Complex behaviors of a two revolute joints robot: harmonic, subharmonic, higher harmonic, fractional harmonic, chaotic responses

Mahout, Vincent; Lopez, P.; Carcasses, Jean-Pierre; Mira, Christian

doi:10.1109/icsmc.1993.390849

Cited by 9 publications

(5 citation statements)

References 2 publications

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“…Mahout et al proved that a two-revolute joint manipulator controlled with proportional-plus-derivative (PD) law exhibited chaotic dynamics for certain values of static variables [23] (see Figure . 7).…”

Section: Initial Chaotic Dynamics Research In Various Manipulators Anmentioning

confidence: 99%

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Applications of Chaotic Dynamics in Robotics

Zang

Iqbal

Zhu

et al. 2016

International Journal of Advanced Robotic Systems

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This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of deterministic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.

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Section: Initial Chaotic Dynamics Research In Various Manipulators Anmentioning

confidence: 99%

“…Figure23. a) Autonomous robot using the "Magician Chassis" platform b) Terrain coverage of the robot during obstacle avoidance behaviour[69] …”

mentioning

confidence: 99%

Applications of Chaotic Dynamics in Robotics

Zang

Iqbal

Zhu

et al. 2016

International Journal of Advanced Robotic Systems

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“…Recent research by Ravishankar and Ghosal [5], Lankalapalli and Ghosal [6], and Mahout et al [7], has explored the potential for chaotic oscillations in certain PD-controlled robotic manipulators of two and three degrees of freedom. In the referenced work, the controller tracks a desired time-periodic trajectory, and therefore is itself the source of non-autonomous terms.…”

Section: Introductionmentioning

confidence: 99%

Pitchfork-Type Bifurcations in a Parametrically Excited, Pd-Controlled Pendulum or Manipulator

Bucklaew¹,

Liu²

2001

Journal of Sound and Vibration

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“…The 2-DOF robot manipulator moving in a vertical plane can be considered as a driven double pendulum. Mahout et al [1992] presented simulation results of a SCARA 2-DOF robot executing repetitive tasks and controlled with a PD algorithm, which may give rise to complex dynamics. Lankalapalli and Ghosal [1996;1997] analyzed a controlled 2-DOF robot manipulator (a PD and a model-based controller).…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a 2-Dof Robot Manipulator Driven by Constant Torques

Verduzco

Álvarez

1999

Int. J. Bifurcation Chaos

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The bifurcations of a two-degree-of-freedom (2-DOF) robot manipulator with linear viscous damping and constant torques at joints are analyzed at three equilibrium points. We show that, provided some conditions on the parameters are satisfied, two of these equilibria have a Jacobian matrix with a double zero eigenvalue and a pair of pure imaginary eigenvalues, while the other one has a quadruple zero eigenvalue. We use the center manifold theorem and the normal form theory to show the presence of different kinds of local bifurcations, ranging from codimension one (Hopf and fold), three (cusp and degenerate zero-Hopf), and higher (double zero, double zero-Hopf, triple zero, quadruple zero and Hopf-Hopf). †

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Complex behaviors of a two revolute joints robot: harmonic, subharmonic, higher harmonic, fractional harmonic, chaotic responses

Cited by 9 publications

References 2 publications

Applications of Chaotic Dynamics in Robotics

Applications of Chaotic Dynamics in Robotics

Pitchfork-Type Bifurcations in a Parametrically Excited, Pd-Controlled Pendulum or Manipulator

Bifurcation Analysis of a 2-Dof Robot Manipulator Driven by Constant Torques

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