Boundary-aware value function generation for safe stochastic motion planning

INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH(2024)

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Abstract
Navigation safety is critical for many autonomous systems such as self-driving vehicles in an urban environment. It requires an explicit consideration of boundary constraints that describe the borders of any infeasible, non-navigable, or unsafe regions. We propose a principled boundary-aware safe stochastic planning framework with promising results. Our method generates a value function that can strictly distinguish the state values between free (safe) and non-navigable (boundary) spaces in the continuous state, naturally leading to a safe boundary-aware policy. At the core of our solution lies a seamless integration of finite elements and kernel-based functions, where the finite elements allow us to characterize safety-critical states' borders accurately, and the kernel-based function speeds up computation for the non-safety-critical states. The proposed method was evaluated through extensive simulations and demonstrated safe navigation behaviors in mobile navigation tasks. Additionally, we demonstrate that our approach can maneuver safely and efficiently in cluttered real-world environments using a ground vehicle with strong external disturbances, such as navigating on a slippery floor and against external human intervention.
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Key words
Autonomous navigation,motion planning and control,diffusion Markov decision process,value function,finite elements methods,kernels,second order HJB equation
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