Actuator arrays are planar arrangements of simple actuators that cooperate to translate and orient objects. This paper derives the equations of motion for manipulating an object in stick/slip contact with the actuators. A controller derived from kinematics considerations is presented and its stability analyzed with the multivariable circle criterion. Stability results are verified through simulation and experimental results on a 20 unit macroscopic actuator array.
Bedillion, M. and Messner, W. (2003). The multi-variable circle criterion for switched continuous systems. Proceedings of the IEEE Conference on Decision and Control.
2.
Bedillion, M., Messner, W. and Choset, H. (2000). Rolling Contact dynamics and optimal feedforward control for the modular distributed manipulator system. Proceedings of the International Congress on Mechanical Engineering.
3.
Bedillion, M., Messner, W. and Choset, H. (2001). Limitations imposed by single DOF actuators on discrete actuator arrays. Proceedings of the IEEE International Conference on Intelligent Robots and Systems.
4.
Bohringer, K.F., Bhatt, V. and Goldberg, K. (1995). Sensorless manipulation using transverse vibrations of a plate. Proceedings of the IEEE International Conference on Robotics and Automation, vol. 2, pp. 1986-1989.
5.
Bohringer, K. et al. (1994). Sensorless manipulation using massively parallel microfabricated actuator arrays. Proceedings of the IEEE International Conference on Robotics and Automation, pp. 826-833.
6.
Bohringer, K. et al. (2000). A distributed, universal device for planar parts feeding: unique part orientation in programmable force fields. Distributed Manipulation, Bohringer, K. F. and Choset, H. (eds). Kluwer Academic Publishers, pp. 1-28.
7.
Filippov, A.F. (1988). Differential Equations with Discontinuous Righthand Sides, Scott, F. M. (ed). Kluwer Academic Publishers.
8.
Goldberg, K. (1993). Orienting polygonal parts without sensors. Algorithmica: Special Issue on Computational Robotics, 10(2/3/4): 201-225.
9.
Khalil, H. (2001). Nonlinear Systems. Prentice Hall.
10.
Luntz, J., Rollins, E. and Messner, W. (1995). The virtual vehicle - materials handling using distributed actuation and highly distributed coordination control. Proceedings of the IEEE Conference on Control Applications, pp. 742-747.
11.
Luntz, J.E., Messner, W. and Choset, H. (2000). Discreteness issues in actuator arrays. Distributed Manipulation, Bohringer, K. F. and Choset, H. (eds). Kluwer Academic Publishers, pp. 103-126.
12.
Murphey, T.D. (2008). On multiple model control for multiple contact systems. Automatica, 44: 451-458.
13.
Murphey, T.D. and Burdick, J.W. (2001). On the stability and design of distributed manipulation control systems. Proceedings of the IEEE International Conference on Robotics and Automation.
14.
Murphey, T.D. and Burdick, J.W. (2004). Feedback control methods for distributed manipulation systems that involve mechanical contact. Int. J. Robot. Res. , 23(7-8): 763-781.
15.
Reznik, D., Moshkovich, E. and Canny, J. (1999). Building a universal part manipulator. Distributed Manipulation, Bohringer, K. F. and Choset, H. (eds). Kluwer Academic Publishers.
16.
Vose, T., Umbanhowar, P. and Lynch, K. (2007). Vibration-induced frictional force fields on a rigid plate. Proceedings of the IEEE International Conference on Robotics and Automation, pp. 660-667.
