Influence of parallel kinematic machine dimensional tolerances on the estimation of payload inertia

Estimating the inertial parameters of a rigid body linked to the end effector of a parallel kinematic machine may be useful in many applications (e.g., set-up of control parameters, orientation estimation, inertial compensation). The quality of the estimation depends on different aspects such as the implemented method, the excitation movement trajectories and the disturbances of the input signals. The model inputs are generally the forces and torques at the interface between the end effector and the workpiece under estimation, commonly measured through a 6-axis load cell, and the related motion. However, when evaluating the imposed motion based on the motion of the actuators, rather than the most common adoption of an Inertial Measurement Unit for direct measurement, geometrical tolerances of the machine links are likely to affect the identification results, since they introduce uncertainty in the terms of the Jacobian matrix.The paper studies the influence of the variability of the robot link lengths on the accuracy in the estimation of the inertial properties of the payload, when the end effector motion is evaluated based on the actuator motion and forward kinematics. It is found that, under a certain limit of geometrical tolerances, the error in the estimation of the center of gravity and inertia tensor can be contained to acceptable values, comparable to those achievable through direct measurement of the end effector motion.For a given geometrical error in the link lengths, the influence of the excitation trajectory (i.e. matrix conditioning number) on the identification error is also addressed. Finally, the analysis points out how much the accelerations used as input can differ from the real ones, which is useful information to size the sensitivity of the IMU sensor to be used when direct measurement is possible or required.