Distributed manipulation along trajectories using open-loop force fields

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 elements, which cooperate to manipulate larger objects through the generation of a programmable force field. The paper demonstrates a methodology to perform trajectory following to transport objects with specified position and orientation. Open-loop "elliptic" force fields transport objects by pulling them along the trajectory both in position and orientation. This is done in three stages: purely open loop, open loop with feed-forward compensation to correct for steady-state error on lines and around circular curves, and closed-loop with both feed-forward and small-signal linearized feedback. These approaches apply to arbitrary paths through linear and circular trajectory approximations. Results are verified through simulation