Conference Paper

# Exact structured singular value of robotic manipulators andquantitative analysis of passivity based control.

Graduate Sch. of Mech. & Electr. Eng., Chiba Univ.

DOI: 10.1109/IROS.2006.282418 Conference: 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2006, October 9-15, 2006, Beijing, China Source: IEEE Xplore

- Citations (19)
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- Journal of Dynamic Systems Measurement and Control 01/1981; 103(2). · 0.76 Impact Factor
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**ABSTRACT:**This paper addresses trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations and passivity-based control. The main strategy adopted in this paper is to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. After obtaining the error system, tracking control of the original system can be achieved by stabilizing the error system via passivity-based approach. First, a fundamental framework is provided for constructing the error system via generalized canonical transformations. Then a concrete design procedure is derived for a class of electro-mechanical systems. Furthermore, the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness.Automatica 01/2003; · 2.92 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A robot designed to mimic a human becomes kinematically redundant, i.e.its total degrees of freedom becomes larger than the number of physical variables required for description of a given task. Kinematic redundancy may contribute to enhancement of dexterity and versatility, but incurs a problem of ill-posedness of inverse kinematics from the task-description space to the robot joint space. Such ill-posedness of inverse kinematics was originally found by A.N. Bernstein as the 'degrees-of-freedom problem' in physiology, who also pointed out the importance of unveiling the secret of the central nervous system in how nicely it coordinates a skeletomotor system with so many degrees of freedom interacting in complex ways. However, in the history of robotics research, such ill-posedness of inverse kinematics has not yet been tackled directly, but circumvented by introducing an artificial performance index and determining uniquely an inverse kinematics solution by minimizing it. This paper aims at challenging one of Bernstein's problems and proposes a new method for resolving such an ill-posedness problem in a natural way and in a dynamic sense without invoking any artificial performance index. Instead, a novel concept named 'stability on a manifold' is introduced and it is shown that there exists a sensory feedback signal from the task space to the joint space such that it enables the overall closed-loop dynamics to converge naturally and coordinately to a lower-dimensional manifold describing a set of joint states fulfilling a given motion task. This result is also extended by using the concept of 'transferability to a submanifold' in the case of short- or middle-range movement such as a task of multi-joint reaching.Advanced Robotics 01/2005; 19:401-434. · 0.51 Impact Factor

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