Goal-Reaching Trajectory Design Near Danger with Piecewise Affine Reach-avoid Computation
CoRR(2024)
摘要
Autonomous mobile robots must maintain safety, but should not sacrifice
performance, leading to the classical reach-avoid problem. This paper seeks to
compute trajectory plans for which a robot is guaranteed to reach a goal and
avoid obstacles in the specific near-danger case that the obstacles and goal
are near each other. The proposed method builds off of a common approach of
using a simplified planning model to generate plans, which are then tracked
using a high-fidelity tracking model and controller. Existing safe planning
approaches use reachability analysis to overapproximate the error between these
models, but this introduces additional numerical approximation error and
thereby conservativeness that prevents goal-reaching. The present work instead
proposes a Piecewise Affine Reach-avoid Computation (PARC) method to tightly
approximate the reachable set of the planning model. With PARC, the main source
of conservativeness is the model mismatch, which can be mitigated by careful
controller and planning model design. The utility of this method is
demonstrated through extensive numerical experiments in which PARC outperforms
state-of-the-art reach-avoid methods in near-danger goal-reaching. Furthermore,
in a simulated demonstration, PARC enables the generation of provably-safe
extreme vehicle dynamics drift parking maneuvers.
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