This chapter discusses how to determine the kinematic parameters and the inertial parameters of robot manipulators. Both instances of model identification are cast into a common framework of least-squares parameter estimation, and are shown to have common numerical issues relating to the identifiability of parameters, adequacy of the measurement sets, and numerical robustness. These discussions are generic to any parameter estimation problem, and can be applied in other contexts.
For kinematic calibration, the main aim is to identify the geometric Denavit–Hartenberg (DH) parameters, although joint-based parameters relating to the sensing and transmission elements can also be identified. Endpoint sensing or endpoint constraints can provide equivalent calibration equations. By casting all calibration methods as closed-loop calibration, the calibration index categorizes methods in terms of how many equations per pose are generated.
Inertial parameters may be estimated through the execution of a trajectory while sensing one or more components of force/torque at a joint. Load estimation of a handheld object is simplest because of full mobility and full wrist force-torque sensing. For link inertial parameter estimation, restricted mobility of links nearer the base as well as sensing only the joint torque means that not all inertial parameters can be identified. Those that can be identified are those that affect joint torque, although they may appear in complicated linear combinations.
Calibration and accuracy validation of a FANUC LR Mate 200iC industrial robot
Author Ilian Bonev
Video ID : 430
This video shows excerpts from the process of calibrating a FANUC LR Mate 200iC industrial robot using two different methods.
In the first method, the position of one of three points on the robot end-effector is measured using a FARO laser tracker in 50 specially selected robot configurations (not shown in the video). Then, the robot parameters are identified. Next, the position of one of the three points on the robot's end-effector is measured using the laser tracker in 10,000 completely arbitrary robot configurations. The mean positioning error after calibration was found to be 0.156 mm, the standard deviation (std) 0.067 mm, the mean+3*std 0.356 mm, and the maximum 0.490 mm.
In the second method, the complete pose (position and orientation) of the robot end-effector is measured in about 60 robot configurations using an innovative method based on Renishaw's telescoping ballbar. Then, the robot parameters are identified. Next, the position of one of the three points on the robot's end-effector is measured using the laser tracker in 10,000 completely arbitrary robot configurations. The mean position error after calibration was found to be 0.479 mm, the standard deviation (std) 0.214 mm, and the maximum 1.039 mm. However, if we limit the zone for validations, the accuracy of the robot is much better.
The second calibration method is less efficient but relies on a piece of equipment that costs only $12,000 (only one tenth the cost of a laser tracker).