Energy-Minimized Gait for a Biped Robot

This paper describes a method of calculation of quasi optimal in energy trajectories for a biped robot. This method is based on the expansion in Fourier series of angles of each axis. This expansion takes the periodicity of the step into account and provides a simple way to take initial state constraints into account. The precision of the obtained trajectory depends only on the precision of the model which can be strongly non linear. In addition, this method allows the optimization of the physical parameters of the robot. An algorithm of optimization under constraints, based on the Nelder and Mead method is given. Some experimental results are given.