DAE Aspects in Vehicle Dynamics and Mobile Robotics

Burger, Michael; Gerdts, Matthias

doi:10.1007/11221_2018_6

Cited by 5 publications

(5 citation statements)

References 37 publications

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“…Definition 2.1. A point x ∈ R is called a singular equilibrium if it lies in the intersection of the singular set Σ α given by (5) with the zeros set of f (x, α) for some α ∈ R m .…”

Section: Quasilinear Daes: One-dimensional Casementioning

confidence: 99%

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Classification of Codimension-1 Singular Bifurcations in Low-dimensional DAEs

Ovsyannikov¹,

Ruan²

2022

Preprint

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The study of bifurcations of differential-algebraic equations (DAEs) is the topic of interest for many applied sciences, such as electrical engineering, robotics, etc. While some of them were investigated already, the full classification of such bifurcations has not been done yet. In this paper, we consider bifurcations of quasilinear DAEs with a singularity and provide a full list of all codimension-one bifurcations in lower-dimensional cases. Among others, it includes singularityinduced bifurcations (SIBs), which occur when an equilibrium branch intersects a singular manifold causing certain eigenvalues of the linearized problem to diverge to infinity. For these and other bifurcations, we construct the normal forms, establish the non-degeneracy conditions and give a qualitative description of the dynamics. Also, we study singular homoclinic and heteroclinic bifurcations, which were not considered before.

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Section: Quasilinear Daes: One-dimensional Casementioning

confidence: 99%

“…[1,2]), nonlinear-circuits ( [3,4]), robotics (cf. [5]), flight control systems ( [6]), multi-body systems ( [7]), numeric PDEs ( [8] and references in [9]).…”

Section: Introductionmentioning

confidence: 99%

Classification of Codimension-1 Singular Bifurcations in Low-dimensional DAEs

Ovsyannikov¹,

Ruan²

2022

Preprint

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“…These two models are included in order to illustrate that heterogeneous agents can be considered. Further vehicle models and models for mobile robots can be found in [5]. We like to point out that further models can be integrated into ROCS in a straightforward way.…”

Section: Vehicle Modelsmentioning

confidence: 99%

“…In both, path tracking and path planning, the aim is to realize the feedback law µ i in (2). Currently, a dynamic inversion controller and a linear model-predictive controller are used for path tracking, see [5,3] for details. These controllers can be applied to both models in Section 3.1.…”

Section: Control and Path Planningmentioning

confidence: 99%

ROCS: A Realtime Optimization and Control Simulator

Britzelmeier,

Gerdts,

Moslehi Rad

et al. 2020

Proceedings ASIM SST 2020

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The Realtime Optimization and Control Simulator (ROCS) is a software package written with Qt. It is conceived to be a versatile tool to develop, investigate, and visualize control and trajectory optimization tasks for automated vehicles, aircrafts, and robots in multi-modal scenarios. It is also conceived as a platform which allows to combine real driving data with virtual simulation using a vehicle in the loop.

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“…[1,2]), nonlinear-circuits [3][4][5][6][7], robotics (cf. [8]), flight control systems [9], multi-body systems [10], numeric PDEs ( [11] and references in Kunkel and Mehrmann [12]).…”

Section: Introductionmentioning

confidence: 99%

Classification of Codimension-1 Singular Bifurcations in Low-Dimensional DAEs

Ovsyannikov

Ruan

2022

Front. Appl. Math. Stat.

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The study of bifurcations of differential-algebraic equations (DAEs) is the topic of interest for many applied sciences, such as electrical engineering, robotics, etc. While some of them were investigated already, the full classification of such bifurcations has not been done yet. In this paper, we consider bifurcations of quasilinear DAEs with a singularity and provide a full list of all codimension-one bifurcations in lower-dimensional cases. Among others, it includes singularity-induced bifurcations (SIBs), which occur when an equilibrium branch intersects a singular manifold causing certain eigenvalues of the linearized problem to diverge to infinity. For these and other bifurcations, we construct the normal forms, establish the non-degeneracy conditions and give a qualitative description of the dynamics. Also, we study singular homoclinic and heteroclinic bifurcations, which were not considered before.

show abstract

DAE Aspects in Vehicle Dynamics and Mobile Robotics

Cited by 5 publications

References 37 publications

Classification of Codimension-1 Singular Bifurcations in Low-dimensional DAEs

Classification of Codimension-1 Singular Bifurcations in Low-dimensional DAEs

ROCS: A Realtime Optimization and Control Simulator

Classification of Codimension-1 Singular Bifurcations in Low-Dimensional DAEs

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