Simultaneous Control of Position and Orientation for Ball-Plate Manipulation Problem Based on Time-State Control Form

Date, Hisashi; Sampei, Mitsuji; Ishikawa, Masato; Koga, Masanobu

doi:10.1109/tra.2004.825267

Cited by 43 publications

(26 citation statements)

References 20 publications

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“…Recently, feedback control of the plate-ball manipulation system was also independently addressed in [7] and [28]. In these works, however, only local convergence, not asymptotic stability in the sense of Lyapunov, is shown.…”

Section: Case Study: the Plate-ball Systemmentioning

confidence: 99%

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A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism

Oriolo

Vendittelli

2005

IEEE Trans. Robot.

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Abstract-We present a framework for the stabilization of nonholonomic systems that do not possess special properties such as flatness or exact nilpotentizability. Our approach makes use of two tools: an iterative control scheme and a nilpotent approximation of the system dynamics. The latter is used to compute an approximate steering control which, repeatedly applied to the system, guarantees asymptotic stability with exponential convergence to any desired set point, under appropriate conditions. For illustration, we apply the proposed strategy to design a stabilizing controller for the plate-ball manipulation system, a canonical example of nonflat nonholonomic mechanism. The theoretical performance and robustness of the controller are confirmed by simulations, both in the nominal case and in the presence of a perturbation on the ball radius.Index Terms-Iterative steering (IS), nilpotent approximations (NAs), nonholonomic systems, plate-ball mechanism, stabilization.

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Section: Case Study: the Plate-ball Systemmentioning

confidence: 99%

“…We shall not pursue this approach for two reasons. First, such a modification is not trivial 7 and may even prove impossible for some planners. Second, we wish to explore the potential of the stabilization strategy presented in Section IV.…”

Section: A Kinematic Modelmentioning

confidence: 99%

A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism

Oriolo

Vendittelli

2005

IEEE Trans. Robot.

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“…The simplest example of such systems is found in the case of 2 inputs and 5 states with secondorder controllability structure, which we call the crosschained system in this paper. This system is not only stimulating from theoretical viewpoint, but also includes interesting physical applications, such as rolling sphere control [7], 3-link snake robot [9], double trailer system with off-axle hitch [17], attitude control of free-flying robot with two actuators [16]. So far, the quest for definitive control method for this system is still on the way; the author proposed a control algorithm based on generator-switching and extended time-state control form [8], but its convergence analysis was not sufficient.…”

Section: Introductionmentioning

confidence: 99%

Finite-time control of cross-chained nonholomic systems by switched state feedback

Ishikawa

Astolfi

2008

2008 47th IEEE Conference on Decision and Control

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This paper is concerned with the control problem of a class of nonholonomic systems having cross-chained structure. Such systems are structurally incompatible with the chained systems, so the conventional methods proposed for chained systems are not valid any more and an entirely new control approach is required. In this paper, we propose a switched state feedback law which delivers the initial state to the origin in finite time using bounded control inputs, without infinitely high gain and frequent switchings in spite of its discontinuity. The effectiveness of the proposed method is shown by numerical simulations. Possible mechanical applications of this study include snake robots, rolling sphere problem and attitude control of free-flying robots.

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“…As far as the driftless (kinematic) problems are concerned, there have already been several studies on both feedforward and feedback control of nonholonomic rolling contact systems [5]. However, the proposed model of the spherical USM is essentially dynamic, in the sense that it undergoes indispensable influence of the 'drift' term.…”

Section: Introductionmentioning

confidence: 99%

Modeling and control of spherical ultrasonic motor based on nonholonomic mechanics

Ishikawa

Kinouchi

2008

2008 IEEE/RSJ International Conference on Intelligent Robots and Systems

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In this paper, we propose a new dynamical model of a spherical multi-degree-of-freedom (DOF) ultrasonic motor (USM) and its fundamental control method based on nonholonomic mechanics. This system is analogous to the so-called rolling sphere manipulation system as far as the kinematics is concerned, but there is also an indispensable influence of the momentum dynamics. We propose multi-cycle phase switching (MCPS) method to keep this influence under control, using only two pieces of piezoelectric oscillators for bending vibrations rather than three including a longitudinal vibration as required in the conventional methods.

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Simultaneous Control of Position and Orientation for Ball-Plate Manipulation Problem Based on Time-State Control Form

Cited by 43 publications

References 20 publications

A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism

A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism

Finite-time control of cross-chained nonholomic systems by switched state feedback

Modeling and control of spherical ultrasonic motor based on nonholonomic mechanics

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