Path Following for a Class of Mechanical Systems

Hladio, Andre; Nielsen, Christopher; Wang, David

doi:10.1109/tcst.2012.2223470

Cited by 52 publications

(72 citation statements)

References 20 publications

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“…In this section we review the path following control design methodology from [13] which applies to a large class of mechanical systems. In Section IV we show that our 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) November 3-7, 2013.…”

Section: Path Following For Mechanical Systemsmentioning

confidence: 99%

“…The objective in path following is to design a feedback control law so that the output (2) of the closed-loop system follows a given, smooth parametrized curve σ : R → R p . In [13] geometric restrictions on the allowable class of curves are imposed.…”

Section: A Tfl For Mechanical Systemsmentioning

confidence: 99%

“…Assumption 2 requires that the entire path be represented as the zero level set of a smooth function s : R p → R p−1 in the output space of the system (2), and that its Jacobian is full rank at each point of the curve γ. Locally this is always possible if Assumption 1 holds [13].…”

Section: A Tfl For Mechanical Systemsmentioning

confidence: 99%

“…This inspired the work in [12] in which an arbitrary non-periodic path in the output space can be made attractive and invariant using transverse feedback linzearization (TFL). This idea was further extended in [13] by providing conditions for which desired motions can be achieved on the path; as opposed to orbital stabilization where a limit cycle is forced in the closed loop system. This simplifies the controller design and decomposes the path following design problem into two independent sub-problems: staying on the path and moving along the path (summarized in Section II).…”

Section: Introductionmentioning

confidence: 99%

“…This simplifies the controller design and decomposes the path following design problem into two independent sub-problems: staying on the path and moving along the path (summarized in Section II). However, in [13], perfect knowledge of the dynamic parameters of the system was assumed, and performance was demonstrated only for a linear, decoupled system. In this paper, the TFL approach is applied to a nonlinear, coupled manipulator system, and a robust controller is developed to overcome modelling inaccuracies.…”

Section: Introductionmentioning

confidence: 99%

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Robust path following for robot manipulators

Gill

Kulić

Nielsen

2013

2013 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-Path following controllers make the output of a control system approach and traverse a pre-specified path with no a priori time-parametrization. This paper implements a path following controller, based on transverse feedback linearization (TFL), which guarantees invariance of the path to be followed. The coordinate and feedback transformation employed allows one to easily design control laws to generate arbitrary desired motions on the path for the closed-loop system. The approach is applied to an uncertain and simplified model of a robot manipulator for which none of the dynamic parameters are measured. The controller is made robust to modelling uncertainties using Lyapunov redesign. The robustified controller is tested on a 4-degree-of-freedom (4-DOF) manipulator with a combination of revolute and linear actuated links. The experimental results show a substantial improvement when using the robust controller for path following versus standard state feedback.

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Section: Path Following For Mechanical Systemsmentioning

confidence: 99%

Section: A Tfl For Mechanical Systemsmentioning

confidence: 99%

Section: A Tfl For Mechanical Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust path following for robot manipulators

Gill

Kulić

Nielsen

2013

2013 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Path following of a class of underactuated mechanical systems via immersion and invariance‐based orbital stabilization

Manchester

Siguerdidjane

2020

Intl J Robust & Nonlinear

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This article aims to provide a new problem formulation of path following for mechanical systems without time parameterization nor guidance laws, namely, we express the control objective as an orbital stabilization problem. It is shown that it is possible to adapt the immersion and invariance technique to design static state-feedback controllers that solve this problem. In particular, we select the target dynamics adopting the recently introduced Mexican sombrero energy assignment method. To demonstrate the effectiveness of the proposed method we apply it to control underactuated marine surface vessels. K E Y W O R D S energy shaping, immersion and invariance, orbital stabilization, path following 1 INTRODUCTION Tracking a geometric path in mechanical systems is a task often encountered in various application fields, for example, robotics, aerospace, and autonomous vehicles. There are two approaches to formulate this problem, depending on whether the predefined path is parameterized by time or not, and they are known as trajectory tracking or path following, respectively. The former approach largely dominates the control literature and it has been extensively studied. Unfortunately, for nonminimum phase systems, which are common in these applications, the achievable performance has a fundamental limitation, first identified in Reference 1. It is possible to circumvent this limitation removing the time

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Singularity Robust Inverse Kinematics of Serial Manipulators by Means of a Joint Arc Length Parameterization

Marauli

Gattringer

Müller

2022

Mechanisms and Machine Science

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The inverse kinematics problem is ill-posed near kinematic singularities leading to extremely large joint velocities. This classical problem is addressed from a different perspective; instead of prescribing the end-effector (EE) motion in terms of a path parameter, the motion is parameterized in terms of the arc length in joint space. This allows tackling the inverse kinematics problem when approaching kinematic singularities. Thereupon a singularity consistent sampling scheme can easily be devised. A sampling of the arc length gives direct control over the joint motion for prescribed EE motion. The arc length parameterization can be used for solving the (time) optimal path following problem, avoiding the ill-conditioning upfront.

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Path Following for a Class of Mechanical Systems

Cited by 52 publications

References 20 publications

Robust path following for robot manipulators

Robust path following for robot manipulators

Path following of a class of underactuated mechanical systems via immersion and invariance‐based orbital stabilization

Singularity Robust Inverse Kinematics of Serial Manipulators by Means of a Joint Arc Length Parameterization

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