Probabilistically safe motion planning to avoid dynamic obstacles with uncertain motion patterns
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Probabilistically safe motion planning to avoid dynamic obstacles with uncertain motion patterns Georges S. Aoude · Brandon D. Luders · Joshua M. Joseph · Nicholas Roy · Jonathan P. How
Received: 1 August 2011 / Accepted: 4 April 2013 / Published online: 3 May 2013 © Springer Science+Business Media New York 2013
Abstract This paper presents a real-time path planning algorithm that guarantees probabilistic feasibility for autonomous robots with uncertain dynamics operating amidst one or more dynamic obstacles with uncertain motion patterns. Planning safe trajectories under such conditions requires both accurate prediction and proper integration of future obstacle behavior within the planner. Given that available observation data is limited, the motion model must provide generalizable predictions that satisfy dynamic and environmental constraints, a limitation of existing approaches. This work presents a novel solution, named RR-GP, which builds a learned motion pattern model by combining the flexibility of Gaussian processes (GP) with the efficiency of RRTElectronic supplementary material The online version of this article (doi:10.1007/s10514-013-9334-3) contains supplementary material, which is available to authorized users. G. S. Aoude (B)· B. D. Luders Massachusetts Institute of Technology, Room 41-105, 77 Massachusetts Avenue, Cambridge, MA, USA e-mail: [email protected] B. D. Luders e-mail: [email protected] J. M. Joseph Massachusetts Institute of Technology, Room 32-331, 77 Massachusetts Avenue, Cambridge, MA, USA e-mail: [email protected] N. Roy Massachusetts Institute of Technology, Room 33-315, 77 Massachusetts Avenue, Cambridge, MA, USA e-mail: [email protected] J. P. How Massachusetts Institute of Technology, Room 33-326, 77 Massachusetts Avenue, Cambridge, MA, USA e-mail: [email protected]
Reach, a sampling-based reachability computation. Obstacle trajectory GP predictions are conditioned on dynamically feasible paths identified from the reachability analysis, yielding more accurate predictions of future behavior. RR-GP predictions are integrated with a robust path planner, using chance-constrained RRT, to identify probabilistically feasible paths. Theoretical guarantees of probabilistic feasibility are shown for linear systems under Gaussian uncertainty; approximations for nonlinear dynamics and/or non-Gaussian uncertainty are also presented. Simulations demonstrate that, with this planner, an autonomous vehicle can safely navigate a complex environment in real-time while significantly reducing the risk of collisions with dynamic obstacles. Keywords Planning under uncertainty · Trajectory prediction · Gaussian processes
1 Introduction To operate safely in stochastic environments, it is crucial for agents to be able to plan in real-time in the presence of uncertainty. However, the nature of such environments often precludes the existence of guaranteed-safe, collisionfree paths. Therefore, this work considers probabilistically safe planning, in which paths must be able to satisfy all constraints with a user-mand
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