B*: Efficient and Optimal Base Placement for Fixed-Base Manipulators

Proper base placement is crucial for task execution feasibility and performance of fixed-base manipulators, the dom- inant solution in robotic automation. Current methods rely on pre-computed kinematics databases generated through sampling to search for solutions. However, they face an inherent trade-off between solution optimality and computational efficiency when determining sampling resolution—a challenge that intensifies when considering long-horizon trajectories, self-collision avoidance, and task-specific requirements. To address these limitations, we present B∗, a novel optimization framework for determining the optimal base placement that unifies these multiple objectives without re- lying on pre-computed databases. B∗addresses this inherently non-convex problem via a two-layer hierarchical approach: The outer layer systematically manages terminal constraints through progressively tightening them, particularly the base mobility con- straint, enabling feasible initialization and broad solution space exploration. Concurrently, the inner layer addresses the non- convexities of each outer-layer subproblem by sequential local linearization, effectively transforming the original problem into a tractable sequential linear program (SLP). Comprehensive evalua- tions across multiple robot platforms and task complexities demon- strate the effectiveness of B∗: it achieves solution optimality five orders of magnitude better than sampling-based approaches while Received 16 April 2025; accepted 22 August 2025. Date of publication 2 September 2025; date of current version 8 September 2025. This article was recommended for publication by Associate Editor H. Chen and Editor C.-B Yan upon evaluation of the reviewers’ comments. This work was supported in part by the National Science and Technology Major Project under Grant 2022ZD0114900, in part by the National Natural Science Foundation of China under Grant 62376031, in part by Beijing Nova Program, in part by the State Key Lab of General AI at Peking University, in part by the PKU-BingJi Joint Laboratory for Artificial Intelligence, and in part by the National Comprehensive Experimental Base for Governance of Intelligent Society, Wuhan East Lake High-Tech Development Zone. (Zihang Zhao, Leiyao Cui, and Sirui Xie contributed equally to this work.) (Corresponding author: Yixin Zhu.) Zihang Zhao is with the Institute for Artificial Intelligence, Peking University, Beijing 100871, China, also with the School of Psychological and Cognitive Sciences Peking University, Beijing 100871, China, also with the Beijing Key Laboratory of Behavior and Mental Health, Peking University, Beijing 100871, China, and also with the LeapZenith AI Research Shanghai 201707, China. Leiyao Cui and Saiyao Zhang are with the University of Chinese Academy of Sciences, Beijing 100049, China, and also with the the School of Psychological and Cognitive Sciences, Peking University, Beijing 100871, China. Sirui Xieand Yixin Zhu are with the Institute for Artificial Intelligence, Peking University, Beijing 100871, China, and with the School of Psychological and Cognitive Sciences, Peking University, Beijing 100871, China, and also with the Beijing Key Laboratory of Behavior and Mental Health, Peking University, Beijing 100871, China (e-mail: yixin.zhu@pku.edu.cn). Zhi Han is with the University of Chinese Academy of Sciences, Beijing 100049, China. Lecheng Ruan is with the College of Engineering, Peking University, Beijing 100871, China. Data is available online at https://bstar-planning.github.io This article has supplementary downloadable material available at https://doi.org/10.1109/LRA.2025.3604741, provided by the authors. Digital Object Identifier 10.1109/LRA.2025.3604741 maintaining perfect success rates, all with reduced computational overhead. Operating directly in configuration space, B∗not only solves the base placement problem but also enables simultaneous path planning with customizable optimization criteria, making it a versatile framework for various robotic motion planning chal- lenges. B∗serves as a crucial initialization tool for robotic ap- plications, bridging the gap between theoretical motion planning and practical deployment where feasible trajectory existence is fundamental.