Central Pattern Generators for Gait Generation in Bipedal Robots

Abstract

An obvious problem confronting humanoid robotics is the generation of stable and efficient gaits. Whereas wheeled robots normally are statically balanced and remain upright regardless of the torques applied to the wheels, a bipedal robot must be actively balanced, particularly if it is to execute a human-like, dynamic gait. The success of gait generation methods based on classical control theory, such as the zero-moment point (ZMP) method (Takanishi et al., 1985), relies on the calculation of reference trajectories for the robot to follow. In the ZMP method, control torques are generated in order to keep the zero-moment point within the convex hull of the support area defined by the feet. When the robot is moving in a well-known environment, the ZMP method certainly works well. However, when the robot finds itself in a dynamically changing real-world environment, it will encounter unexpected situations that cannot be accounted for in advance. Hence, reference trajectories can rarely be specified under such circumstances. In order to address this problem, alternative, biologically inspired control methods have been proposed, which do not require the specification of reference trajectories. The aim of this chapter is to describe one such method, based on central pattern generators (CPGs), for control of bipedal robots. 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 (Grillner, 1996). There exists biological evidence for the presence of central pattern generators in both lower and higher animals. The lamprey, which is one of the earliest and simplest vertebrate animals, swims by propagating an undulation along its body. The wave-like motion is produced by an alternating activation of motor neurons on the left and right sides of the segments along the body. The lamprey has a brain stem and spinal cord with all basic vertebrate features, but with orders of magnitude fewer nerve cells of each type than higher vertebrates. Therefore, it has served as a prototype organism for the detailed analysis of the nervous system, including CPGs, in neurophysiological studies (Grillner, 1991; Grillner, 1995). In some early experiments by Brown (Brown, 1911, Brown, 1912), it was shown that cats with transected spinal cord and with cut dorsal roots still showed rhythmic alternating contractions in ankle flexors and extensors. This was the basis of the concept of a spinal locomotor center, which Brown termed the half-center model (Brown, 1914). Further biological support for the existence of a spinal CPG structure in vertebrates is presented in (Duysens & Van de Crommert, 1998).