Modeling of CPG-based control mechanisms for leech swimming

Rhythmic locomotion, such as flying, swimming, walking and crawling, is common behavior in the animal world. According to the research from biology, these periodic movements are realized automatically by certain neuronal circuits in the central nervous system, which are named Central Pattern Generators (CPGs). Research on such biological control systems from engineering viewpoint is emerging for both biological understanding and engineering design. In this dissertation work, a mathematical model to describe the leech swimming system has been developed. The integrated swimming system consists of several parts: CPG in the central nerve cord, body dynamics, muscle actuator and fluid environment, among which the swimming CPG is the research focus.; The model of the neuronal CPG that controls the rhythmic body motion is developed based on general biophysical facts and detailed physiological properties of leeches. The systems approach is employed to capture the neuronal dynamics essential for generating coordinated oscillations of cell membrane potentials by a simple CPG architecture with a minimal number of parameters. Based on input/output data from physiological experiments, dynamical components (neurons and synaptic interactions) are first modeled individually and then integrated into a chain of nonlinear oscillators to form a CPG.; Numerical analysis are performed to find the basic oscillation behavior and the effects of different parameters on CPG performance, which helps to validate known parameter values and to estimate unknown parameters. The oscillation properties of interest include oscillation period, amplitude and phase, among which the phase is the most important one for motion coordination. With the estimation of a few unknown parameters within physiologically reasonable ranges, the CPG system is capable of producing an oscillation profile reasonably close to that observed in the isolated nerve cord.; Theoretical analysis are further performed to reveal the underlying relationship between the system performance and parameter values. The explicit oscillation conditions are derived for single oscillators. The harmonic balance method is applied to both the segmental oscillator and the CPG system to find the oscillation properties. Most of the qualitative relationships are accurately predicted. The harmonic balance method turns out to be an effective method for oscillation analysis of nonlinear systems.; Finally the integrated swimming system is developed, which includes the models of CPG, body dynamics, muscle activation and fluid interaction. Based on the equation of motion derived, simulation analysis are performed to investigate the swimming behavior of the leech model with three links. PID controllers are first adopted to validate the models of body-fluid interaction and muscle dynamics by showing that the system achieves normal swimming motion with reasonable speed under proper periodic control signals. The muscle tensions required for swimming are also estimated. Then the open-loop swimming system controlled by the CPG system is investigated. Although certain discrepancies exist between the CPG controlled system and the real leech, such as the circular trajectory, the coordinated swimming-like motion with reasonable speed has been achieved.