Dynamics Modeling, Control System Design and Simulation of Manipulator Based on Lagrange Equation
To improve the servo performance of the manipulator and further obtain higher motion accuracy, dynamics equation of the series manipulator is developed based on Lagrange dynamics method. Simultaneously, the control algorithm is studied to ensure the error
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Abstract To improve the servo performance of the manipulator and further obtain higher motion accuracy, dynamics equation of the series manipulator is developed based on Lagrange dynamics method. Simultaneously, the control algorithm is studied to ensure the error system is globally asymptotically stable near the equilibrium point. With full consideration of the dynamic characteristics of the system, a controller is designed and the control system simulation model is established subsequently. The simulation results show that the controller designed in this paper has good dynamic and static performances, the manipulator system can follow the control directives effectively with the tracking error of joint angles limited to 10-5 rad. Methods of dynamics modeling, controller design and control system simulation are universal to the multi-degree-of-freedom series manipulators, which has a certain reference value for the research of similar mechanisms. Keywords Manipulator
Lagrange equation Control system Simulation
1 Introduction With the rapid development of microelectronic technology, sensor technology, control theory and machinery manufacturing technology, the automation and intelligence of manufacturing industry are gradually improved and higher requirements to digital performance of manufacturing equipment are also put forward. As the typical joint type robots, manipulators have been widely used in D. Li (&) H. Hong X. Jiang College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410073, China e-mail: [email protected] H. Hong e-mail: [email protected] X. Jiang e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 X. Zhang et al. (eds.), Mechanism and Machine Science, Lecture Notes in Electrical Engineering 408, DOI 10.1007/978-981-10-2875-5_91
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industrial production with the advantages of compact structure, small space occupation, large movement space and so on. Therefore, it is an important research direction in the field of mechanical arms to establish its dynamic model and explore the general method of controller design. Methods on dynamics modeling, control and simulation of manipulators are in varied forms, and the related research is also a lot. In paper [1], the kinematic model of the robot manipulator is established by D-H parameters. Based on the Newton-Euler iterative dynamics algorithms, the forward and inverse dynamic simulation is done by Robotics Toolbox in MATLAB; Paper [2] and [3] simplify the multi-input and strongly coupled manipulator as a single output decoupled servo control system in the process of modeling and controller design, which ignore its dynamic characteristics. The control structure is shown in Fig. 1. Under the _ its control quality is limited because of the control principle s ¼ Kp ðhd hÞ Kv h, idealized assumption; Based on the principle of multi-rigid body kinematics and Lagrange dynamics equations of the manipulator, paper [4] obtains its Jacobian matrix and proposes the 3D
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