Distributed manipulation using discrete actuator arrays

Distributed manipulation systems induce motions on objects through the appl ication of many external forces. An actuator array performs distributed man ipulation using a planar array of many small stationary elements (which are called cells) that cooperate to manipulate larger objects. Typically, high ly dense actuator arrays are modeled as spatially continuous, programmable force fields, although in many implementations a relatively small number of actuators supports an object and continuous assumptions break down. This p aper serves two purposes: to present a methodology for modeling and analyzi ng the dynamics of manipulation on a highly discrete actuator array and to present a methodology for designing manipulation strategies on discrete act uator arrays. This is done in the context of a particular macro-scale actua tor array comprising a fixed planar array of motorized wheels. Modeling of the dynamics takes into account several models of the interaction between t he actuators and the object, the distribution of the weight of the object a mong the supports, and the discrete nature of the system. Under certain mod eling assumptions, the manipulation dynamics of an object are extremely sim ple for a given set of supporting cells. An inversion of these piecewise-co ntinuous dynamics generates a fully continuous open-loop manipulation strat egy, effectively smoothing out the discontinuities. The authors show that a lthough the resulting manipulation field may stably position and orient any object in the continuous field case, discreteness causes many objects to e xperience unstable rotational equilibria. Thus, poor orientation precision is a limitation of open-loop manipulation using discrete actuator arrays an d motivates the use of feedback. The authors also derive closed-loop manipu lation strategies through an inversion of the discrete dynamics that reduce the man,V-input, three-output distributed control problem to a standard th ree-input, three-output control problem that operates under distributed con trol. In effect, the array of actuators is reduced to a single virtual actu ator capable of applying a desired net force and moment on an object. It is proven that even in the presence of dynamic coupling and nonlinearities in troduced due to discreteness, these closed-loop strategies are asymptotical ly stable. Multimedia extensions include a complete simulator and videos of the experimental prototype.