On-demand optimal gait generation for a compass biped robot based on the double generating function method

Recently, the double generating function method for finite time linear quadratic optimal control problems was proposed. This paper applies it to the on-demand optimal gaits generation of a compass biped robot walking on the level ground. The double generating function method is employed to generate reference optimal gaits and inputs considering the energy consumption by linearizing the compass biped robot. The simulation result shows that the modeling error caused by the linearization is small when the robot walks with a reasonable step length and a appropriate time period. This implies that the optimal states and inputs for the linearized system can be treated as the optimal ones for the original nonlinear system. The biggest advantage of the double generating function method is that it can generate a parametrization of optimal gaits for different boundary conditions and different time periods. Therefore, it is very useful to generate the optimal states and inputs on demand and in real time for the real biped robots.