A robust two-stage active disturbance rejection control for the stabilization of a riderless bicycle

Baquero-Suárez, Mauro; Cortés‐Romero, John; Arcos-Legarda, Jaime; Coral-Enríquez, Horacio

doi:10.1007/s11044-018-9614-y

Cited by 24 publications

(12 citation statements)

References 29 publications

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“…If ω 0 0, we know from (28) and (29), A 1 3 (ξ 0 ) = A 2 3 (ξ 0 ) = 0 and c 333 (ξ 0 ) = P 3 (ξ 0 ) = 0, resulting in [A 3 ] 2×1 = [0] 2×1 and [L] 3 = 0. In addition, based on (19), the partial derivatives of c 333 and P 3 take the following forms,…”

Section: Mathematical Properties Of the Jacobian Matricesmentioning

confidence: 99%

“…Studies on bicycle dynamics started at the end of the 19th century with the seminal work by Carvallo [1] and Whipple [2]. Since then this topic has drawn attentions from J. Boussinesq [3], F. Klein and A. Sommerfeld [4], S. P. Timoshenko and D. H. Young [5], and many recent researchers from different areas including classical mechanics [6][7][8][9][10][11][12][13][14], applied mathematics [15][16][17], system control [18][19][20], etc. Meijaard et al [11] did a comprehensive review of the history of bicycle dynamics, while Kooijman and Schwab [21,22] presented the state of the art of the literature.…”

Section: Introductionmentioning

confidence: 99%

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Symmetry and relative equilibria of a bicycle system moving on a revolution surface

Xiong¹,

Liu²

2021

Preprint

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Finding the relative equilibria and analyzing their stabilities are of great significance to revealing the intrinsic properties of mechanical systems and developing effective controller. In this paper, we study the symmetry and relative equilibria of a bicycle system moving on a revolution surface. We note that the symmetry group of the bicycle is a three-dimensional Abelian Lie group, and the rolling condition of the two wheels produces four time-invariant first-order linear constraints to the bicycle system. Therefore, we can classify the bicycle dynamics as a general Voronets system whose Lagrangian and constraint distribution are kept invariant under the action of the symmetry group. Applying the Voronets equations to the bicycle dynamics, we obtain a seven-dimensional reduced dynamic system on the reduced constraint space. This system takes time-reversal and lateral symmetries, and has two kinds of relative equilibria: the static equilibria and the dynamic equilibria. Further theoretical analysis shows that both kinds of relative equilibria form one-parameter solution families, and their Jacobian matrices take some specific properties. We then show that a static equilibrium cannot be stable unless all the eigenvalues of the Jacobian matrix are located at the imaginary axis of the complex plane. The stability of the dynamic equilibria is studied by limiting the reduced dynamic system to an invariant manifold, which is established based on the conservation of energy of the system. We prove in a strict mathematical sense that the dynamic equilibria may be Lyapunov stable, but cannot be asymptotically stable. Finally, we employ symbolic computation to carry out numerical simulations in conjunction with the benchmark parameters of a Whipple bicycle. How the revolution surface affects the relative equilibria and their stabilities is then investigated through our numerical simulations.

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Section: Mathematical Properties Of the Jacobian Matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetry and relative equilibria of a bicycle system moving on a revolution surface

Xiong¹,

Liu²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…They developed a simulation model in the ADAMS software and demonstrated the feasibility of the system. Baquero-Suárez et al [15] designed a two-stage observer based feedback controller for lateral stability. They built a prototype and demonstrated the effectiveness of the controller.…”

Section: Controlled Dynamicsmentioning

confidence: 99%

State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches

et al. 2020

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A review of the current use of multibody dynamics methods in the analysis of the dynamics of vehicles is given. Railway vehicle dynamics as well as road vehicle dynamics are considered, where for the latter the dynamics of cars and trucks and the dynamics of single-track vehicles, in particular motorcycles and bicycles, are reviewed. Commonalities and differences are shown, and open questions and challenges are given as directions for further research in this field.

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“…Studies on bicycle dynamics started at the end of the 19th century with the seminal work by Carvallo [1] and Whipple [2]. Since then this topic has drawn attention from J. Boussinesq [3], F. Klein and A. Sommerfeld [4], S. P. Timoshenko and D. H. Young [5], and many recent researchers from different areas including classical mechanics [6][7][8][9][10][11][12][13][14], applied mathematics [15][16][17], system control [18][19][20], etc. Meijaard et al [11] did a comprehensive review of the history of bicycle dynamics, while Kooijman and Schwab [21,22] presented the state of the art of the literature.…”

Section: Introductionmentioning

confidence: 99%

Symmetry and Relative Equilibria of a Bicycle System

Xiong¹,

Jia²,

Liu³

2021

Nelin. Dinam.

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In this paper, we study the symmetry of a bicycle moving on a flat, level ground. Applying the Gibbs – Appell equations to the bicycle dynamics, we previously observed that the coefficients of these equations appeared to depend on the lean and steer angles only, and in one such equation, a term quadratic in the rear wheel’s angular velocity and a pseudoforce term would always vanish. These properties indeed arise from the symmetry of the bicycle system. From the point of view of the geometric mechanics, the bicycle’s configuration space is a trivial principal fiber bundle whose structure group plays the role of a symmetry group to keep the Lagrangian and constraint distribution invariant. We analyze the dimension relationship between the space of admissible velocities and the tangent space to the group orbit, and then employ the reduced nonholonomic Lagrange – d’Alembert equations to directly prove the previously observed properties of the bicycle dynamics. We then point out that the Gibbs – Appell equations give the local representative of the reduced dynamic system on the reduced constraint space, whose relative equilibria are related to the bicycle’s uniform upright straight or circular motion. Under the full rank condition of a Jacobian matrix, these relative equilibria are not isolated, but form several families of one-parameter solutions. Finally, we prove that these relative equilibria are Lyapunov (but not asymptotically) stable under certain conditions. However, an isolated asymptotically stable equilibrium may be achieved by restricting the system to an invariant manifold, which is the level set of the reduced constrained energy.

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A robust two-stage active disturbance rejection control for the stabilization of a riderless bicycle

Cited by 24 publications

References 29 publications

Symmetry and relative equilibria of a bicycle system moving on a revolution surface

Symmetry and relative equilibria of a bicycle system moving on a revolution surface

State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches

Symmetry and Relative Equilibria of a Bicycle System

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