Evolution and development of a central pattern generator for the swimming of a lamprey

This article describes the design of neural control architectures for locom otion using an evolutionary approach. Inspired by the central pattern gener ators found in animals, we develop neural controllers that can produce the patterns of oscillations necessary for the swimming of a simulated lamprey. This work is inspired by Ekeberg's neuronal and mechanical model of a lampr ey [11] and follows experiments in which swimming controllers were evolved using a simple encoding scheme [25, 26]. Here, controllers are developed us ing an evolutionary algorithm based on the SGOCE encoding [31, 32] in which a genetic programming approach is used to evolve developmental programs th at encode the growing of a dynamical neural network. The developmental prog rams determine how neurons located on a two-dimensional substrate produce n ew cells through cellular division and how they form efferent or afferent i nterconnections. Swimming controllers are generated when the growing networ ks eventually create connections to the muscles located on both sides of th e rectangular substrate. These muscles are part of a two-dimensional mechan ical simulation of the body of the lamprey in interaction with water. The motivation of this article is to develop a method for the design of con trol mechanisms for animal- like locomotion. Such a locomotion is character ized by a large number of actuators, a rhythmic activity, and the fact that efficient motion is only obtained when the actuators are well coordinated. The task of the control mechanism is therefore to transform commands conce rning the speed and direction of motion into the signals sent to the multip le actuators. We define a fitness function, based on several simulations of the controller with different commands settings, that rewards the capacity of modulating the speed and the direction of swimming in response to simpl e, varying input signals. Central pattern generators are thus evolved capab le of producing the relatively complex patterns of oscillations necessary f or swimming. The best solutions generate traveling waves of neural activity , and propagate, similarly to the swimming of a real lamprey, undulations o f the body from head to tail propelling the lamprey forward through water. By simply varying the amplitude of two input signals, the speed and the dir ection of swimming can be modulated.