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Characteristics analysis and stabilization of a planar 2R underactuated manipulator

Published online by Cambridge University Press:  09 July 2014

Guang-Ping He
Affiliation:
Department of Mechanical and Electrical Engineering, North China University of Technology, Beijing 100144, P. R. China State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, P. R. China
Zhi-Lü Wang
Affiliation:
Department of Mechanical and Electrical Engineering, North China University of Technology, Beijing 100144, P. R. China
Jie Zhang
Affiliation:
Department of Mechanical and Electrical Engineering, North China University of Technology, Beijing 100144, P. R. China
Zhi-Yong Geng
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, P. R. China
Corresponding
E-mail address:

Summary

The weightless planar 2R underactuated manipulators with passive last joint are considered in this paper for investigating a feasible method to stabilize the system, which is a second-order nonholonomic-constraint mechanical system with drifts. The characteristics including the controllability of the linear approximation model, the minimum phase property, the Small Time Local Controllability (STLC), the differential flatness, and the exactly nilpotentizable properties, are analyzed. Unfortunately, these negative characteristics indicate that the simplest underactuated mechanical system is difficult to design a stable closed-loop control system. In this paper, nilpotent approximation and iterative steering methods are utilized to solve the problem. A globally effective nilpotent approximation model is developed and the parameterized polynomial input is adopted to stabilize the system to its non-singularity equilibrium configuration. In accordance with this scheme, it is shown that designing a stable closed-loop control system for the underactuated mechanical system can be ascribed to solving a set of nonlinear algebraic equations. If the nonlinear algebraic equations are solvable, then the controller is asymptotically stable. Some numerical simulations demonstrate the effectiveness of the presented approach.

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Copyright
Copyright © Cambridge University Press 2014 

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