[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82804-en":3,"doc-seo-82804-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82804,4398048950312,"Violet","https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908",8,"Research & Report","GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance","Optimization-based local planning and control need high-rate evaluation of collision-avoidance constraints over a prediction horizon, yet obstacle-dense settings make these constraints computationally dominant. A geometry-exact Polygonal Signed Distance Function (PSDF) is introduced for convex polygonal robot footprints versus obstacles defined by boundary edges. The weight-free, branch-free tensor pipeline enables batched GPU execution and automatic differentiation. PSDF is integrated into model predictive control via real-time sequential quadratic programming iterations, producing a PSDF-embedded MPC with CPU/GPU separation. Benchmarks and navigation experiments confirm real-time feasibility and robust avoidance in dense polygonal environments.","GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance  \nTaekwon Ga and Jongeun Choi  \narXiv :2607 .043 10v 1 [ cs .RO] 5 Jul 2026  \nAbstract—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 solvesa 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.  \nNote to Practitioners—Mobile robots and automated vehicles often must navigate narrow, obstacle-dense spaces while computing collision-avoidance actions in real time. In these environments, costmaps, distance transforms, or simple primitives such as circles, ellipses, and boxes may shrink the feasible space or miss boundary details. This conservatism can reduce mobilerobot traversability even when a safe trajectory exists. The proposed controller addresses this issue by using the PSDF to evaluate signed-distance between a convex polygonal robot footprint and an obstacle edge set. The edge set can be generated by any detection module matched to the operating environment and sensor configuration. In the experiments, it was obtained from 2D bounding boxes or from safety-inflated rectangles produced by 2D projection and line fitting of 3D LiDAR point clouds. The key practical point is that PSDF-MPC enables predictive control to handle richer polygonal obstacle descriptions without introducing obstacle-dependent decision variables, since additional obstacle edges increase only the PSDF evaluation workload and do not enlarge the QP. The method still depends on the quality of edge extraction from perception. Future work should address dynamic obstacles, richer 3D geometry, and robustness to noisy or incomplete perception.  \nIndex Terms—Collision Avoidance, Signed Distance Function,  \nThe authors are with the School of Mechanical Engineering, Yonsei University, Seoul 03722, South Korea (e-mail: [taek111@yonsei.ac.kr](taek111@yonsei.ac.kr); jonge[unchoi@yonsei.ac.kr](unchoi@yonsei.ac.kr)).  \nCorresponding author: Jongeun Choi.  \nGPU Acceleration, Real-Time Optimization  \nI. INTRODUCTION  \nOptimization-based local planning and control methods, including nonlinear model predictive control (NMPC), have become a standard paradigm for autonomous mobile robots because they provide a unified framework for handling system dynamics, reference tracking, and operational constraints [1] . Collision avoidance is commonly formulated as a set of state constraints along the prediction horizon and must therefore be evaluated at high rate within each control cycle. In dense, obstacle-rich scenes, the cost of","cbCaiqunyeEc1UJH","https://ap.wps.com/l/cbCaiqunyeEc1UJH","pdf",10657011,1,13,"English","en",105,"# Abstract\n# Note to Practitioners\n# Index Terms\n# I. 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bottleneck does the proposed method address in collision avoidance?","Question",{"text":75,"@type":76},"In obstacle-dense environments, evaluating collision-avoidance constraint geometry at high rate can dominate the control-cycle runtime, becoming the primary computational bottleneck.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the Polygonal Signed Distance Function (PSDF) represent collision geometry?",{"text":80,"@type":76},"PSDF computes a geometry-exact signed distance between a convex polygonal robot footprint and obstacles represented by their boundary edges.",{"name":82,"@type":73,"acceptedAnswer":83},"How is PSDF integrated into real-time MPC while keeping optimization fast?",{"text":84,"@type":76},"PSDF is embedded into model predictive control by locally linearizing stage-wise safety constraints within a sequential quadratic programming–based real-time iteration scheme, while GPU evaluates batched PSDF values/gradients and the CPU solves a sparse QP whose 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