GPU高速化ポリゴン符号付き距離関数によるリアルタイム衝突回避
GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance
凸多角形ロボットと障害物境界間の幾何学的に正確な符号付き距離関数をGPUで並列計算し、モデル予測制御に組み込んでリアルタイム衝突回避を実現した。
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著者: Taekwon Ga, Jongeun Choi
分類: cs.RO
原文アブストラクト
Optimization-based local planning and control require high-rate collision-avoidance constraint evaluation over a prediction horizon. In obstacle-dense environments, where feasible space is limited and the constraints become increasingly complex, the computational workload often dominates the control-cycle runtime. The resulting bottleneck motivates collision-avoidance constraints that combine computational efficiency with geometric fidelity. The proposed Polygonal Signed Distance Function (PSDF) is a geometry-exact signed distance function between a convex polygonal robot footprint and obstacles represented by their boundary edges. It is implemented as a weight-free, branch-free tensorized geometric pipeline enabling batched GPU execution and automatic differentiation. The PSDF is embedded into model predictive control by locally linearizing the stage-wise safety constraints within a sequential quadratic programming-based real-time iteration scheme, yielding the PSDF-embedded model predictive controller (PSDF-MPC). The design separates CPU/GPU computation so that the GPU evaluates batched PSDF values and gradients while the CPU solves a sparse quadratic program whose dimension is determined by system dimensions and horizon length, not by obstacle features. Microbenchmarks show that PSDF scales favorably against signed-distance query baselines. Closed-loop simulated and real-world navigation experiments, including comparisons with optimization-based baselines, demonstrate that PSDF-MPC maintains real-time feasibility and robust collision avoidance in dense polygonal environments.
