Linear controllers for exponential tracking of systems in chained-form

Lefeber, Erjen; Robertsson, Anders; Nijmeijer, Henk

doi:10.1002/(sici)1099-1239(20000415)10:4<243::aid-rnc472>3.0.co;2-p

Cited by 46 publications

(36 citation statements)

References 31 publications

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“…This is not true in general. However, global uniform asymptotic stability (GUAS) of (19) is proved in (Lefeber et al, 2000, Theorem 2.7) under three assumptions.…”

Section: Cascaded Systemsmentioning

confidence: 99%

“…The control of nonholonomic systems has received a lot of attention in the last decades (Kolmanovsky and McClamroch, 1995;Lefeber et al, 2000;Aneke et al, 2003b;Behal et al, 2002;Ma et al, 2002). Here attention will be drawn to underactuated mechanical systems with acceleration constraints (Reyhanoglu et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

“…This is done by making use of properties for systems in cascaded form, as defined in (Panteley and Loria, 1998), which make it possible to divide the nonlinear system into a linear part and a linear time-varying part. In this way, this work forms an extension of (Lefeber et al, 2000), where the same problem is addressed for first order chained form systems. The controller/observer combination is validated on an experimental set-up consisting of an underactuated H-drive manipulator with a freely rotating arm.…”

Section: Introductionmentioning

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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“…This is not true in general. However, global uniform asymptotic stability (GUAS) of (19) is proved in (Lefeber et al, 2000, Theorem 2.7) under three assumptions.…”

Section: Cascaded Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Based on the kinematic model or dynamic model of nonholonomic systems, the tracking problem can be classified as either kinematic tracking or dynamic tracking problem. For the kinematic tracking problem, where the systems are represented by their kinematic models and velocity acts as the control input, several methods have been proposed in [3] [4]. In practice, however, it is more realistic to formulate the nonholonomic system control problem at the dynamic level, where the torque and force are taken as the control inputs.…”

Section: Introductionmentioning

confidence: 99%

Approximation Based Adaptive Tracking Control of Uncertain Nonholonomic Mechanical Systems

Wang

Obeng

et al. 2009

Control and Intelligent Systems

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Abstract-In this paper, the trajectory tracking control problem of uncertain nonholonomic mechanical systems is investigated. By separately considering kinematic and dynamic models of a nonholonomic mechanical system, a new adaptive tracking control is proposed based on neural network approximation. The proposed design consists of two steps. First, the nonholonomic kinematic subsystem is transformed into a chained form, and the corresponding optimal control is derived. Second, an adaptive neural control is designed for the dynamic subsystem to make the outputs of the dynamic subsystem asymptotically track the optimal control signals chosen for the kinematic subsystem. The proposed control is simulated on a unicycle wheeled mobile robot.

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“…A problem of motion planning with measurements of the position coordinates was solved in Guillaume and Rouchon (1998) and Jiang and Nijmeijer (1999). Results concerning a position error observer were presented in Lefeber (2000) and Lefeber et al (2001). In Jakubiak et al (2002) an output-feedback trajectory tracking controller was developed under the assumption that one of the tracking error coordinates is unknown.…”

Section: Introductionmentioning

confidence: 99%

An observer-controller combination for a unicycle mobile robot

Noijen

Lambrechts²,

Nijmeijer

2005

International Journal of Control

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This paper considers the problem of output feedback trajectory tracking with a unicycle mobile robot system. A state-feedback controller for the non-linear error dynamics of the robot is combined with an observer that estimates the orientation error based on available trajectory information and measurement of the position coordinates. A stability analysis, derivation and implementation of the resulting controller is given and tested on an experimental mobile robot.

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Linear controllers for exponential tracking of systems in chained-form

Cited by 46 publications

References 31 publications

Output Based Control for an Underactuated System: Experimental Results

Output Based Control for an Underactuated System: Experimental Results

Approximation Based Adaptive Tracking Control of Uncertain Nonholonomic Mechanical Systems

An observer-controller combination for a unicycle mobile robot

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