0
TECHNICAL PAPERS

Optimal Motion Generation for Groups of Robots: A Geometric Approach

[+] Author and Article Information
Calin Belta

MEM Department, Drexel University, Philadelphia, PA 19104e-mail: calin@drexel.edu

Vijay Kumar

GRASP Laboratory, University of Pennsylvania, Philadelphia, PA 19104e-mail: kumar@grasp.cis.upenn.edu

J. Mech. Des 126(1), 63-70 (Mar 11, 2004) (8 pages) doi:10.1115/1.1641190 History: Received August 01, 2002; Revised June 01, 2003; Online March 11, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.

References

Yamashita, A., Fukuchi, M., Ota, J., Arai, T., and Asama, H., 2000, “Motion Planning for Cooperative Transportation of a Large Object by Multiple Mobile Robots in a 3D Environment,” Proc. IEEE Int. Conf. Robot. Automat., San Francisco, CA, pp. 3144–3151.
Kang, W., Xi, N., and Sparks, A., 2000, “Formation control of autonomous agents in 3D workspace,” Proc. IEEE Int. Conf. Robot. Automat., San Francisco, CA, pp. 1755–1760.
Fox,  D., Burgard,  W., Kruppa,  H., and Thrun,  S., 2000, “Collaborative Multi-robot Exploration,” Autonomous Robots, 8(3), pp. 325–344.
Balch,  T., and Arkin,  R. C., 1998, “Behavior-based Formation Control for Multi-Robot Teams,” IEEE Trans. Rob. Autom., 14(6), pp. 1–15.
Parker, L. E., 2000, “Current State of the Art in Distributed Autonomous Mobile Robotics,” Proc. International Symposium on Distributed Autonomous Robotic Systems, Knoxville, TN, pp. 3–12.
L. Chaimowicz, Sugar, T., Kumar, V., and Campos, M., 2001, “An Architecture for Tightly Coupled Multi-robot Cooperation,” Proc. IEEE Int. Conf. Robot. Automat., Seoul, Korea, pp. 2992–2997.
Spletzer, J., and Taylor, C. J., 2001, “A Framework for Sensor Planning and Control with Applications to Vision Guided Multi-Robot Systems,” Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Hawaii, USA.
Chichka, D. F., Speyer, J. L., and Park, C. G., 1999, “Peak-seeking Control with Application to Formation Flight,” Proc. IEEE Conf. Decision and Control, Phoenix, AZ, pp. 2463–2470.
Fierro, R., Song, P., Das, A. K., and Kumar, V., 2002, “Cooperative Control of Robot Formations,” Cooperative Control and Optimization Series, R. Murphey and P. Pardalos, eds., Kluwer Academic Press, pp. 73–93.
Tan,  K., and Lewis,  M. A., 1997, “Virtual Structures for High-precision Cooperative Mobile Robot Control,” Autonomous Robots, 4(4), pp. 387–403.
Beard, R. W., and Hadaegh, F. Y., 1998, “Constellation Templates: An Approach to Autonomous Formation Flying,” Proc. World Automation Congress, Anchorage, Alaska.
Zefran,  M., Kumar,  V., and Croke,  C., 1995, “On the Generation of Smooth Three-dimensional Rigid Body Motions,” IEEE Trans. Rob. Autom., 14(4), pp. 579–589.
Bloch,  A. M., Leonard,  N. E., and Marsden,  J. E., 2000, “Controlled Lagrangians and the Stabilization of Mechanical Systems I: The First Matching Theorem,” IEEE Trans. Autom. Control, 45(12), pp. 2253–2270.
Woolsey, C. A., Bloch, A. M., Leonard, N. E., and Marsden, J. E., 2001, “Physical Dissipation and the Method of Controlled Lagrangians,” Proc. European Control Conference, Porto, Portugal, pp. 2570–2575.
Belta,  C., and Kumar,  V., 2002, “An SVD-based Projection Method for Interpolation on SE(3),” IEEE Trans. Rob. Autom., 18(3), pp. 334–345.
Belta, C., and Kumar, V., 2001, “Motion Generation for Formations of Robots: A Geometric Approach,” Proc. IEEE Int. Conf. Robot. Automat., Seoul, Korea.
do Carmo, M. P., 1992, Riemannian Geometry, Birkhauser, Boston.
Park,  F. C., and Brockett,  R. W. R. W., 1994, “Kinematic Dexterity of Robotic Mechanisms,” Int. J. Robot. Res., 13(1), pp. 1–15.
Belta,  C., and Kumar,  V., 2002, “Euclidean Metrics for Motion Generation on SE(3),” J. Mech. Eng. Sci. Part C 216(C1), pp. 47–61.
Roth,  B., 1981, “Rigid and Flexible Frameworks,” Am. Math. Monthly, 88, pp. 6–21.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1998, Numerical Recipes inC, Cambridge University Press.

Figures

Grahic Jump Location
Geometry of the robots and of the virtual structure showing the initial and the final configurations. The relevant dimensions are chosen to be: a=c=2,b=10,h=20,l=10,X=20,Z=20,m=12.
Grahic Jump Location
Optimal motion for five identical robots required to maintain a rigid formation
Grahic Jump Location
Three interpolating motions for a set of two planar robots as geodesics of a modified metric defined in the configuration space.
Grahic Jump Location
Three interpolating motions for a set of three planar robots as geodesics of a modified metric defined in the configuration space.

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.

Related Journal Articles
Related eBook Content
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