Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T14:15:08.681Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematic reductions for uncertain mechanical contact

Published online by Cambridge University Press:  01 November 2007

Todd D. Murphey
Todd D. Murphey*
Affiliation:
Electrical and Computer Engineering, University of Colorado at Boulder, Boulder, CO 80309-0425
*
*Corresponding author. E-mail: murphy@colorado.edu
Get access Rights & Permissions [Opens in a new window]

Summary

This paper describes the methods applicable to the modeling and control of mechanical contact, particularly those systems that experience uncertain stick/slip phenomena. Geometric kinematic reductions are used to reduce a system's description from a second-order dynamic model with frictional disturbances coming from a function space to a first-order model with frictional disturbances coming from a space of finite automata over a finite set. As a result, modeling for purposes of control is made more straight-forward by getting rid of some dependencies on low-level mechanics (in particular, the details of friction modeling). Moreover, the online estimation of the uncertain, discrete-valued variables has reduced sensing requirements. The primary contributions of this paper are the introduction of a simplifying representation of friction and formal tests for kinematic reducibility. Results are illustrated using a slip-steered vehicle model and an actuator array model.

Keywords

Geometric modelingfriction modeling
Type
Article
Information
Robotica , Volume 25 , Issue 6 , November 2007 , pp. 751 - 764
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Akiyama, T. and Shonu, K., “Controlled stepwise motion in polysilicon micro-structures,” J. Microelectromech. Syst. 2 (3), 106–110 (1993).Google Scholar
2.Bicchi, A. and Kumar, V., “Robotic grasping and Contact: A Review,” Proceedings of the IEEE International Conference on Robotics and Automation (2000) pp. 348–353.Google Scholar
3.Böhringer, K., Donald, B. and MacDonald, N., “Upper and Lower Bounds for Programmable Vector Fields With Applications to MEMS and Vibratory Plate Parts Feeders,” In: Algorithms for Robotic Motion and Manipulation (A. K. Peters, Ltd., Wellesley, MA, 1997) pp. 255–276.Google Scholar
4.Böhringer, K. F., Donald, B. R., Kavraki, L. E. and Lamiraux, F., “A Distributed, Universal Device for Planar Parts Feeding: Unique Part Orientation in Programmable Force Fields,” In: Distributed Manipulation (Kluwer, Norwell, MA, 2000) pp. 1–28.Google Scholar
5.Bullo, F. and Lewis, A., Geometric Control of Mechanical Systems. Texts in Applied Mathematics 49 (Springer-Verlag, Berlin, Germany, 2004).Google Scholar
6.Bullo, F. and Lewis, A., “Low-order controllability and kinematic reductions for affine connection control systems,” SIAM J. Control Optim. 44 (3), 885–908 (2005).CrossRefGoogle Scholar
7.Bullo, F. and Lynch, K., “Kinematic Controllability and Decoupled Trajectory Planning for Underactuated Mechanical Systems,” Proceedings of the IEEE International Conference on Robotics and Automation (2001) pp. 3300–3307.Google Scholar
8.Bullo, F. and Lynch, K. M., “Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems,” IEEE Trans. Robot. Autom. 17 (4), 402–412 (Aug. 2001).Google Scholar
9.Filippov, A., Differential Equations With Discontinuous Right-Hand Sides (Kluwer, Norwell, MA, 1988).CrossRefGoogle Scholar
10.Goodwine, B. and Burdick, J., “Controllability of kinematic control systems on stratified configuration spaces,” IEEE Trans. Autom. Control 46 (3), 358–368 (2000).Google Scholar
11.La Valle, S., Planning Algorithms (Cambridge University Press, Cambridge, UK, 2006).Google Scholar
12.Lewis, A., “When is a Mechanical Control System Kinematic?” Proceedings of the 38th IEEE Conference on Decision and Control (Dec. 1999) pp. 1162–1167.Google Scholar
13.Linderman, R. and Bright, V., “Nanometer precision positioning robots utilizing optimized scratch drive actuators,” Sens. Actuators A 91, 292–300, (2001).Google Scholar
14.Luntz, J., Messner, W. and Choset, H., “Distributed manipulation using discrete actuator arrays,” Int. J. Robot. Res. 20 (7), 553–583 (Jul. 2001).Google Scholar
15.Murphey, T. D., “On multiple model control for multiple contact systems,” Automatica, (2007), in press.Google Scholar
16.Murphey, T. D. and Burdick, J. W., “A Controllability Test and Motion Planning Primitives for Overconstrained Vehicles,” Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea (2001) pp. 2716–2722.Google Scholar
17.Murphey, T. D. and Burdick, J. W., “Feedback control for distributed manipulation with changing contacts,” Int. J. Robot. Res. 23 (7/8), 763–782 (Jul. 2004).CrossRefGoogle Scholar
18.Murphey, T. D. and Burdick, J. W., “The power dissipation method and kinematic reducibility of multiple model robotic systems,” IEEE Trans. Robot. 22 (4), 694–710 (Aug. 2006).Google Scholar
19.Murray, R., Li, Z. and Sastry, S.. A Mathematical Introduction to Robotic Manipulation (CRC Press, Boca Raton, FL, 1994).Google Scholar
20.Olsson, H., Astrom, K., Wit, C. C. de, Gafvert, M. and Lischinsky, P., “Friction models and friction compensation,” Eur. J. Control 4 (3), 176–195 (1998).Google Scholar
21.Vidyasagar, M., Nonlinear Systems Analysis (Prentice Hall, Englewood Cliffs, NJ, 1978).Google Scholar