Evolution of Biped Locomotion Using Linear Genetic Programming

Gait generation for bipedal robots is a very complex problem. The basic cycle of a bipedal gait, called a stride, consists of two main phases, namely the single-support phase and the double-support phase, which take place in sequence. During the single-support phase, one foot is in contact with the ground and the other foot is in swing motion, being transferred from back to front position. In the double-support phase, both feet simultaneously touch the ground, and the weight of the robot is shifted from one foot to the other. During the completion of a stride, the stability of the robot changes dynamically, and there is always a risk of tipping over. Thus it is crucial to actively maintain the stability and walking balance of the robot at all times. In the conventional engineering approach, there are two main methods for bipedal gait synthesis: Off-line trajectory generation, and on-line motion planning (Wahde and Pettersson, 2002; Katic and Vukobratovic, 2003). Both these methods rely on the calculation of reference trajectories, such as e.g. trajectories of joint angles, for the robot to follow. An off-line controller assumes that there exists an adequate dynamic model of the robot and its environment, which can be used to derive a body motion that adheres to a stability criterion, such as e.g. the zero-moment point (ZMP) criterion (Li et al., 1992; Huang et al., 2001; Huang and Nakamura, 2005; Hirai et al., 1998; Yamaguchi et al., 1999; Takanishi et al., 1985) that requires the ZMP to stay within an allowable region, namely the convex hull of the support region defined by the feet. An on-line motion controller, on the other hand, uses limited knowledge of the kinematics and dynamics of the robot and its environment (Furusho and Sano, 1990; Fujimoto et al., 1998; Kajita and Tani, 1996; Park and Cho, 2000; Zheng and Shen, 1990). Instead, simplified models are used to describe the relationship between input and output. This method also relies much on real-time feedback information. Control policies based on classical control theory, like the ones outlined above, have been successfully implemented on bipedal robots in a number of cases, see e.g. the references mentioned in the previous paragraph. When the robot is operating in a well-known, structured environment, the abovementioned control methods normally work well. However, the success of these methods relies on the calculation of reference trajectories for the robot to follow. When the robot is moving in a realistic, dynamically changing environment such reference trajectories can rarely be specified, since the events that might occur can never be predicted completely. Furthermore, a control policy based on O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m