This article describes the design of neural control architectures for locomotion using an evolutionary approach. Inspired by the central pattern generators 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 lamprey [11] and follows experiments in which swimming controllers were evolved using a simple encoding scheme [25, 26]. Here, controllers are developed using an evolutionary algorithm based on the SGOCE encoding [31, 32] in which a genetic programming approach is used to evolve developmental programs that encode the growing of a dynamical neural network. The developmental programs determine how neurons located on a two-dimensional substrate produce new cells through cellular division and how they form efferent or afferent interconnections. Swimming controllers are generated when the growing networks eventually create connections to the muscles located on both sides of the rectangular substrate. These muscles are part of a two-dimensional mechanical 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 control mechanisms for animal-like locomotion. Such a locomotion is characterized 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 concerning the speed and direction of motion into the signals sent to the multiple 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 simple, varying input signals. Central pattern generators are thus evolved capable of producing the relatively complex patterns of oscillations necessary for swimming. The best solutions generate traveling waves of neural activity, and propagate, similarly to the swimming of a real lamprey, undulations of 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 direction of swimming can be modulated.

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