Research On Kinematic Calibration Of Serial Mechanisms Based On Product-of-Exponential Formula

In order to improve absolute accuracy of the digitalized stereotactic apparatus without increasing manufacturing costs excessively, kinematic calibration for serial mechanisms has been investigated. As a key procedure of kinematic calibration, the kinematic parameter identification of serial mechanisms is focused on in this dissertation. Although product-of-exponential formula (POE formula) has many advantages over the other kinematic modeling methods, such few researches have given close attention to the kinematic parameter identification based on POE formula that:1) It is still not clear that whether the error model based on POE formula is involved in any redundant parameters or not.2) The POE formula has not been introduced into kinematic identification based on each joint trajectory. Not only implementation and procefure of the kinematic parameter identifcation based on POE formula was presented, but also some simulations and experiments have been conducted in this dissertation. The main contributions of this dissertation are as follows:To clearify the identifiability of parameters in error model based on POE formula, the explicit-form error model was built for serial mechanisms after some existing approaches to solving the differential of the exponential map at twist have been analyzed. Then, the identifiability of parameters in this error model was analyzed by the linear dependence of vectors in the identification Jacobian matrix, and three practicable error models were obtained. The analysis shows that:(1) Errors in all joint twists are identifiable. (2) If the matrix formed by all joint twists is full column rank, the joint zero-position errors can be identified.The iterative least-squares algorithm was proved to be convergent by using the characteristic of exponential map and logarithm map, which is the important part of identification algorithm based on error modeling method.The POE formula was introduced into kinematic identification based on each joint trajectory. The procedure of kinematic identification was presented. The experiment has been conducted to demonstrate the feasibility and effectiveness of this method. This method has an advantage over the other this type of kinematic identification:joint twists and joint motion resolutions can be directly obtained from joint trajectories without the complicated procedures of the link coordinate frames'reconstruction.Simulation results show that all kinematic parameters of common industrial robots and CMM are identifiable under the ideal experimental condition. In comparison to the simulation results in references, the identified results are closer to the true values with the suggested method. The number of measurement configurations, measurement noise and the initial values of iterative calculation, which are the influence factors on kinematic identification, are also analyzed. Although the identification algorithm was in some bad situations, such as few measurement configurations, injected measurement noise or big deviations between the computational initial values and the presetted true values, the algorithm is robust.The experimental results of calibrating the digitalized stereotactic apparatus show that the kinematic parameter identification based on either error modeling or joint trajectory is effective and practicable. After the kinematic parameter identification, the position error and the mesuring distance error of digitalized stereotactic apparatus is reduced from 1.87 mm to 1.04 mm and from 1.02 mm to 0.46 mm respectively, which meets the requirement of design.According to the study, three practical error models based on the exponential product formula were established, which are in explicit expressions. The exponential product formula was introduced into the kinematic parameter identification based on joint trajectories. The condition of identifying the joint zero-position errors was illustrated. The least-squares iterative algorithm using the exponential product formula based error model was proved to be convergent. Simulation and experiment results show that the two kinematic parameter identification methods are versatile and practical.