Actuator placement in the multi-link inverted pendulum

The problem of locating actuators in the multi-link inverted pendulum is considered. Two open-loop measures, namely the distance to uncontrollability and a measure of dynamic coupling, as well as a closed-loop measure based on simulation under LQR control are considered separately as measures to aid the choice of actuator placement. It is observed that it is not in general possible to find a single actuator configuration that will be optimal with respect to all of these measures and that a trade off between them is inevitable. The open-loop and closed-loop measures are thus combined in a weighted sum to give a single measure. The choice of actuator configuration for a given number of actuators is then made based on this measure.