Abstract
In this paper, a novel constraint-following control for uncertain robot manipulators that is inspired by analytical dynamics is developed. The motion can be regarded as external constraints of the system. However, it is not easy to obtain explicit equations for dynamic modeling of constrained systems. For a multibody system subject to motion constraints, it is a common practice to introduce Lagrange multipliers, but using these to obtain explicit dynamical equations is a very difficult task. In order to obtain such equations more simply, motion constraints are handled here using the Udwadia-Kalaba equation(UKE). Then, considering real-life robot manipulators are usually uncertain(but bounded), by using continuous controllers compensate for the uncertainties. No linearizations/approximations of the robot manipulators systems are made throughout, and the tracking errors are bounds. A redundant manipulator of the SCARA type as the example to illustrates the methodology. Numerical results are demonstrates the simplicity and ease of implementation of the methodology.
Highlights
The main methods currently used for dynamic modeling of robot manipulators with motion constraints are the Newton–Euler method [1,2,3], Lagrange’s method [4,5], and Kane’s method [6]
The fundamental vector projection of the main force and the inertial force of the system is extended directly to derive the equations of motion. With this method, these dynamical equations cannot be obtained in the appropriate analytical form for a constrained mechanical system
The task description is given by the end-effector of robot manipulators trajectory as constraint with h(q, t) = f (q(t)) − xd (t) = x(t) −
Summary
The main methods currently used for dynamic modeling of robot manipulators with motion constraints are the Newton–Euler method [1,2,3], Lagrange’s method [4,5], and Kane’s method [6]. For a multibody system with motion constraints, Lagrange’s method can be used, generally with the introduction of Lagrange multipliers, a widely used technique for constrained systems Controlling these multipliers is difficult, and the approach is not very well suited for symbolic considerations. The fundamental vector projection of the main force and the inertial force of the system is extended directly to derive the equations of motion With this method, these dynamical equations cannot be obtained in the appropriate analytical form for a constrained mechanical system. This equation takes constraints into account in the dynamical equation and involves the generalized Moore–Penrose inverse [19] It provides a simple and general explicit equation of motion for constrained mechanical systems without the need for Lagrange multipliers [14,20].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
