B* is a novel optimization framework that addresses a critical challenge in fixed-base manipulator robotics: optimal base placement. 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. To address these limitations, B* unifies multiple objectives without database dependence. The framework employs a two-layer hierarchical approach. The outer layer systematically manages terminal constraints through progressive tightening, particularly for base mobility, enabling feasible initialization and broad solution exploration. The inner layer addresses non-convexities in each outer-layer subproblem through sequential local linearization, converting the original problem into tractable sequential linear programming (SLP). Testing across multiple robot platforms demonstrates B*'s effectiveness. The framework achieves solution optimality five orders of magnitude better than sampling-based approaches while maintaining perfect success rates and reduced computational overhead. Operating directly in configuration space, B* enables simultaneous path planning with customizable optimization criteria. B* serves as a crucial initialization tool that bridges the gap between theoretical motion planning and practical deployment, where feasible trajectory existence is fundamental.
View on arXiv@article{zhao2025_2504.12719,
title={ B*: Efficient and Optimal Base Placement for Fixed-Base Manipulators },
author={ Zihang Zhao and Leiyao Cui and Sirui Xie and Saiyao Zhang and Zhi Han and Lecheng Ruan and Yixin Zhu },
journal={arXiv preprint arXiv:2504.12719},
year={ 2025 }
}