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Research Papers

Motion Planning for an Underactuated Planar Robot in a Viscous Environment

[+] Author and Article Information
Elie Shammas

Assistant Professor
Department of Mechanical Engineering,
American University of Beirut,
Beirut 11-0236, Lebanon
e-mail: es34@aub.edu.lb

Daniel Asmar

Assistant Professor
Department of Mechanical Engineering,
American University of Beirut,
Beirut 11-0236, Lebanon
e-mail: da20@aub.edu.lb

Manuscript received May 29, 2013; final manuscript received December 27, 2014; published online April 2, 2015. Assoc. Editor: Jozsef Kovecses.

J. Comput. Nonlinear Dynam 10(5), 051002 (Sep 01, 2015) (11 pages) Paper No: CND-13-1159; doi: 10.1115/1.4029509 History: Received May 29, 2013; Revised December 27, 2014; Online April 02, 2015

In this paper, we solve the motion planning problem for a class of underactuated multibodied planar mechanical systems. These systems interact with the environment via viscous frictional forces. The motion planning problem is solved by specifying the location of friction pads on the robot as well as by specifying the input of the actuated degrees of freedom. Moreover, through the proposed novel motion planning analysis, we identify the simplest planar swimming robot, the two-link swimmer.

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Figures

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Fig. 1

A two-link underactuated planar system

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Fig. 2

An allowable input, ri = fa,b,A,B,s(t) − fa,b,A,B,s(t + κ)

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Fig. 3

Numerical simulation for the two inputs, φ1(t)=f0.5,5.5,0,2,5(t) and its reverse φ¯1(t)=-f0.5,5.5,0,2,5(t)

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Fig. 4

Same signed regions for the push term Γp

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Fig. 5

The evolution of y, φ1, the push term, and the drift term for the two-link system

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Fig. 6

Net motion along the y of the two-link system, ti ⇔ (t = i sec)

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Fig. 7

Simulation using webots depicting motion along y

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Fig. 8

The drift terms of the two-link system

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Fig. 9

The evolution of the degrees of freedom for the two-link system

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Fig. 10

Net motion along the x direction of the two-link system

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Fig. 11

Simulation using webots depicting motion along x

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Fig. 12

Motion of the proposed two-link robot in a viscous environment (dashed lines) versus the motion of the roller racer (solid lines). (a) Motion along the y axis. (b) Motion along the x axis.

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