Using backstepping for control of elastic-joint robots with smaller gear ratios

Tracking control of an elastic-joint robot is investigated. Normally, the gear-ratios are assumed to be large, which results in Spong's simplified model where the cross-inertial effects between the link and joint dynamics are ignored. The Lyapunov stable method of backstepping can be applied to design a high-performance control. In this paper, a redesign of the backstepping method results in a control that accounts for the larger effects of inertial cross-coupling. If the joint stiffnesses are large, the resulting Lyapunov derivative has much smaller disturbances from the cross-coupling than the original design. The result is that the requirement for a large-gear ratio is significantly relaxed. Simulation results demonstrate the improved stability qualities of the system.