Jonathan E. Luntz, University of Michigan, Ann Arbor, MI

William Messner, Carnegie Mellon University, Pittsburgh, PA

Howie Choset, Carnegie Mellon University, Pittsburgh, PA

Distributed manipulation systems induce motions on objects through the application of many external forces. An actuator array performs distributed manipulation using a planar array of many small stationary actuators (which we call cells) each of which applies a force in the plane to larger objects which rest atop many cells at once. An actuator array can transport and orient flat objects in the plane. The authors have developed a table-top scale actuator array consisting of many motorized wheels. In such a macroscopic array, a fairly small number of cells support the object. The work of the authors builds upon and extends the work of researchers in microelectromechanical (MEMS) actuator arrays by explicitly modeling the discreteness in the system, including the set of supports, distribution of weight, and generation of traction forces and by using the resulting model to directly design classes of actuation fields (sets of wheel speeds). Using a constant (open-loop) wheel velocity field, discreteness causes undesirable behavior such as unstable rotational equilibria, suggesting the use of object feedback. Discrete distributed control algorithms are derived by inverting the dynamics of manipulation (the relationship between wheels speeds and forces on the object) to come up with wheel velocity fields which effect the desired forces and moments on the object. These algorithms reduce the many-input-three-output control problem to a three-input-three-output control problem.