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.

The paper addresses the loop shaping problem in the altitude control of an unmanned aerial vehicle to land the flying robot with a specific landing scenario adopted. The proposed solution is optimal, in the sense of the selected performance indices, namely minimum-time, minimum-energy, and velocity-penalized related functions, achieving their minimal values, with numerous experiments conducted throughout the development and preparation to the Mohamed Bin Zayed International Robotics Challenge (MBZIRC 2020). A novel approach to generation of a reference altitude trajectory is presented, which is then tracked in a standard, though optimized, control loop. Three landing scenarios are considered, namely: minimum-time, minimum-energy, and velocity-penalized landing scenarios. The experimental results obtained with the use of the Simulink Support Package for Parrot Minidrones, and the OptiTrack motion capture system proved the effectiveness of the proposed approach.

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