Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty
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.