This paper describes how the SGOCE paradigm has been used to evolve developmental programs capable of generating recurrent neural networks that control the behavior of simulated insects. This paradigm is characterized by an encoding scheme, by an evolutionary algorithm, by syntactic constraints, and by an incremental strategy that are described in turn. The additional use of an insect model equipped with six legs and two antennae made it possible to generate control modules that allowed it to successively add gradient-following and obstacle-avoidance capacities to walking behavior. The advantages of this evolutionary approach, together with directions for future work, are discussed.

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.

An evolutionar y approach is used to design neural control architectures for virtual sixlegged anim ats. Using a geom etry-or iented variation of the cellular encoding scheme and syntactic constraints that reduce the size of the genetic search space, the developmental prog rams of straight locom otion controllers are ® rst evolved. One such controller is then included as the ® rst module in a larger architecture, in which a second neural module is evolved and develops connections to the ® rst one, so as to set locom otion on or oþ according to sustained or instantaneous exter nal control signals. Such an incremental approach should prove useful to the autom atic design of relatively complex control architectures that might, in particular, implement some cognitive abilities over and above mere stimulus± response mechanisms.KEYW ORDS: Evolution, developm ent, dynam ical neural networks, SGO CE, hexapod locom otion.

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