[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85658-en":3,"doc-seo-85658-105":28,"detail-sidebar-cat-0-en-105":90},{"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":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},85658,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Fast Asymptotically Optimal Kinodynamic Planning via Vectorization","Sampling-based motion planners work well for robots with complex kinodynamic constraints and high-dimensional state spaces, yet achieving real-time performance remains difficult. The proposed work introduces PAKR, a massively parallel kinodynamic planner that uses JAX with the XLA compiler to obtain GPU acceleration via standard Python tooling, avoiding specialized CUDA coding. Combining the parallel planner with the AO-x meta-algorithm enables asymptotic optimality through fast iterative replanning, with theoretical completeness and convergence analysis.","Fast Asymptotically Optimal Kinodynamic Planning via Vectorization  \nYitian Gao, Andrew Lu, and Zachary Kingston  \narXiv :2607 .03987v2 [ cs .RO] 12 Jul 2026  \nAbstract—Sampling-based motion planners have been shown to be effective for systems with complex kinodynamic constraints and high dimensionality. However, these algorithms struggle to achieve real-time performance, leading to recent efforts to parallelize planning. While GPU-accelerated planners have achieved significant speedups, existing approaches require specialized CUDA programming that limits accessibility and portability. We present Parallel Asymptotically Optimal Kinodynamic RRT (PAKR), a massively parallel kinodynamic planner leveraging JAX and the XLA compiler to achieve GPU acceleration through standard Python tooling. By combining our parallel planner with the AO-x meta-algorithm, we achieve asymptotic optimality through fast iterative replanning. We provide a theoretical analysis of probabilistic completeness, analyze the effects of batch size and branching factor on convergence, and demonstrate scalability to complex dynamics using the MuJoCoXLA simulator. Experiments show competitive runtimes with state-of-the-art GPU planners and superior solution quality.  \nI. INTRODUCTION  \nRobotic systems deployed in dynamic environments require fast, reactive motion planning that accounts for the robot’s dynamics. One approach is kinodynamic motion planning, which is concerned with finding trajectories that satisfy both kinematic constraints and equations governing the robot’s dynamics, and can be quite challenging for even low-dimensional problems [1], [2] . Sampling-based motion planners (SBMPs) have proven effective due to their ability to handle high-dimensional state spaces and complex nonlinear dynamics [3], [4], [5] . Still, finding solutions can take hundreds of milliseconds for simple systems and tens of seconds for complex nonlinear dynamics, which is insufficient for real-time reactivity in changing environments.  \nRecent advances in parallel computing offer a solution. GPU and CPU parallelization have demonstrated significant speedups by batching operations such as collision checking [6], [7], parallelizing entire expansion iterations [8],[9], or running multiple independent planner instances [10],[11] . For kinodynamic systems specifically, Kino-PAX [9] achieves real-time performance through GPU-accelerated tree expansion, finding solutions in tens of milliseconds.  \nHowever, parallel motion planning algorithms often compromise on solution quality. Many asymptotically optimal (AO) planners achieve high-quality solutions through mechanisms like rewiring [12], [13] or maintaining best-cost nodes within witness regions [4] . These techniques rely on ordering; each node’s insertion depends on the current global state of the tree. In a batched parallel context, samples within the same batch lack mutual visibility: a node may  \nYG, AL, and ZK are with the Department of Computer Science, Purdue University, {gao634, lu987, [zkingston](zkingston}@purdue.edu)[}](zkingston}@purdue.edu)[@purdue.edu](zkingston}@purdue.edu).  \nattach to a sub-optimal parent because the optimal parent is still being processed. This staleness problem leads to redundant exploration and sub-optimal decisions, making it difficult to maintain theoretical convergence guarantees without introducing significant synchronization overhead.  \nWe present PAKR, a massively parallel kinodynamic motion planner that achieves both speed and solution quality. Our key insight is that the AO-x meta-algorithm [14], which transforms any probabilistically complete planner into an asymptotically optimal one through iterative cost-bounded replanning, is naturally suited to parallelization; rather than fighting stale information, we embrace fast, sub-optimal planning and use rapid replanning to converge toward optimal solutions. Our implementation uses JAX [15] to fuse the entire planning loop into a single GPU ","cbCaiidkwqiVO0pQ","https://ap.wps.com/l/cbCaiidkwqiVO0pQ","pdf",4774614,1,"English","en",105,"# Introduction\n## Kinodynamic planning\n## Parallel motion planning\n# Related Work\n## Geometric sampling-based motion planners\n## Kinodynamic planning","[{\"question\":\"What problem does PAKR address in kinodynamic motion planning?\",\"answer\":\"It targets the gap between effective sampling-based kinodynamic planning and real-time responsiveness, where existing methods can be too slow for dynamic environments.\"},{\"question\":\"How does PAKR achieve GPU acceleration without CUDA specialization?\",\"answer\":\"It implements the planning loop in JAX and relies on XLA compilation to fuse the computation into GPU kernels using standard Python tooling.\"},{\"question\":\"How does PAKR attain asymptotic optimality in a parallel, batched setting?\",\"answer\":\"It combines a massively parallel kinodynamic planner with the AO-x meta-algorithm, using fast iterative replanning to converge toward optimal solutions despite batched 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problem does PAKR address in kinodynamic motion planning?","Question",{"text":74,"@type":75},"It targets the gap between effective sampling-based kinodynamic planning and real-time responsiveness, where existing methods can be too slow for dynamic environments.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does PAKR achieve GPU acceleration without CUDA specialization?",{"text":79,"@type":75},"It implements the planning loop in JAX and relies on XLA compilation to fuse the computation into GPU kernels using standard Python tooling.",{"name":81,"@type":72,"acceptedAnswer":82},"How does PAKR attain asymptotic optimality in a parallel, batched setting?",{"text":83,"@type":75},"It combines a massively parallel kinodynamic planner with the AO-x meta-algorithm, using fast iterative replanning to converge toward optimal solutions despite batched 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