Prescribed motion of a two-legged walking robot on a rough cylinder

Abstract

We consider the walking robot with n legs, where each leg contacts the surface in a single foothold. Given the motion of the robot's legs with respect to its body, we solve the problem of finding the reaction forces, both analytically and numerically. We describe the robot motion in terms of the general dynamics theorems, with six different equations of the robot's dynamics from the momentum and angular momentum theorems. In the special case a robot with two legs, the existence of the solution is related to a set of straightforward inequalities. Using numerical simulations we develop the classification of footholds positions for different values of the friction coefficient.