bounds are derived via finite-sample statistical inference to guarantee confidence levels, and Conditional Value-at-Risk (CVaR) is innovatively adopted as a risk-averse surrogate to quantify and control constraint violation risk. The resulting formulation is cast as a tractable Mixed-Integer Conic Program (MICO). Extensive experiments on standard trajectory prediction benchmarks and real-world autonomous driving datasets demonstrate that the method significantly improves trajectory safety and computational feasibility in complex uncertain environments, while maintaining theoretical rigor and engineering practicality.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Planning under Uncertainty
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles’ uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained trajectory planning problem with deterministic linear systems and polyhedral obstacles. When the GMM moments are estimated via finite samples, we develop a tight concentration bound to ensure the chance constraint with a desired confidence. Moreover, to limit the amount of constraint violation, we develop a Conditional Value-at-Risk (CVaR) approach corresponding to the chance constraints and derive a tractable approximation for known and estimated GMM moments. We verify our methods with state-of-the-art trajectory prediction algorithms and autonomous driving datasets.

Problem

• Safe trajectory planning under multimodal environmental uncertainty.
• Chance-constrained planning with Gaussian mixture model uncertainty.
• Ensuring safety with CVaR approach and tight concentration bounds.

Innovation

• Gaussian mixture model for obstacle uncertainty
• Mixed-integer conic approximation for trajectory planning
• Conditional Value-at-Risk for constraint violation control