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Technical Briefs

Differentially Flat Designs of Underactuated Mobile Manipulators

[+] Author and Article Information
Ji-Chul Ryu

Department of Mechanical Engineering, Mechanical Systems Laboratory, University of Delaware, Newark, DE 19716jcryu@udel.edu

Vivek Sangwan

Department of Mechanical Engineering, Mechanical Systems Laboratory, University of Delaware, Newark, DE 19716sangwan@udel.edu

Sunil K. Agrawal1

Department of Mechanical Engineering, Mechanical Systems Laboratory, University of Delaware, Newark, DE 19716agrawal@udel.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(2), 024502 (Feb 02, 2010) (6 pages) doi:10.1115/1.4000815 History: Received September 05, 2008; Revised November 13, 2009; Published February 02, 2010; Online February 02, 2010

This paper presents a methodology for design of mobile vehicles, mounted with underactuated manipulators operating in a horizontal plane, such that the combined system is differentially flat. A challenging question of how to perform point-to-point motions in the state space of such a highly nonlinear system, in spite of the absence of some actuators in the arm, is answered in this paper. We show that, by appropriate inertia distribution of the links and addition of torsion springs at the joints, a range of underactuated designs is possible, where the underactuated mobile manipulator system is differentially flat. The differential flatness property allows one to efficiently solve the problem of trajectory planning and feedback controller design for point-to-point motions in the state space. The proposed method is illustrated by the example of a mobile vehicle with an underactuated three-link manipulator.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

A mobile manipulator consisting of a mobile vehicle mounted with a n-link planar manipulator. The configuration of the system is described by (x,y,ϕ,θ1,…,θn).

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Figure 2

A mobile vehicle mounted with a three-link underactuated manipulator. The first two joints P1 and P2 have torque inputs, and the last joint P3 is passive with a torsion spring of stiffness k3.

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Figure 3

The integrated planner and controller with the dynamic model of the mobile manipulator

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Figure 4

(a) The mobile vehicle’s desired and actual trajectories. Initial error of 1.0 m in the y-axis is given to check the controller performance. (b) The desired and actual trajectories for ϕ, θ1, θ2, and θ3.

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