Compensation of Robot joint variables using special Jacobian matrices

摘要

Abstract In dealing with an industrial manipulator, the end‐effector accuracy is a major concern. The positioning of the end effector is determined by the controller that utilizes the data from a closed‐form kinematic inversion. The closed‐form inversion uses nominal, i.e., manufacturer specified, values of link lengths, twists, and offsets. Due to manufacturing tolerances, set‐up, and usage, these nominal parameters may be inaccurate. If the nominal parameters contain built‐in error values, the closed‐form kinematic inversion will yield incorrect joint values, and the actual end‐effector position will deviate from its desired position. One may use a parameter identification method to identify the position‐independent error parameter values. This article assumes that this has been done and it presents an iterative compensation algorithm (ICA) through which the identified position‐independent parameter error values may be used to correct the joint values obtained through the closed‐form kinematic inversion. The Denavit and Hartenberg (D‐H) parameters (θ s α a ) are used to model the given M ‐jointed manipulator, and a set of four special Jacobian matrices ( J θ , J s , J α , and J a ) are formulated. The iterative compensation algorithm allows one to determine the M unknown position‐dependent joint error values by using these four special Jacobian matrices. The improvements obtained through the use of the compensation algorithm will be presented for regular trajectories, as well as when the robot nears certain singularity conditions. Since it is important to know a priori a definite number of iterations that must be performed, the level of compensation after a fixed number of iterations is also studied. Through the presentation of numerous examples, it is shown that the proposed compensation algorithm is simple and straightforward to implement, and it increases the end‐effector accuracy.