Equilibrium analysis for quasi-static, multi-roped walking robots

The paper discusses an algorithm for assessing online the static equilibrium of walking robots with quasi-static locomotion. The robot under discussion can have any number of legs; ropes connect the robot frame to ground. When legs and rope winches are blocked, the robot is a hyperstatic system; the equilibrium problem is statically undetermined. Moreover, both the foot-ground and the frame-rope constraints are unilateral. Firstly, the paper proposes an algorithm for solving the equilibrium problem under bilateral constraints; then, this algorithm is run iteratively for solving the equilibrium problem under unilateral constraints; at each iteration step, suitable constraints are one by one released. The running time is very low and makes the algorithm useful for real-time control. As explanatory example the method is used for mapping the workspace static stability of the four-legged, two-roped climbing robot Roboclimber.