Safe and optimal navigation for autonomous multi-rotor aerial vehicle in a dynamic known environment by a decomposition-coordination method

In this paper, we present a new solution for the Autonomous navigation problem, using a Decomposition-Coordination Method (DCM) 1. The main purpose of this work is to compute an optimal and safe path for the multi-rotor Unmanned Aerial Vehicle (UAV) in a dynamic environment, moving from an initial location to the desired state. We assume that the flight environment is totally known to a supervisory unit, and the positions and trajectories of dynamic obstacles could be known in real-time, thus to perform in such environment a high reactivity is required as well as good connectivity with the supervisory unit that provides the safe path, each time one obstacle or more are detected on the road, so that the UAV could autonomously diverts from the unsafe path to the new safe one, and avoid the potential collisions. First and foremost, we choose a generalized nonlinear model for the multi-rotors in view of the rotational and translational dynamics of the UAV. We then associate that model with the objective functions. After that, we proceed to the resolution of the multi-objective optimization problem using our approach of decomposition-coordination. The principle of this method consists in decomposing the system into several smaller subsystems to simplify the treatment. Then we achieve the coordination afterward using Lagrange multipliers. To prove the convergence and stability of our method we make use of a Lyapunov function chosen particularly for this system. In the last section we present the simulation results, to confirm the reliability of our method.