Application of the double generating function method to optimal gait generation for a biped robot

Recently, the double generating function method for finite-time linear optimal control problems was proposed. It gives a family of optimal trajectories for different boundary conditions directly. This paper applies it to a compass gait biped robot to generate optimal gaits on the level ground. It allows the robot to obtain optimal gaits to reach the designed location with the designed velocity for every step with almost none online computation. It can also give optimal cycle gaits for different step lengths and different time periods. Furthermore, some simulation results show the effectiveness of the double generating function method for optimal gaits generation of biped walking robots.