{"ID":5937697,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-08T13:43:20.341700643Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04310","arxiv_id":"2607.04310","title":"GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2607.04310","url_pdf":"https://arxiv.org/pdf/2607.04310v1","authors":"[\"Taekwon Ga\",\"Jongeun Choi\"]","published":"2026-07-05T13:46:59Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false}