A Generalized Theory of Load Distribution in Redundantly-actuated Robotic Systems

2026-03-11

AI Summary

This work addresses the challenge of distributing rigid-body loads among multiple independent closed-loop kinematic chains in redundantly actuated robotic systems, particularly the torque allocation ambiguity encountered in force-controlled scenarios. The authors propose a general analytical framework grounded in rigid-body mechanics and redundancy modeling, which leverages analytic geometry and linear algebra to derive a closed-form solution. This approach avoids numerical optimization or large matrix inversion, achieving linear computational complexity. It fully characterizes the complete set of feasible manipulation force distributions for a given resultant wrench, enabling efficient synthesis and analysis of forces and moments. Theoretical findings are validated through illustrative examples, demonstrating significantly improved computational efficiency and force control accuracy in overconstrained mechanisms such as multifingered grippers and legged robots, thereby providing a robust foundation for multi-robot collaboration and dexterous manipulation.

Technology Category

• Intelligent Robots: Manipulation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Distributed Problem Solving

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

This paper presents a generalized theory which describes how applied loads are distributed within rigid bodies handled by redundantly-actuated robotic systems composed of multiple independent closed-loop kinematic chains. The theory fully characterizes the feasible set of manipulating wrench distributions for a given resultant wrench applied to the rigid body and has important implications for the force-control of multifingered grippers, legged robots, cooperating robots, and other overconstrained mechanisms. We also derive explicit solutions to the wrench synthesis and wrench analysis problems. These solutions are computationally efficient and scale linearly with the number of applied wrenches, requiring neither numerical methods nor the inversion of large matrices. Finally, we identify significant shortcomings in current state-of-the-art approaches and propose corrections. These are supported by illustrative examples that demonstrate the advantages of the improved methods.

Problem

• load distribution
• redundantly-actuated robotic systems
• wrench distribution
• overconstrained mechanisms
• rigid body manipulation

Innovation

• redundantly-actuated systems
• wrench distribution
• closed-loop kinematic chains
• force control
• computational efficiency