Trade-off between flight performance and energy consumption of a quadrotor

This paper studies analytically and quantitatively the influence of the power source on the dynamic performance of the altitude control system of a quadrotor powered by an electrochemical battery. This paper also proposes the formulation of the altitude as a constrained optimization problem in which the drone, actuators, control law, and electrochemical battery models are considered, to define a trade-off between the power consumption rate and the closed-loop dynamic performance loss. An analytical representation of the effect of the battery discharge over the altitude dynamics is obtained through a linear approximation, enabling an analysis of the system poles. The problem of designing an altitude controller is then posed as a constrained optimization problem that can include the battery as a factor. A comparison of the error dynamics between the cases of the battery-unaware controller design and the battery-aware controller design is performed in simulations and experimental flight tests. The results lead to the following conclusions: i. the analytical demonstration agrees with the worse performance observed in the in-flight dynamics as the battery discharges and ii. through a battery-aware controller design approach this effect can be diminished, at the cost of a trade-off in the battery discharge rate.