Nonholonomic control of 3 link planar manipulator with a free joint

Imura, Jun‐ichi; Kobayashi, Keigo; Yoshikawa, Tsuneo

doi:10.1109/cdc.1996.572714

Cited by 60 publications

(45 citation statements)

References 3 publications

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“…Using the coordinate-and feedback transformation presented in (Imura et al, 1996) in this dynamical system a perturbed second-order chained form is obtainedξ…”

Section: Resultsmentioning

confidence: 99%

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Output Based Control for an Underactuated System: Experimental Results

Steen

Nijmeijer

2005

IFAC Proceedings Volumes

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This paper considers output based tracking control for an experimental underactuated H-drive manipulator. This manipulator can be transformed into a so-called second-order chained form by a coordinate-and feedback transformation. An observer is proposed to solve the output feedback problem for systems in second-order chained form. For the designed observer global stability of the closed loop system is proved. Due to friction in the unactuated rotational joint the closed loop system is no longer asymptotically stable, but with a heuristic modification of the observer both the tracking and observer errors are bounded. Experimental results show the validity of this approach.

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“…Using the coordinate-and feedback transformation presented in (Imura et al, 1996) in this dynamical system a perturbed second-order chained form is obtainedξ…”

Section: Resultsmentioning

confidence: 99%

“…The dynamical system (29) can be transformed into the second-order chained form (1) by the coordinate-and feedback transformation given in (Imura et al, 1996). The relation between ξ and the generalized coordinates q is denoted by…”

Section: Resultsmentioning

confidence: 99%

Output Based Control for an Underactuated System: Experimental Results

Steen

Nijmeijer

2005

IFAC Proceedings Volumes

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“…It can be seen fromq 2 = f 2 + σ 2 τ , thatq 2 = 0 impliesq 1 = 0. Next, q (3) 2 is proportional to τq 1 = 0, and τ remains undetermined asq 1 = 0. Considering an extra derivative, q (4) 2 is proportional to τ 2 = 0 which forces τ = 0.…”

Section: Nonminimum-phase Propertymentioning

confidence: 99%

“…Underactuated mechanical systems have recently gained research attention due to the variety of new problems they have generated [3,10,12]. In most cases, simple control methodologies fail and sophisticated control techniques based on heuristics and empirical observation have been used for the control of such systems [6,7].…”

Section: Introductionmentioning

confidence: 99%

Analysis of exclusively kinetic two-link underactuated mechanical systems

2002

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Analysis of exclusively-kinetic two-link underactuated mechanical systems is undertaken in this paper. It is first shown that such systems are not full-state feedback linearizable around any equilibirium point. Also, the equilibrium points for which the system is small-time locally controllable (STLC) is at most a one dimensional submanifold. A concept less restrictive than STLC, termed the small-time local output controllability (STLOC) is introduced, the satisfaction of which guarantees that a chosen configuration output can be controlled at its desired value. It is shown that the class of systems considered are STLOC, if the inertial coupling between the input and output is non-zero. Also, in such a case, the system is nonminimum phase (NMP). An example section illustrates all results presented.

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“…In [8], the model of a planar PPR manipulator was directly transformed into the ECF (PPR denotes a manipulator with two prismatic joints and one revolute joint at its most distal end; the bar above "R" designates an unactuated or passive joint). Among the two-input, three-DOF systems that are feedback-equivalent to the ECF one finds the planar, vertical take-off and landing (VTOL) system in the absence of gravity [25], a simplified underwater vehicle [22], the planar, serial-drive RRR manipulator [32], and the planar, parallel-drive RRR manipulators with any two joints actuated.…”

mentioning

confidence: 99%

Robust Point Stabilization of Underactuated Mechanical Systems via the Extended Chained Form

Lizárraga¹,

Aneke²,

Nijmeijer³

2004

SIAM J. Control Optim.

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Abstract. This paper addresses point stabilization for the extended chained form (ECF), a control system that may be used to model a number of mechanical underactuated systems. A control law is proposed, based on well-known hybrid open-loop/feedback techniques, which exponentially stabilizes the origin of a dynamic extension of the ECF and ensures a degree of robustness to additive disturbance terms that may represent, for instance, model uncertainties. Numerical simulations are included to illustrate the performance of the presented stabilizers.

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Nonholonomic control of 3 link planar manipulator with a free joint

Cited by 60 publications

References 3 publications

Output Based Control for an Underactuated System: Experimental Results

Output Based Control for an Underactuated System: Experimental Results

Analysis of exclusively kinetic two-link underactuated mechanical systems

Robust Point Stabilization of Underactuated Mechanical Systems via the Extended Chained Form

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