On Obtaining Energy-Optimal Trajectories for Landing of UAVs

Abstract

The optimization issues connected to a landing task of an unmanned aerial vehicle are discussed in the paper, based on a model of a mini-class drone. Three landing scenarios are considered, including minimum-time landing, landing with minimum energy consumption, and planned landing. With the use of classical dynamic programming techniques, including the minimum principle of Pontryagin, as well as the calculus of variations, the optimal altitude reference trajectories are found, to form the altitude control system in such a way as to mimic the profile of the reference trajectory by the actual altitude of the UAV. The simulation results conducted with the use of the Simulink Support Package for Parrot Minidrones verify the correctness and effectiveness of the method, and open the research directions for further analysis, especially to tune altitude controller in a way, as to track the reference profile. Up to this point, optimization tasks considered in the literature, with respect to the drones, were connected to swarm formation optimization, optimization of the take-off process or landing process limited to optimal path planning. This paper thus considers a new topic in the field.

Altitude Measurement-Based Optimization of the Landing Process of UAVs

“…By no means is this model necessary to conduct experimental tuning runs, nevertheless the understanding of the interaction between signals, makes the performance index-related discussion put in a good context. The model of the Parrot Rolling Spider quadrotor driven by DC motors requires the introduction of coordinate systems at first (see [ 5 ]), to obtain information about position and orientation of the UAV. In the North-East-Down (NED) convention, x and y axes point towards the motors 1 and 2, whereas the axis z points downwards.…”

“…Based on the derivations given in [ 5 ], the acceleration vector in three axes of a local coordinate system of the UAV and the thrust generated by the propellers ( is a mass of the UAV, and is the gravity force) where denotes the rotational speed of the i -th propeller, [kg·m] is the aerodynamical constant, refers to the thrust constant, denotes air density, gives vertical distance between the center of mass (COM) of the UAV and mounting height of the propellers, is propellers’ surface area, refers to the propeller’s radius, and n is the number of propellers.…”

“…Having assumed that the air density does not vary during the experiment, with , , , and , the simplified model of dynamics in the z axis is obtained. For a complete derivation of the model, see [ 5 ]. As can be seen, the simplified model actually presents the relation between the thrust force, gravitational constant, and position-velocity interplay.…”

“…The major components of the optimized landing approach from the control side are described in this paper, where the core calculations to obtain optimal landing trajectories have been presented in the paper [ 5 ], and now, the complete experimental results are presented, to enable deployment of optimal procedure of landing UAVs by other researchers.…”

“…This paper presents a complete approach to tuning the altitude control system to achieve optimal performance for optimal landing trajectories and different landing scenarios generated in [ 5 ]. The results include minimum-time landing scenario (emergency landing), energy-optimal landing and velocity-penalized landing scenarios.…”