State-incremental optimal control of 3D COG pattern generation for humanoid robots

Many researchers have proposed walking pattern generation methods with zero moment point – center of gravity (ZMP–COG) constraints. Some of the researchers used a neural-networks (NN), a central pattern generator (CPG), or a genetic algorithm (GA) for ZMP–COG pattern generation. However, the parameters used in those methods are too many, and the procedure to learn or to search them costs too much computation time. Other researchers designed controllers or used analytical solution method to generate COG trajectories. These methods generate the ZMP-COG pattern very quickly, but the COG height is limited to a constant to linearize the inverted pendulum model of the robot. Due to this limitation, the robots cannot walk freely on surfaces that change in height. To solve this problem, researchers start to use the original nonlinear inverted pendulum model to make the COG height changeable such as using a numerical method or a feedback controller. In this paper, an optimal control-based pattern generator that can allow COG height change is proposed. It can solve sagittal and lateral COG patterns with arbitrarily assigned COG height and ZMP trajectories in real time. Thus, dynamic walking on height-changing surfaces can be achieved.