Optimal Gait Generation for a Compass Biped Robot via the Double Generating Functions Method

Abstract

To control a compass biped robot walking in a complex environment, it is necessary to adjust its step length and walking speed for every step. Therefore, the computation time to calculate the suitable gait for each step, which is called on-demand computation time in this paper, should be short enough to walk continuously. Recently, the double generating functions method for finite time linear quadratic optimal control problems was proposed, whose advantage is that it can generate a parametrization of optimal trajectories for different boundary conditions and different time periods. It is very useful to the on-demand computation of optimal gait for the real biped robots walking in a complex environment. This paper applies the double generating functions method to a compass biped robot walking on the level ground. Considering the energy consumption, we generate a family of reference optimal gaits and inputs for different boundary conditions (the step length and the walking speed) for the linearized model by employing the double generating functions method. The simulation result shows that the modeling error caused by the linear approximation is small enough when the compass biped robot walks with a suitable step length and walking speed. This implies that the optimal gaits and inputs for the linearized system can be used as the optimal gaits and inputs for the original nonlinear system.