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Research Papers

# Projection-Based Control of Parallel Mechanisms

[+] Author and Article Information

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

The fundamental relationship between the null-space and the range space of a linear transformation $S$ is $R(ST)=[N(S)]⊥$(12,26).

J. Comput. Nonlinear Dynam 6(3), 031009 (Feb 01, 2011) (8 pages) doi:10.1115/1.4002942 History: Received January 12, 2010; Revised October 25, 2010; Published February 01, 2011; Online February 01, 2011

## Abstract

The unifying idea for most model-based control approaches for parallel mechanism is to derive a minimal-order dynamics model of the system and then design the corresponding controller. The problem with such a control approach is that the controller needs to change its structure whenever the mechanical system changes its number of degrees-of-freedom. This paper presents a projection-based control scheme for parallel mechanism that works whether the system is overactuated or not; it does not require derivation of the minimal-order dynamics model. Since the dimension of the projection matrix is fixed, the projection-based controller does not need to change its structure whenever the mechanical system changes its number of degrees-of-freedom. The controller also allows to specify lower and upper bounds on the actuator forces/torques, making it suitable not only for the control of parallel manipulators with limited force/torque capability of the actuators but also for backlash-free control of parallel manipulators as well as for control of tendon driven parallel manipulators. The stability of the projection-based controllers is rigourously proved, while the condition for the controllability of parallel manipulators is also derived in detail. Finally, experimental results obtained from a simple parallel mechanism, which changes its degrees-of-freedom, are appended. The results also demonstrate that the maximum actuator torque can be reduced by 20% if the actuator saturation is taken into account by the controller.

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## Figures

Figure 1

Estimating the states of the passive joints

Figure 2

The control system based on nonminimal order dynamics model

Figure 3

The experimental setup

Figure 4

The schematic of the experimental setup

Figure 5

Trajectories of the task space variables

Figure 6

Trajectories of the joint angles

Figure 7

Trajectories of the joint torque with applying projection filter

Figure 8

Trajectories of the joint torque without applying projection filter

Figure 9

Euclidean norm of joint torques

Figure 10

Trajectories of the joint torque under the joint torque limit constraint

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