Structural Evolution of Central Pattern Generators for Bipedal Walking in 3D Simulation Krister Wolff, Jimmy Pettersson, Almir Herali´ c, and Mattias Wahde Abstract— Anthropomorphic walking for a simulated bipedal robot has been realized by means of artificial evolution of central pattern generator (CPG) networks. The approach has been investigated through full rigid-body dynamics simulations in 3D of a bipedal robot with 14 degrees of freedom. The half- center CPG model has been used as an oscillator unit, with interconnection paths between oscillators undergoing structural modifications using a genetic algorithm. In addition, the con- nection weights in a feedback network of predefined structure were evolved. Furthermore, a supporting structure was added to the robot in order to guide the evolutionary process towards natural, human-like gaits. Subsequently, this structure was removed, and the ability of the best evolved controller to generate a bipedal gait without the help of the supporting structure was verified. Stable, natural gait patterns were obtained, with a maximum walking speed of around 0.9 m/s. I. INTRODUCTION AND MOTIVATION The great interest in humanoid robots during the last decade is motivated by the many advantages of bipedal robots over wheeled robots. First of all, humanoid robots (and bipedal robots in general) are able to move in areas that are inaccessible to wheeled robots, such as staircases and rugged outdoor terrain. In addition, their human-like shape allows such robots to function in constructed environments, such as homes or industries which, naturally, are adapted to people. Furthermore, recent studies [1], [2], [3] have claimed that people are more comfortable interacting with a robot with an approximately human shape, rather than a tin can- like wheeled robot. However, an obvious problem confronting humanoid robotics is the generation of stable gaits. Whereas wheeled robots normally are statically balanced and remain upright regardless of the torques applied to the wheels, a humanoid robot must be actively balanced, particularly if it is to execute a human-like, dynamic gait. Several methods for generating bipedal gaits have been proposed in the literature. An important example is the ZMP method [4], where control torques are generated in order to keep the zero-moment point within the convex hull of the support area defined by the feet. However, the success of gait generation methods based on classical control theory, such as the ZMP method, relies on the calculation of reference trajectories for the robot to follow. That is, trajectories of joint angles, joint torques, or the centre-of-mass of the robot are calculated so as to satisfy the ZMP constraint [5], [6]. When the robot is acting The authors are affiliated with the Department of Applied Mechanics, Chalmers University of Technology, 412 96 G¨ oteborg, Sweden. Correspond- ing author: krister.wolff@chalmers.se in a well-known constructed environment, the ZMP method should work well. When acting in a dynamically changing real world environment, however, the robot will encounter unexpected situations which cannot all be accounted for beforehand. Hence, reference trajectories can rarely be speci- fied under such circumstances. To address this problem, there has recently been a movement in the robotics community towards alternative, biologically inspired control methods. Such methods do not, in general, require any reference tra- jectory. Typically, robotics researchers employ bio-inspired control strategies based on artificial neural networks (ANNs) [7], [8] or central pattern generators (CPGs) [9]. Often some kind of evolutionary algorithm (EA) is utilized for the design of the controller [10], [11], [12], [13], and [14]. Clearly, walking is a rhythmic phenomenon, and many biological organisms are indeed equipped with CPGs, i.e. neural circuits capable of producing oscillatory output given tonic (non-oscillating) activation [15]. CPGs have been stud- ied in several simple animals, such as the lamprey [16] for which mathematical models have been developed as well [17], [18]. CPGs have also been studied in more complex animals, such as cats and primates ([19], [20], [21]), and there are also observations that support the notion of CPGs in humans. For example, treadmill training of patients with spinal cord lesions is assumed to rely on the adequate activation of a CPG [21]. Developing artificial counterparts to biological CPGs, with the aim of generating robust gaits for bipedal robots, is an active field of research. In seminal works by Taga et al., [9], [22], a gait controller based on the half-center CPG model (see below) has been investigated. It was demonstrated in a 2D simulation of a five-link biped that the controller made the robot robust against physical perturbations [9]. Furthermore, obstacle avoidance through regulation of the step length was realized [22]. Shan et al. [11] generated bipedal walking in a 2D simu- lation using CPGs. A multi-objective genetic algorithm was used to optimize the synaptic weights in a network composed of nine CPG units. Reil and Husbands [23] used genetic al- gorithms (GAs) to optimize fully connected recurrent neural networks (RNNs), which were used as CPGs to generate bipedal walking in 3D simulation. They used a GA, with a real-valued encoding scheme, to optimize weights, time constants, and biases in fixed architecture RNNs. Their biped model had six degrees-of-freedom (DOFs), and consisted of a pair of articulated legs connected with a link. The resulting CPGs were capable of generating bipedal, straight-line walk- ing on a planar surface. Furthermore, simple sensory input to