Linear quadratic optimal control of contact transition with fingertip

This paper proposes an optimal control methodology that addresses the problem of control of fingertip during a general class of task that requires the fingertip to make a transition from non-contact motion to contact motion. Specifically, the task that the fingertip makes and transitions from motion to static well-directed force production. Here we present a mathematical framework for controlling the contact transition, while switching between non-contact and contact controller is needed and handled by the optimal control strategy. The non-linear differential algebraic equation that describes the dynamics of the index finger is linearized, and then a modified linear quadratic optimal control problem is solved. The resulting optimal feedback control law guarantees good regulation of contact force, velocity and position. Simulation results are presented to demonstrate the effectiveness of the new approach.