Coupling the Neural and Physical Dynamics in Rhythmic Movements

Abstract

A pair of coupled oscillators simulating a central pattern generator (CPG) interacting with a pendular limb were numerically integrated. The CPG was represented as a van der Pol oscillator and the pendular limb was modeled as a linearized, hybrid spring-pendulum system. The CPG oscillator drove the pendular limb while the pendular limb modulated the frequency of the CPG. Three results were observed. First, sensory feedback influenced the oscillation frequency of the coupled system. The oscillation frequency was lower in the absence of sensory feedback. Moreover, if the muscle gain was decreased, thereby decreasing the oscillation amplitude of the pendular limb and indirectly lowering the effect of sensory feedback, the oscillation frequency decreased monotonically. This is consistent with experimental data (Williamson and Roberts 1986). Second, the CPG output usually led the angular displacement of the pendular limb by a phase of 90" regardless of the length of the limb. Third, the frequency of the coupled system tuned itself to the resonant frequency of the pendular limb. Also, the frequency of the coupled system was highly resistant to changes in the endogenous frequency of the CPG. The results of these simulations support the view that motor behavior emerges from the interaction of the neural dynamics of the nervous system and the physical dynamics of the periphery.

Resonance tuning of a neuromechanical system with two negative sensory feedback configurations

“…The CPG receives inhibitory and/or excitatory position feedback from a linear, one-degree-of-freedom mechanical subsystem. As with previously published results [5,15], resonance tuning is limited to frequencies that are greater than the intrinsic CPG frequency with endogenously bursting neurons. In contrast, with tonically spiking neurons, the resonance tuning range is expanded to frequencies that are below the intrinsic CPG frequency.…”

“…Previous resonance tuning studies have shown that sensory feedback is essential to adjust the frequency of the CPG to the mechanical resonant frequency [5,15]. Biological systems have evolved with several strategies to synchronize the mechanical and neural dynamics using sensory feedback.…”

Altered Gravity Highlights Central Pattern Generator Mechanisms

“…In such systems, a particular frequency-the resonant frequency-is critical: it requires the minimum force to maintain the oscillations and therefore the minimum muscle activity. When interacting with the environment, the preferred oscillatory movements are not simply dictated by the CNS, but are constrained by the dynamics of the system as well (Hatsopoulos 1996;Kugler and Turvey 1987). For instance, a giraffe moves with a much slower pace than small mammals because giraffes have very long legs.…”

“…In another context, Neil Armstrong walked on the Moon in 1969 at a much slower velocity than on Earth because gravitational attraction on the Moon is decreased by a factor of six. From the neuronal control perspective, one functional benefit of modulating the CPG frequency with sensory feedback is that it enables a system to exploit the resonant properties of musculoskeletal dynamics (Hatsopoulos 1996;Hatsopoulos and Warren Jr 1996;Iwasaki and Zheng 2006;Williams and DeWeerth 2007).…”

Computational approaches to motor learning by imitation

“…a qualitatively similar movement will always lead to a similarly parameterized movement primitive, irrespective of the timing of the movement and the target to which the movement was executed. Coupling terms to the differential equations allowed natural robustness towards external perturbations (see also Hatsopoulos (1996)). The effectiveness of imitation learning with these dynamic systems primitives was successfully demonstrated on a humanoid robot that learned a series of movements such as tennis forehand, tennis backhand and drumming sequences from a human teacher (figure 3), and that was subsequently able to re-use the learned movement in modified behavioural contexts.…”