Compensation of kinematic errors using kinematic sensitivities

Two approaches for the compensation of the position and orientation errors of robot manipulators due to variations of geometric parameters are considered. The first approach is based on the correction of the joint displacements obtained by using nominal inverse kinematics for desired position and orientation, while the second approach is based on redefining the desired position and orientation before applying the nominal inverse kinematics. It is shown that both approaches are equivalent in terms of compensation effect if the parameter variations are sufficiently small. However, the second approach does not require computation of the inverse Jacobian and can be used in the singular configurations of the manipulator. For computation of the position and orientation errors, which are required in both approaches, kinematic sensitivity functions are used. This eliminates the need for kinematic models, which considerably improves the time efficiency of the compensation algorithms. Closed-form expressions for kinematic compensation are derived for the PUMA manipulator