Estimation of the transverse sway motion of a biped robot during the march

Due to the balancing generated by the natural dynamics and disturbances during the march of a biped robot, it is difficult to predict its position at a certain moment along the same, thus complicating the development of tasks like manipulation, cooperation, obstacles, avoidance, servo-visual feedback, among others. In this document, we describe a methodology to predict the sway motion in the transverse plane of a biped robot, given the trajectory of a fixed point in its mechanical structure. It is considered the study of two mathematical models to approximate the rolling movement of the robot: approximation by means of a sinusoidal function and approximation by Fourier series. In both cases, it is necessary to know the parameters involved in each mathematical model, so three parametric approximation techniques are implemented: least squares indentification and algebraic identification for the case of the sinusoidal approach, and the calculation of coefficients for the case of the Fourier series. To validate the methodology, real-time monitoring of a biped robot is carried out since the trajectory of the point of interest is affected by various factors such as friction, inclination and imperfections of the surface, the state of conservation of the robot, among others. From different experiments, a quantitative comparison between the different approaches is developed to verify the one that best reproduces the dynamis of the robot's sway.