Calibration for mobile robots with an invariant Jacobian

The kinematics of some mobile robots is described through a strictly invariant Jacobian matrix [J][J]. This is the case for robots with three degrees of freedom and suitable omnidirectional wheels, and that for robots with conventional wheels and differential kinematics. This article proposes a calibration technique for the matrix [J][J] of such robots. It is based on four accurate configuration measurements associated with particular nominal motions where the generalized velocities maintain a constant proportional relationship. As a consequence, the nominal trajectories are arcs of circumference and may be part of the actual trajectories of the robot. An application example is presented.