Derivation of the Time Optimal Control for an Underactuated Free Flying Mechanism and Its Analysis

Abstract

In order to build gymnastic robots and jumping robots, we have derived the complete analytical solution to the posture control problem of a two-link free flying object with initial angular momentum. We have shown that the problem becomes singular when initial body angle is far from the reference point and derived formulae to calculate the optimal switching condition, optimal terminal time and optimal trajectories. As an application, the high diving motion is simulated.