Analysis of Oscillators for the Generation of Rhythmic Patterns in Legged Robot Locomotion

Ralev, Dimitar; Cappelletto, José; Grieco, Juan C.; Certad, Novel; Cabrera, María Eugenia

doi:10.1109/lars.2013.68

Cited by 7 publications

(7 citation statements)

References 12 publications

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“…The Hopf oscillator is governed by the following ordinary differential equations: [ 37 ]

\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\dot{u} = - 2{{\pi}}fv + \sigma (\mu - {u}^2 - {v}^2)u}\\ {\dot{v} = 2{{\pi}}fu + \sigma (\mu - {u}^2 - {v}^2)v} \end{array} } \right.\end{equation}

f and

\sqrt \mu

specify the oscillation frequency and the amplitude, respectively, and σ is a constant controlling the convergence speed of u and v to the limit cycle, as shown in the phase portrait in Figure S1a,b, Supporting Information.…”

Section: Methodsmentioning

confidence: 99%

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A CPG‐Based Versatile Control Framework for Metameric Earthworm‐Like Robotic Locomotion

2023

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Annelids such as earthworms are considered to have central pattern generators (CPGs) that generate rhythms in neural circuits to coordinate the deformation of body segments for effective locomotion. At present, the states of earthworm‐like robot segments are often assigned holistically and artificially by mimicking the earthworms’ retrograde peristalsis wave, which is unable to adapt their gaits for variable environments and tasks. This motivates the authors to extend the bioinspired research from morphology to neurobiology by mimicking the CPG to build a versatile framework for spontaneous motion control. Here, the spatiotemporal dynamics is exploited from the coupled Hopf oscillators to not only unify the two existing gait generators for restoring temporal‐symmetric phase‐coordinated gaits and discrete gaits but also generate novel temporal‐asymmetric phase‐coordinated gaits. Theoretical and experimental tests consistently confirm that the introduction of temporal asymmetry improves the robot's locomotion performance. The CPG‐based controller also enables seamless online switching of locomotion gaits to avoid abrupt changes, sharp stops, and starts, thus improving the robot's adaptability in variable working scenarios.

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“…The Hopf oscillator is governed by the following ordinary differential equations: [ 37 ]

\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\dot{u} = - 2{{\pi}}fv + \sigma (\mu - {u}^2 - {v}^2)u}\\ {\dot{v} = 2{{\pi}}fu + \sigma (\mu - {u}^2 - {v}^2)v} \end{array} } \right.\end{equation}

f and

\sqrt \mu

Section: Methodsmentioning

confidence: 99%

“…Hopf Oscillators: The Hopf oscillator is governed by the following ordinary differential equations: [37] {…”

Section: Methodsmentioning

confidence: 99%

A CPG‐Based Versatile Control Framework for Metameric Earthworm‐Like Robotic Locomotion

2023

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“…Van der Pol oscillator equations are given bywhere italicω affects the frequency of the oscillator, p controls the amplitude of the oscillation and µ affects the shape of the limit cycle. More investigation on these parameters was done in Ralev et al (2013). The initial conditions for a Van der Pol system without any coupling to others are not important.…”

Section: Methodsmentioning

confidence: 99%

“…The initial conditions for a Van der Pol system without any coupling to others are not important. This oscillator has only one attractor, and more investigation for the behavior of this oscillator can be seen in Ralev et al (2013). To have a CPG, we need to build a network of oscillators.…”

Section: Methodsmentioning

confidence: 99%

“…Different properties of three types of nonlinear oscillators, i.e. Van der Pol oscillator, Hopf oscillator and amplitude coupled phase oscillator, are compared with each other (Ralev et al, 2013). In another research, a comparison is done between Matsuoka and McMillen oscillators to reveal the differences and behavior of each one in system structures (Watanabe et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

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Introducing a nonlinear coupling for central pattern generator: Improvement on robustness by expanding basin of attraction and performance by decreasing the transient time

Bahramian

Nouri

Towhidkhah

et al. 2020

Journal of Vibration and Control

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Different types of models have been introduced for central pattern generators mostly based on coupled nonlinear oscillators. One of the most important responsibilities of a central pattern generators is to make an acceptable phase for each limb to make a stable motion. In nonlinear oscillators, the phase difference is made by means of commensurate coupling between them. Linear coupling between oscillators has been widely used in the literature. It is used to make a suitable phase difference between oscillators appropriate to the kind of motion (e.g. walking and running). In this research, it is shown that there are some coexisting attractors in the same coupling, in which phases between oscillators are not ideal to generate rhythms of motion. Consequently, there will be some undesired oscillator states, in which their functionality is significantly decreased. In this article, a novel nonlinear coupling is introduced as a solution for this problem to have a more robust central pattern generators by tackling inappropriate attractors and expanding the basin of attraction of the suitable attractor. In addition, this nonlinear coupling for central pattern generators cues arrived their steady state 2.8 times faster than central pattern generators with linear ones.

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Modulation of Central Pattern Generators (CPG) for the Locomotion Planning of an Articulated Robot

Mesa

Hernández-Riveros

2018

Communications in Computer and Information Science

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Analysis of Oscillators for the Generation of Rhythmic Patterns in Legged Robot Locomotion

Cited by 7 publications

References 12 publications

A CPG‐Based Versatile Control Framework for Metameric Earthworm‐Like Robotic Locomotion

A CPG‐Based Versatile Control Framework for Metameric Earthworm‐Like Robotic Locomotion

Introducing a nonlinear coupling for central pattern generator: Improvement on robustness by expanding basin of attraction and performance by decreasing the transient time

Modulation of Central Pattern Generators (CPG) for the Locomotion Planning of an Articulated Robot

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