Observer design for apex height and vertical velocity of a single-leg hopping robot during stance phase

Abstract

This article proposes an observer design for two important variables in the studies of single-leg hopping robot (SLHR), the apex height, and the vertical velocity of SLHR during its stance phase. At first, the Euler–Lagrange (EL) dynamics of SLHR are obtained and apex height is identified in the state-space representation of the EL dynamics. Apex height is the state variable that represents the robot body’s height at the top point, which keeps on changing as the robot functions. Vertical velocity is the velocity of the robot in the vertical direction. An observer design is presented in this article which will estimate these variables when required. The quality of the estimation is validated by the simulation results where the estimation error is zero which means the model output is correct and observer performance is good.

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

“…• Hopping robots: most of the studies are based on compliant contact [328,329,184,330], hence can be recast into a complementarity framework, see section 3.6.1. In view of the material in the forefoing sections, would it be possible to use of the stability results in [150] for a bouncing ball with moving base, and of the equivalence between the one degree-of-freedom juggler and the vertical hopper, to design a controller for the hopper based on internal sinusoidal excitation ?…”