Robotics: Science and Systems XVI

Collision Probabilities for Continuous-Time Systems Without Sampling

Kristoffer Frey, Ted Steiner, Jonathan How


Demand for high-performance, robust, and safe autonomous systems has grown substantially in recent years. These objectives motivate the desire for efficient risk estimation that can be embedded in core decision-making tasks such as motion planning. On one hand, Monte-Carlo (MC) and other sampling-based techniques provide accurate solutions for a wide variety of motion models but are cumbersome in the context of continuous optimization. On the other hand, “direct” approximations aim to compute (or upper-bound) the failure probability as a smooth function of the decision variables, and thus are convenient for optimization. However, existing direct approaches fundamentally assume discrete-time dynamics and can perform unpredictably when applied to continuous-time systems ubiquitous in the real world, often manifesting as severe conservatism. State-of-the-art attempts to address this within a conventional discrete-time framework require additional Gaussianity approximations that ultimately produce inconsistency of their own. In this paper we take a fundamentally different approach, deriving a risk approximation framework directly in continuous time and producing a lightweight estimate that actually converges as the underlying discretization is refined. Our approximation is shown to significantly outperform state-of-the-art techniques in replicating the MC estimate while maintaining the functional and computational benefits of a direct method. This enables robust, risk-aware, continuous motion-planning for a broad class of nonlinear, partially-observable systems.



    AUTHOR    = {Kristoffer Frey AND Ted Steiner AND Jonathan How}, 
    TITLE     = {{Collision Probabilities for Continuous-Time Systems Without Sampling}}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2020}, 
    ADDRESS   = {Corvalis, Oregon, USA}, 
    MONTH     = {July}, 
    DOI       = {10.15607/RSS.2020.XVI.019}