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This paper introduces a generalized theory for load distribution in redundantly-actuated robotic systems, crucial for understanding how forces are managed in multi-chain systems. It fully characterizes the feasible set of manipulating wrench distributions for a given resultant wrench. The theory provides computationally efficient solutions for wrench synthesis and analysis, scaling linearly with the number of applied wrenches, and identifies/corrects shortcomings in existing approaches.
Current methods for load distribution in redundantly-actuated robots have significant shortcomings, but this new theory offers computationally efficient solutions that scale linearly without numerical methods or large matrix inversions.
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.
