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Stable phase-shift despite quasi-rhythmic movements: a CPG-driven dynamic model of active tactile exploration in an insect.

Harischandra N, Krause AF, Dürr V - Front Comput Neurosci (2015)

Bottom Line: The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only.We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency.Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Cybernetics, Faculty of Biology, Bielefeld University Bielefeld, Germany ; Cognitive Interaction Technology Center of Excellence (CITEC), Bielefeld University Bielefeld, Germany.

ABSTRACT
An essential component of autonomous and flexible behavior in animals is active exploration of the environment, allowing for perception-guided planning and control of actions. An important sensory system involved is active touch. Here, we introduce a general modeling framework of Central Pattern Generators (CPGs) for movement generation in active tactile exploration behavior. The CPG consists of two network levels: (i) phase-coupled Hopf oscillators for rhythm generation, and (ii) pattern formation networks for capturing the frequency and phase characteristics of individual joint oscillations. The model captured the natural, quasi-rhythmic joint kinematics as observed in coordinated antennal movements of walking stick insects. Moreover, it successfully produced tactile exploration behavior on a three-dimensional skeletal model of the insect antennal system with physically realistic parameters. The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only. As in the animal, the movement of both antennal joints was coupled with a stable phase difference, despite the quasi-rhythmicity of the joint angle time courses. We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency. For realistic movement patterns, the phase-lead could vary within a limited range of 10-30° only. Tests with artificial movement patterns strongly suggest that this phase sensitivity is not a matter of the frequency composition of the natural movement pattern. Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

No MeSH data available.


Frequency spectra for the antennal joint angle time courses. Both head-scape (A) and scape-pedicel (B) joints have the dominant frequency component at around 1.56 Hz. Mean values are represented by the sign +. Whiskers show the minimum to maximum range. Boxes show the inter-quartile range. The values for the model variant Mc are shown by ◇ signs. The total data set comprises n = 10 trials from five animals, with two trials per animal (data from Krause et al., 2013).
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Figure 2: Frequency spectra for the antennal joint angle time courses. Both head-scape (A) and scape-pedicel (B) joints have the dominant frequency component at around 1.56 Hz. Mean values are represented by the sign +. Whiskers show the minimum to maximum range. Boxes show the inter-quartile range. The values for the model variant Mc are shown by ◇ signs. The total data set comprises n = 10 trials from five animals, with two trials per animal (data from Krause et al., 2013).

Mentions: We tested the model with three different pattern formation networks, all of which were designed according to measurements on unrestrained walking stick insects. To give an impression of the variation of the real antennal movement patterns, Figure 2 shows the amplitude spectra [/zn/, where zn = (an, bn)] of the joint angle time courses for five different animals (two trials per animal). The frequency components of the three pattern formation networks [Fi(θi, fk)] were set according to these spectra. Since the sampling rate of the experimental data was 50 Hz, we set the time span, T, to 5.12 s, resulting in 256 discretized points for the computation of the FFT. Only the first 20 frequency components are shown in the figure, and the first 16 (= L) were chosen for the pattern formation network. The root mean squared error (RMSE), between the original data and the time course produced with the first 16 frequency components, was less than 3°. Since this RMSE is less than the natural amplitude variation, we concluded that 16 components were sufficient to faithfully reproduce natural time courses. The three variants correspond to (i) a single representative trial (◇), (ii) mean frequencies from all 10 trials (+), and (iii) mean frequencies with added variability of one standard deviation. From here onwards, we denote the three CPG patterning networks as Mc, Mm and Mmsd, respectively. Additionally, stochasticity was introduced to the amplitude variable (μi) of all three models. Statistical data for the variation of upper and lower bounds of the joint angle time courses were taken from Krause et al. (2013).


Stable phase-shift despite quasi-rhythmic movements: a CPG-driven dynamic model of active tactile exploration in an insect.

Harischandra N, Krause AF, Dürr V - Front Comput Neurosci (2015)

Frequency spectra for the antennal joint angle time courses. Both head-scape (A) and scape-pedicel (B) joints have the dominant frequency component at around 1.56 Hz. Mean values are represented by the sign +. Whiskers show the minimum to maximum range. Boxes show the inter-quartile range. The values for the model variant Mc are shown by ◇ signs. The total data set comprises n = 10 trials from five animals, with two trials per animal (data from Krause et al., 2013).
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4543877&req=5

Figure 2: Frequency spectra for the antennal joint angle time courses. Both head-scape (A) and scape-pedicel (B) joints have the dominant frequency component at around 1.56 Hz. Mean values are represented by the sign +. Whiskers show the minimum to maximum range. Boxes show the inter-quartile range. The values for the model variant Mc are shown by ◇ signs. The total data set comprises n = 10 trials from five animals, with two trials per animal (data from Krause et al., 2013).
Mentions: We tested the model with three different pattern formation networks, all of which were designed according to measurements on unrestrained walking stick insects. To give an impression of the variation of the real antennal movement patterns, Figure 2 shows the amplitude spectra [/zn/, where zn = (an, bn)] of the joint angle time courses for five different animals (two trials per animal). The frequency components of the three pattern formation networks [Fi(θi, fk)] were set according to these spectra. Since the sampling rate of the experimental data was 50 Hz, we set the time span, T, to 5.12 s, resulting in 256 discretized points for the computation of the FFT. Only the first 20 frequency components are shown in the figure, and the first 16 (= L) were chosen for the pattern formation network. The root mean squared error (RMSE), between the original data and the time course produced with the first 16 frequency components, was less than 3°. Since this RMSE is less than the natural amplitude variation, we concluded that 16 components were sufficient to faithfully reproduce natural time courses. The three variants correspond to (i) a single representative trial (◇), (ii) mean frequencies from all 10 trials (+), and (iii) mean frequencies with added variability of one standard deviation. From here onwards, we denote the three CPG patterning networks as Mc, Mm and Mmsd, respectively. Additionally, stochasticity was introduced to the amplitude variable (μi) of all three models. Statistical data for the variation of upper and lower bounds of the joint angle time courses were taken from Krause et al. (2013).

Bottom Line: The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only.We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency.Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Cybernetics, Faculty of Biology, Bielefeld University Bielefeld, Germany ; Cognitive Interaction Technology Center of Excellence (CITEC), Bielefeld University Bielefeld, Germany.

ABSTRACT
An essential component of autonomous and flexible behavior in animals is active exploration of the environment, allowing for perception-guided planning and control of actions. An important sensory system involved is active touch. Here, we introduce a general modeling framework of Central Pattern Generators (CPGs) for movement generation in active tactile exploration behavior. The CPG consists of two network levels: (i) phase-coupled Hopf oscillators for rhythm generation, and (ii) pattern formation networks for capturing the frequency and phase characteristics of individual joint oscillations. The model captured the natural, quasi-rhythmic joint kinematics as observed in coordinated antennal movements of walking stick insects. Moreover, it successfully produced tactile exploration behavior on a three-dimensional skeletal model of the insect antennal system with physically realistic parameters. The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only. As in the animal, the movement of both antennal joints was coupled with a stable phase difference, despite the quasi-rhythmicity of the joint angle time courses. We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency. For realistic movement patterns, the phase-lead could vary within a limited range of 10-30° only. Tests with artificial movement patterns strongly suggest that this phase sensitivity is not a matter of the frequency composition of the natural movement pattern. Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

No MeSH data available.