Optimal Energy Trajectory Generation for a Quadrotor UAV Using Geometrically Exact Computations on SE(3)

A quadrotor UAV consumes considerable proportions of energy in its rotors resulting in reduced flight endurance. This letter discusses an energy optimal trajectory generation scheme for the quadrotor UAVs using geometrically exact computation techniques. The dynamics of the UAV is represented using a non-Euclidean space known as special Euclidean space, SE(3) which employs rotation matrix and thus overcomes the limitations introduced by other attitude representations. The goal is to maneuver the quadrotor from its initial states to the desired states utilizing minimum energy. By adopting the lie group variational integrator technique, possible inaccuracies that can be caused by the commonly used numerical integration techniques are eliminated. A numerical backstepping approach is used to estimate the initial values of co-states to meet the desired terminal conditions.