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

2025-04-17

AI Summary

This paper addresses the optimal base pose planning problem for fixed-base robotic manipulators. We propose a two-level optimization framework that eliminates the need for precomputed kinematic databases: an outer loop progressively tightens task constraints imposed on the end-effector, while an inner loop solves the resulting nonconvex subproblems via sequential linear programming (SLP). Our approach achieves, for the first time, sampling-free globally optimal base placement—overcoming the classical trade-off between accuracy and efficiency inherent in sampling-based methods—and jointly optimizes both base pose and configuration-space paths. Extensive experiments across multiple robotic platforms demonstrate a five-order-of-magnitude improvement in solution optimality, 100% success rate, and significantly reduced computational overhead. The method serves as a robust and efficient initialization module for motion planning pipelines.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• Optimal base placement for fixed-base manipulators
• Balancing solution optimality and computational efficiency
• Simultaneous path planning with customizable optimization criteria

Innovation

• Two-layer hierarchical optimization framework
• Sequential linear programming for non-convexities
• Progressive tightening for constraint management