Dead‐beat regulation of mechanical juggling systems

Abstract

In this paper, mechanical systems subject to impacts and contacts, that would be not controllable if the impacts were absent (usually called jugglers), are considered. On the basis of an algorithm taken from the literature and of a new procedure to determine a reference trajectory for such a class of systems, a fully algorithmic procedure, able to compute a control input that achieves dead-beat regulation of the "uncontrollable" subsystem just by using impacts, is given. Such a procedure exploits some tools borrowed from algebraic geometry that allow to solve parametric systems of equalities and inequalities. A practical example of application of the given procedure is reported.

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

“…Dead-beat control τ of the robot is useful in order to assure a desired robot's state (q 2 (t), q2 (t − )) is reached in a desired finite time t, a property which is quite powerful when combined with impacts to impose some desired motion of the object, because it allows the robot to hit the object with pre-specified pre-impact velocities and time (see section 3.1.1). It has been applied in [13,14,313,257,314,185,10,11,210,315,316,210,314,317,176]. Robustness is studied numerically in [13,14,316].…”