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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.


Phase sensitivity of antennal tip trajectories with the pattern-generating network producing the same frequency spectrum but distinct phase spectrum. In (A), the oscillators were driven with a symmetric triangular waveform (sine function only). In (B), the driving waveform contained the same frequency components but differed in phase (sines and cosines). As in Figure 6, the phase lead of the SP joint with respect to the HS joint varied from −60 (a) to 180° (f). Units for abscissa and ordinate for the HS and SP waveforms are seconds and degrees.
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Figure 7: Phase sensitivity of antennal tip trajectories with the pattern-generating network producing the same frequency spectrum but distinct phase spectrum. In (A), the oscillators were driven with a symmetric triangular waveform (sine function only). In (B), the driving waveform contained the same frequency components but differed in phase (sines and cosines). As in Figure 6, the phase lead of the SP joint with respect to the HS joint varied from −60 (a) to 180° (f). Units for abscissa and ordinate for the HS and SP waveforms are seconds and degrees.

Mentions: Having observed that the phase lead between the SP and the HS joint is a limiting factor for obtaining the typical, elliptical shape of the antennal tip trajectory, we wondered which aspect of the pattern-generating network could be the reason for this limitation. Therefore, we tested the CPG model with two simple patterns of oscillation that contained the same four frequency components but differed in phase. When the joints were driven with symmetrical triangular waveforms with unique phase (e.g., sine functions only), the antennal tip trajectories were elliptical with flat ends along the major axis, except if the phase differences was 0 or 180° (see Figure 7A). In the latter two cases, i.e., in-phase (c) and anti-phase (f) coordination, the antennal tip moved along a slanted vertical or horizontal line, respectively. When the phase difference between the joint oscillators increased, the width of the elliptical trajectory increased, irrespective of which joint was leading or lagging. A similar effect could be seen with frequency-scaled triangular waveforms (see Supplementary Material). Antennal trajectories showed a more complex dependency on phase, as soon as driving waveform contained two distinct phases per joint. Figure 7B shows the effect of augmented triangular waveforms, where the same four frequency components were present as both sine and cosine terms (phase shifted) in its Fourier representation (Equation 5). As a consequence, HS and SP joint angle time courses had slightly asymmetric positive and negative halves (see Figure 7B). With regard to the phase dependency of the antennal tip trajectory, the main effect induced by the augmented waveform was a distinct change in trajectory shape from an ellipse to a figure-eight shape (Figure 7B). In summary, as soon as the pattern-generating network produced waveforms with more than one phase in its phase spectrum, even simple composite waveforms resulted in distinct antennal tip trajectories as soon as the phase difference between the two oscillators changed.


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)

Phase sensitivity of antennal tip trajectories with the pattern-generating network producing the same frequency spectrum but distinct phase spectrum. In (A), the oscillators were driven with a symmetric triangular waveform (sine function only). In (B), the driving waveform contained the same frequency components but differed in phase (sines and cosines). As in Figure 6, the phase lead of the SP joint with respect to the HS joint varied from −60 (a) to 180° (f). Units for abscissa and ordinate for the HS and SP waveforms are seconds and degrees.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4543877&req=5

Figure 7: Phase sensitivity of antennal tip trajectories with the pattern-generating network producing the same frequency spectrum but distinct phase spectrum. In (A), the oscillators were driven with a symmetric triangular waveform (sine function only). In (B), the driving waveform contained the same frequency components but differed in phase (sines and cosines). As in Figure 6, the phase lead of the SP joint with respect to the HS joint varied from −60 (a) to 180° (f). Units for abscissa and ordinate for the HS and SP waveforms are seconds and degrees.
Mentions: Having observed that the phase lead between the SP and the HS joint is a limiting factor for obtaining the typical, elliptical shape of the antennal tip trajectory, we wondered which aspect of the pattern-generating network could be the reason for this limitation. Therefore, we tested the CPG model with two simple patterns of oscillation that contained the same four frequency components but differed in phase. When the joints were driven with symmetrical triangular waveforms with unique phase (e.g., sine functions only), the antennal tip trajectories were elliptical with flat ends along the major axis, except if the phase differences was 0 or 180° (see Figure 7A). In the latter two cases, i.e., in-phase (c) and anti-phase (f) coordination, the antennal tip moved along a slanted vertical or horizontal line, respectively. When the phase difference between the joint oscillators increased, the width of the elliptical trajectory increased, irrespective of which joint was leading or lagging. A similar effect could be seen with frequency-scaled triangular waveforms (see Supplementary Material). Antennal trajectories showed a more complex dependency on phase, as soon as driving waveform contained two distinct phases per joint. Figure 7B shows the effect of augmented triangular waveforms, where the same four frequency components were present as both sine and cosine terms (phase shifted) in its Fourier representation (Equation 5). As a consequence, HS and SP joint angle time courses had slightly asymmetric positive and negative halves (see Figure 7B). With regard to the phase dependency of the antennal tip trajectory, the main effect induced by the augmented waveform was a distinct change in trajectory shape from an ellipse to a figure-eight shape (Figure 7B). In summary, as soon as the pattern-generating network produced waveforms with more than one phase in its phase spectrum, even simple composite waveforms resulted in distinct antennal tip trajectories as soon as the phase difference between the two oscillators changed.

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.