Analytic proportional-derivative control for precise and compliant motion

Precise control with proportional-derivative (PD) control generally requires stiffness. The proposed method determines critically damped PD control trajectories that precisely obtain target position and velocity constraints for arbitrary initial conditions. An analytic solution provides the PD control parameters, thereby determining the required impedance. The resulting controller precisely interpolates the target state by solving the full boundary-value problem. Control parameters are time-invariant, and need only be recomputed if the system diverges from the computed trajectory due to unexpected forces or noise. The resulting method provides control with automatically determined compliance, yielding natural response to perturbation.