Non-Gaussian Chance-Constrained Trajectory Planning for Autonomous Vehicles Under Agent Uncertainty

Wang, Allen; Jasour, Ashkan; Williams, Brian · 2020 · OpenAlex-citations

DOI: 10.1109/lra.2020.3010755

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Summary

This paper addresses the challenge of safe trajectory planning for autonomous vehicles in the presence of uncertain agent behavior. The authors identify agent uncertainty as the primary source of risk, noting that modern behavior prediction systems often generate complex, non-Gaussian, and multi-modal distributions of future agent positions. Existing chance-constrained planning methods are limited because they either assume Gaussian uncertainty, restrict constraints to linear forms, or rely on computationally intractable sampling techniques. To bridge this gap, the paper presents a methodology for enforcing chance constraints defined by polynomials against mixture models of non-Gaussian distributions, enabling efficient online planning. The proposed approach utilizes statistical moments and concentration inequalities to upper-bound the probability of constraint violation. The authors define risk by modeling agents and the ego vehicle with collision ellipsoids and circles, ensuring that the probability of the agent’s center entering the ego vehicle’s scaled collision ellipsoid remains below a specified threshold. By leveraging the linearity of expectation, the method expresses the moments of polynomial functions of random vectors in closed form using the moments of the underlying distributions. For mixture models, the authors prove that applying concentration inequalities (such as Cantelli’s, Vysochanskij-Petunin, or Gauss inequalities) to individual mixture components yields tighter risk bounds than applying them to the aggregate mixture. To facilitate implementation, the authors developed a Python package, *AlgebraicMoments*, which uses symbolic algebra to generate these bounds and corresponding code. Experimental results demonstrate that the resulting optimization problem can be solved efficiently using state-of-the-art nonlinear programming solvers. The method allows for trajectory planning with horizons of up to five seconds at speeds suitable for online use. The formulation accounts for the physical sizes of both the ego vehicle and agents, avoiding the unrealistic point-mass assumptions common in prior work. By relying only on statistical moments, the approach is applicable to a wide range of prediction distributions, including those generated by deep neural networks, without requiring explicit sampling or restrictive Gaussian assumptions. The significance of this work lies in its ability to handle realistic, non-Gaussian uncertainty in autonomous driving scenarios while maintaining computational tractability. It extends the state-of-the-art by generalizing chance-constrained planning from linear constraints and unimodal distributions to polynomial constraints and mixture models. This enables safer and more robust trajectory planning in complex environments where agent behavior is inherently multi-modal and bounded by physical laws, addressing a critical limitation in current autonomous vehicle safety systems.

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