Modification of learning optimal gait generation method in considering discontinuous velocity transitions

In this paper, we propose a modification of our previous learning gait generation method. Our framework can generate an optimal feedforward control input and the corresponding periodic trajectory minimizing the L₂ norm of the control input by iteration of laboratory experiments. In order to generate a periodic gait, the previous result imposed a constraint that the initial state of the robot is equivalent to the state just after the collision between the foot and the ground, by equipping a reference trajectory defined as a time-reversal version of a pair of the output signal and its time derivative. However, it occasionally happens that the reference velocity at the terminal time conflicts a desired terminal velocity for a periodic trajectory. This paper proposes a modified learning algorithm with another reference trajectory whose velocity coincides with the desired one. Although calculation of such reference trajectory generally requires information of the transition mapping, this method estimates the mapping by the least-squares with the stored experimental data. We also propose a technique to generate an optimal gait not only energy-efficient but also avoiding the foot-scuffing problem.