Abstract
Reduction of contour error is a very important issue for high precise contour tracking applications, and many control systems were proposed to deal with contour tracking problems for two/three axial translational motion systems. However, there is no research on cross-coupled contour tracking control for serial multi-DOF robot manipulators. In this paper, the contouring control of multi-DOF serial manipulators is developed for the first time and a new cross-coupled PD (CC-PD) control law is proposed, based on contour errors of the end-effector and tracking errors of the joints. It is a combination of PD control for trajectory tracking at joint level and PD control for contour tracking at the end-effector level. The contour error of the end-effector is transformed to the equivalent tracking errors of the joints using the Jacobian regulation, and the CC-PD control law is implemented in the joint level. Stability analysis of the proposed CC-PD control system is conducted using the Lyapunov method, followed by some simulation studies for linear and nonlinear contour tracking to verify the effectiveness of the proposed CC-PD control system.
Highlights
Robotic manipulators are important for automation and industrial applications in contour tracking and trajectory tracking
Reducing tracking error does not ensure reducing the contour error, because the contour error is a result of combined tracking errors of all axes or joints, and the dynamics of each axis is coupled with other axes for a nonlinear robotic system
From Equation (9), one can see that the proposed cross-coupled PD (CC-PD) is a combination of PD control in the joint space based on the tracking errors and PD control in the task space based on the contour errors
Summary
Robotic manipulators are important for automation and industrial applications in contour tracking and trajectory tracking. One of the most important issues in machining is the reduction of contour errors to ensure the quality of machined parts In robotic applications such as precision machining, a desired task is often defined in terms of the end-effector (task space) motion: contour tracking motion [10,11]. To deal with contour tracking problems, the cross coupling control (CCC) method was first developed by Koren [1] for translational motion systems, followed by a variable-gain CCC in [2]. Algorithms 2016, 9, 81 type cross coupling controller was developed for contour tracking of a linear bi-axis motion system based on linear control theory in [3]. The main motivation of this research is to develop a contouring control system, called cross coupled PD (CC-PD) control, for multi-DOF robot manipulators with the combination of joint error and contour error as the feedback signals [19]. In the developed CC-PD control system, the contour errors in the end-effector are transformed to the equivalent tracking errors in the joint level through the Jacobian regulation [10], and the control law is implemented in the joint level to simplify the control system design and its implementation
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