Planning and control of an internal point of a deformable object

Manipulative operation of a target point inside a deformable object by a robotic system is necessary in many medical and industrial applications. However, this is a challenging problem because of the difficulty of imposing the motion of the target point by a finite number actuation points located at the boundary of the deformable object. In this paper, an approach towards positioning operation of an internal target point of a deformable object to the desired location by a system of three actuators is presented. First, we design an optimization technique that minimizes the total force applied to the object to determine the location of actuation points to effect the desired motion. Then a position-based PI controller is developed to control the motion of the actuators. A passivity observer and a passivity controller are developed to guarantee the stability of the whole system. The simulation results demonstrate the efficacy of the proposed method.