Impulse-based control of joints and muscles

We propose a novel approach to proportional derivative (PD) control exploiting the fact that these equations can be solved analytically for a single degree of freedom. The analytic solution indicates what the PD controller would accomplish in isolation without interference from neighboring joints, gravity and external forces, outboard limbs, etc. Our approach to time integration includes an inverse dynamics formulation that automatically incorporates global feedback so that the per joint predictions are achieved. This effectively decouples stiffness from control so that we obtain the desired target regardless of the stiffness of the joint, which merely determines when we get there. We start with simple examples to illustrate our method, and then move on to more complex examples including PD control of line segment muscle actuators.