0
Research Papers

Repeatable Redundant Manipulator Control Using Nullspace Quasivelocities

[+] Author and Article Information
Alan Bowling

Department of Mechanical and Aerospace Engineering, Robotics and Dynamic Systems Laboratory, University of Texas at Arlington, Box 19018, 500 West First Street, Woolf Hall 315A, Arlington, TX 76019bowling@uta.edu

Sean Harmeyer

 NASA Johnson Space Center, 2101 NASA Parkway, Houston, TX 77058

J. Dyn. Sys., Meas., Control 132(3), 031007 (Apr 23, 2010) (11 pages) doi:10.1115/1.4001334 History: Received March 12, 2009; Revised February 02, 2010; Published April 23, 2010; Online April 23, 2010

This paper presents a repeatable control scheme for redundant manipulators. It is developed in terms of physically meaningful variables, a concept closely related to integrability and homogeneity. This approach sheds a different light on some well-known phenomena related to redundant manipulator control. The control is developed by determining enough physically meaningful variables to describe the manipulator’s motions in the task and nullspaces, in a manner that allows them to be controlled independently. These variables are then used to develop physically meaningful controller error signals. As a consequence, all configurations in the workspace are repeatable, except for those at, or very close, to a kinematic singularity. The approach is illustrated on a 6DOF planar manipulator.

Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

6DOF planar manipulator

Grahic Jump Location
Figure 2

Trajectory for 40 cycles with qo=qx=[45 deg, 45 deg, 45 deg, 45 deg, 45 deg, 45 deg], xNd=[270 deg, 0 m,0.36 m,135 deg], J#=J+, and CPU time=585 s. Clearly the manipulator drifts.

Grahic Jump Location
Figure 3

Trajectories for 20 cycles using eN=∇xNh, J#=J+, and qo=[45 deg, 45 deg, 45 deg, 45 deg,45 deg, 45 deg]. (a) qx=[45 deg, 45 deg, 45 deg, 45 deg, 45 deg, 45 deg] and CPU time=371 s, (b) qx=[50 deg, 45 deg, 42 deg, 43 deg, 47 deg, 52 deg] and CPU time=381 s, and (c) qx=[31 deg, 44 deg,54 deg, 51 deg, 39 deg, 26 deg] and CPU time=451 s.

Grahic Jump Location
Figure 4

h(q) for the simulations in Fig. 3

Grahic Jump Location
Figure 5

Trajectory for 40 cycles with qo=qx=[90 deg,−30 deg, 90 deg, 70 deg, −45 deg, 70 deg], xNd=[245deg, −0.05 m,0.35 m,150 deg], J#=J+, and CPU time=491 s. Clearly the manipulator drifts.

Grahic Jump Location
Figure 6

Trajectories for 20 cycles using ∇xNh, J#=J+, and qo=[90 deg, −30 deg, 90 deg, 70 deg, −45 deg, 70 deg]. (a) qx=[90 deg, −30 deg, 90 deg, 70 deg, −45 deg, 70 deg] and CPU time=521 s, (b) qx=[99 deg,−28 deg, 79 deg, 64 deg, −36 deg, 90 deg] and CPU time=509 s, and (c) qx=[83 deg, −30 deg, 101 deg,73 deg, −53 deg, 52 deg] and CPU time=539 s.

Grahic Jump Location
Figure 7

h(q) for the simulations in Fig. 6

Grahic Jump Location
Figure 8

Trajectory for 40 cycles with qo=qx=[55 deg,60 deg, −45 deg, 45 deg, −30 deg, 45 deg], xNd=[130deg, 0.07 m,0.40 m,70 deg], J#=J+, and CPU time=543 s. Clearly the manipulator drifts.

Grahic Jump Location
Figure 9

Trajectories for 20 cycles using eN=∇xNh, J#=J+, and qo=[55 deg, 60 deg, −45 deg,45 deg, −30 deg, 45 deg]. (a) qx=[55 deg, 60 deg, −45 deg, 45 deg, −30 deg, 45 deg] and CPU time=841 s, (b) qx=[59 deg, 51 deg, −42 deg, 40 deg, −23 deg, 52 deg] and CPU time=964 s, and (c) qx=[66 deg, 73 deg,−50 deg, 35 deg, −55 deg, 21 deg] and CPU time=645 s.

Grahic Jump Location
Figure 10

h(q) for the configurations in Fig. 9

Grahic Jump Location
Figure 11

Trajectory for 40 cycles with qo=qx=[45 deg, 45 deg, 45 deg, 45 deg, 45 deg, 45 deg], xNd=[270 deg, 0 m,0.36 m,135 deg], J#=J¯, and CPU time=650 s

Grahic Jump Location
Figure 12

Trajectories for 20 cycles using eN=∇xNh, J#=J¯, and qo=[45 deg, 45 deg, 45 deg, 45 deg, 45 deg, 45 deg]. (a) qx=[45 deg, 45 deg, 45 deg, 45 deg, 45 deg, 45 deg] and CPU time=587 s, (b) qx=[50 deg,45 deg, 42 deg, 43 deg, 47 deg, 52 deg] and CPU time=561 s, and (c) qx=[31 deg, 44 deg, 54 deg,51 deg, 39 deg, 26 deg] and CPU time=650 s.

Grahic Jump Location
Figure 13

h(q) for the configurations in Fig. 1

Grahic Jump Location
Figure 14

Trajectories for 7 cycles with qo=qx=[45 deg, 45 deg, 45 deg, 45 deg, 45 deg, 45 deg], xNd=[270 deg, 0 m,0.36 m,135 deg], J#=J∗, and CPU time=920 s

Grahic Jump Location
Figure 15

Trajectories for 0 cycle with qx=qo=[45 deg, 45 deg, 45 deg, 45 deg, 45 deg, 45 deg], eN=∇xNh, and J#=J∗

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In