Optimal passive dynamics for torque/force control

For robotic manipulation tasks in uncertain environments, good force control can provide significant benefits. The design of force or torque controlled actuators typically revolves around developing the best possible software control strategy. However, the passive dynamics of the mechanical system, including inertia, stiffness, damping and torque limits, often impose performance limitations that cannot be overcome with software control. Discussions about the passive dynamics are often imprecise, lacking comprehensive details about the physical limitations. In this paper, we develop relationships between an actuator's passive dynamics and the resulting performance, for the purpose of better understanding how to tune the passive dynamics for a force control task. We present two distinct scenarios for the actuator system and calculate the required input to produce a desired output. These exact solutions provide a basis for understanding how the parameters of the mechanical system affect the overall system's bandwidth limit. Our model does not include active control; we computed the optimal input to the system to produce the required torque at the load with zero error. This is important so that our results only reflect the physical system's performance.