Determination of displacement and velocity of an object handled by a three-fingered robot hand

The authors consider the problem of determining the displacement (position and orientation) and the velocity (linear and angular) of a rigid body handled by a three-fingered robot hand with frictional point contact. Direct measurement of configuration and velocity of the grasped object is difficult in practice. It is well known that the displacement of the rigid body is completely specified by the initial and final positions of three noncolinear points fixed on the object. Similarly, the instantaneous velocity of the rigid body can be determined from the linear velocity of three noncolinear points fixed on the body. Previously developed algorithms are computationally involved by the need to compute several trigonometric functions or matrix inverses. The authors present alternate computationally efficient algorithms for determining the displacement and the velocity of an object handled by a three-fingered robot hand.