Title: Nonlinear controllability of an underactuated two-link manipulator

Authors: Chenzi Huang; Klaus Röbenack; Carsten Knoll

Addresses: Faculty of Electrical and Computer Engineering, Institute of Control Theory, Technische Universität Dresden, 01062 Dresden, Germany ' Faculty of Electrical and Computer Engineering, Institute of Control Theory, Technische Universität Dresden, 01062 Dresden, Germany ' Faculty of Electrical and Computer Engineering, Institute of Control Theory, Technische Universität Dresden, 01062 Dresden, Germany

Abstract: In this contribution, we show the global controllability of an underactuated two-link manipulator model using the characteristic of the system's drift vector field and weak Poisson stability. The main idea is to proof the general possibility to let the system return to its starting equilibrium point even though the state space is not compact. After this analysis, a control method based on the controllability property of the system is suggested. More precisely, we concatenate flows of vector field of the system to generate appropriate constant input values. This method is especially useful for underactuated systems which fail to meet the so-called Brockett condition.

Keywords: Nonlinear controllability; underactuated mechanical systems; two-link manipulator; weakly positive Poisson stability; drift vector field; Poincaré's recurrence theorem; piecewise constant input; finite horizon control.

DOI: 10.1504/IJDSSS.2017.088208

International Journal of Digital Signals and Smart Systems, 2017 Vol.1 No.3, pp.239 - 252

Available online: 28 Nov 2017 *

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