Interval Analysis of Kinematic Errors in Serial Manipulators Using Product of Exponentials Formula

This paper proposes a methodology for analysis of kinematic errors in robotic manipulators. The approach is based on interval analysis and predicts end-effector pose deviation from its ideal model using the interval bounds on the errors of the individual axes. In contrast to sampling-based Monte Carlo methods, the proposed methodology offers guaranteed bounds for the error that accumulates at the end-effector. The forward kinematics map is extended to intervals using the product of exponentials formulation with interval joint parameters. This is a convenient method that incorporates both analytical and computational techniques and can be used for error analysis, or inversely, for manipulator design. Simulation and experimental results confirm that the calculated interval bounds fully enclose the end-effector error distribution and provide a measure of its volumetric size. An important application of this method is in the design of modular precision manipulators that can be assembled using individual linear and rotary stages.