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Research Papers

Control of Redundant Mechanical Systems Under Equality and Inequality Constraints on Both Input and Constraint Forces

[+] Author and Article Information
Farhad Aghili

Space Exploration, Canadian Space Agency, Saint-Hubert, PQ, J3Y 8Y9, Canadafarhad.aghili@asc-csa.gc.ca

Cotangent space is defined as the dual space of the tangent space.

J. Comput. Nonlinear Dynam 6(3), 031013 (Feb 02, 2011) (8 pages) doi:10.1115/1.4002689 History: Received June 14, 2010; Revised September 07, 2010; Published February 02, 2011

The equality and inequality constraints on constraint force and/or the actuator force/torque arise in several robotic applications, for which different controllers have been specifically developed. This paper presents a unified approach to control a rather general class of robotic systems with closed loops under a set of linear equality and inequality constraints using the notion of projection operator. The controller does not require the kinematic constraints to be independent, i.e., systems with time-varying topology can be dealt with, while demanding minimum-norm actuation force or torque in the case that the system becomes redundant. The orthogonal decomposition of the control input force yields the null-space component and its orthogonal complement. The null-space component is obtained using the projected inverse dynamics control law, while the orthogonal complement component is found through solving a quadratic programming problem, in which the equality and inequality constraints are derived to be equivalent to the originally specified ones. Finally, a case study is presented to demonstrate how the control technique can be applied to multi-arms manipulation of an object.

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Copyright © 2011 by Canadian Government
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References

Figures

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Figure 1

Two manipulators holding an object

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Figure 3

Trajectories of the object’s center of mass

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Figure 4

The normal forces

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Figure 8

Euclidean norm of input force

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Figure 7

Time history of the potent and impotent components of the joint torques

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Figure 6

The difference between critical friction and tangential force

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Figure 5

The tangential forces

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Figure 2

Number of iterations taken by the optimization solver at each time step

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