Zero-leak steady-state torque allocation

Determine whether the steady-state micro-motor torque floor in the Pi-SEA torque-allocation scheme can be driven to zero by taking the leak parameter \(\lambda\) to zero.

Background

The Pi-SEA uses a leaky mid-ranging integrator, $\dot\eta=\tau_\mu-\lambda\eta$, to transfer the steady load from the load-side micro motor to the series-elastic macro channel. At equilibrium, the micro torque is $\lambda\eta^\star$, so the leak parameter determines a residual steady-state share carried by the micro motor.

Although the paper derives that this floor is proportional to $\lambda$ and experimentally observes an approximately linear relationship, it explicitly leaves unresolved whether the floor can be eliminated in the limit $\lambda\to0$.