Calibration of manipulator kinematics: a singularity theory approach

The calibration of manipulator kinematics subject to both geometric and nongeometric variations is addressed. A general definition of calibration is introduced, based on the concept of the group action. A specific calibration method is proposed, called calibration by diffeomorphisms. For calibration by diffeomorphisms, the existence of calibrating transformations has been shown to be equivalent to the structural stability of the nominal kinematics. In the case of parametric variations of kinematics of either geometric or nongeometric origin, the calibration by diffeomorphisms has yielded approximate affine calibrating transformations defined as solutions to a homological equation. For structurally stable nominal kinematics, the homological equation is solvable and provides calibrating transformations defined globally, applicable to both nonsingular and singular kinematics. The affine calibrating transformations have been illustrated with examples including general 2R position kinematics.