cs.ROMar 12, 2026

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

Authors: Joshua Flight, Clément Gosselin

Organizations: Département de génie mécanique et de génie industriel, Université Laval, Canada.

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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 and a simulation that demonstrate the advantages of the improved methods.

Figures & tables

Figure 1: Examples of rigid objects handled by multiple kinematic chains.
Figure 2: Relevant kinematic quantities (adapted from [ 7 ] ).
Figure 3: Example of a dynamically equivalent system of nn LMIEs.
Figure 4: Illustration of physical significance of constraint wrenches.
Figure 5: When a body is in motion, constraint wrenches are present even in the absence of applied wrenches.
Figure 6: Example of orthogonal torque component cancellation in non-parallel torques causing internal loads.
Figure 7: Three forces applied to a point mass.
Figure 8: Two manipulating force distributions for three planar forces applied to a point mass.
Figure 9: Three forces and one moment applied to a planar rigid body.
Figure 10: Vector fields obtained from x¨f∗\ddot{\mathbf{x}}^{*}_{f} considering different contributions from the manipulating torque τm\tau_{m} .
Figure 11: Unit sphere with four applied wrenches. A dashed line indicates that the wrench is applied on the back-side of the sphere.
Figure 12: Simulation setup. Four UR5 robots cooperatively handle a common spherical payload.
Figure 13: Magnitudes of correction forces fpd,i\mathbf{f}_{pd,i} and constraint forces fc,i\mathbf{f}_{c,i} over one cycle of trajectory using our wrench synthesis method.
Figure 14: Magnitudes of correction forces fpd,i\mathbf{f}_{pd,i} and constraint forces fc,i\mathbf{f}_{c,i} over one cycle of trajectory using torque limit weighting matrix
Figure 15: Magnitudes of correction forces fpd,i\mathbf{f}_{pd,i} and constraint forces fc,i\mathbf{f}_{c,i} over one cycle of trajectory using operational space inertia matrix.
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