Dynamics modeling of nonholonomic mechanical systems: Theory and applications

Jarzębowska, Elżbieta

doi:10.1016/j.na.2005.02.092

Cited by 13 publications

(16 citation statements)

References 9 publications

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“…The analytical approach to dynamics modelling and control of constrained systems starts from the formulation of a unified representation of constraints [11,12], which is…”

Section: Multi-purpose Modelling Framework For Constrained Mechanicalmentioning

confidence: 99%

“…The reference motion is based upon kinematics and the control dynamics is given by (11). The acceleration profile for setting C(t) = 0.5 is presented in Figure 7.…”

Section: Example -Control a Manipulator End-effector Acceleration Changementioning

confidence: 99%

“…With this adopted as the guideline to the paper, a multi-purpose modelling framework for complex mechanical systems is presented. It is based on the latest dynamics modelling method, that is, on the generalized programmed motion equations (GPME) method [11,12]. It enables one to derive motion equations for complex systems subjected to high-order constraints.…”

Section: Introductionmentioning

confidence: 99%

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Model-based control of a third-order nonholonomic system

Jarzębowska

Szklarz

2016

Mathematics and Mechanics of Solids

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This paper addresses dynamics modelling and control of mechanical systems subjected to constraints due to the tasks they are to perform. The researched problem refers to the control of a manipulator end-effector motion subjected to a constraint on an acceleration change, that is, jerk. In the presented approach, the acceleration and jerk constraints are incorporated into a system constrained dynamics and then passed to its control dynamics using a unified approach, which is based on an advanced dynamics modelling method, that is, on the generalized programmed motion equations method. This enables one to derive motion equations for systems subjected to high-order constraints. The novelty of this approach consists of the formulation of a unified representation of constraints by differential equations, merging them into system constrained dynamics and then using nonlinear control theory techniques to design controllers for tracking motions along the pre-specified constraints.

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“…The analytical approach to dynamics modelling and control of constrained systems starts from the formulation of a unified representation of constraints [11,12], which is…”

Section: Multi-purpose Modelling Framework For Constrained Mechanicalmentioning

confidence: 99%

“…The reference motion is based upon kinematics and the control dynamics is given by (11). The acceleration profile for setting C(t) = 0.5 is presented in Figure 7.…”

Section: Example -Control a Manipulator End-effector Acceleration Changementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Model-based control of a third-order nonholonomic system

Jarzębowska

Szklarz

2016

Mathematics and Mechanics of Solids

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“…Recently, a method of the derivation of equations of motion of systems with nonholonomic constraints of high-order has been developed. This is a generalized programmed motion equations (GPME) method [5,6]. The high-order constraints are referred to as programmed, since they are put by a designer to specify tasks that systems have to perform or they may arise from design and control objectives [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…This is a generalized programmed motion equations (GPME) method [5,6]. The high-order constraints are referred to as programmed, since they are put by a designer to specify tasks that systems have to perform or they may arise from design and control objectives [5][6][7]. They are non-material constraints in contrast to materials that are given by nature.…”

Section: Introductionmentioning

confidence: 99%

Stabilizability and Motion Tracking Conditions for Mechanical Nonholonomic Control Systems

Jarzębowska

2007

Mathematical Problems in Engineering

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This paper addresses formulation of stabilizability and motion tracking conditions for mechanical systems from the point of view of constraints put on them. We present a new classification of constraints, which includes nonholonomic constraints that arise in both mechanics and control. Based on our classification we develop kinematic and dynamic control models of systems subjected to these constraints. We demonstrate that a property of being a “hard-to-control” nonholonomic system may not be related to the nature of the constraints. It may result from the formulation of control objectives for a system. We examine two control objectives which are stabilization to the target equilibrium by a continuous static state feedback control and motion tracking. Theory is illustrated with examples of control objective formulations for systems with constraints of various types.

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Dynamics modeling method dedicated to system models with open- and closed-loop structures subjected to kinematic and task based constraints

2023

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The paper presents a development of an automated computational procedure for constrained dynamics (CoPCoD) dedicated to derivation of dynamical models of mechanical systems, e.g. manipulators, both ground and space or mobile robotic systems, which can be composed of rigid and flexible links. They may be subjected to constraints, which are referred to as programmed, which may come from performance requirements, e.g. work or services a system is dedicated to. The CoPCoD structure offers systematic modeling of either open or closed loop constrained structures and results in computationally efficient numerical dynamical equations derivation. The CoPCoD development has its background in the generalized programmed motion equations (GPME) algorithm developed successfully for rigid models of mechanical systems subjected to high order nonholonomic constraints, however, the GPME was not fully automated for computer equation derivations. The two main motivations that underlie the CoPCoD development are to extend the GPME to flexible system models and make it fully automated to computer equation derivations for large classes of systems. The paper presents the general scheme of the CoPCoD architecture and examples which illustrate its application advantages.

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Dynamics modeling of nonholonomic mechanical systems: Theory and applications

Cited by 13 publications

References 9 publications

Model-based control of a third-order nonholonomic system

Model-based control of a third-order nonholonomic system

Stabilizability and Motion Tracking Conditions for Mechanical Nonholonomic Control Systems

Dynamics modeling method dedicated to system models with open- and closed-loop structures subjected to kinematic and task based constraints

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