Algorithms of Terminal Control of Multi-Copters

The article is devoted to the development of algorithms for terminal control of mobile objects. A moving object of multicopter type described by a nonlinear model of motion of a solid body in three-dimensional space is considered. A three-stage procedure for solving the problem of terminal control of a moving object when it moves to a given point is proposed. The main difference of the proposed procedure is the correction of the desired trajectory so that it passes through the current position of the moving object at each moment of time. This method of constructing the desired trajectory allows you to automatically adjust the speed when moving to a given point. The need for correction of the desired trajectory can be caused by the presence of obstacles, differences between the model and the real object, and the influence of external disturbances. At the first stage, the desired trajectory taking into account a given finite time of motion is constructed. The motion trajectory represents the desired velocity and orientation angles of a moving object of multi-copter type. At the second stage, the method of position-trajectory control is used to synthesize feedback, which provides stabilization of the moving object relative to the calculated desired trajectory. The result of the second stage is the thrust and torque generated by the motors, which are then recalculated in the speed of rotation of the rotors. At the third stage, the desired trajectory is corrected depending on the current position of the moving object. As a result of the correction, a singularity occurs at the target point. In order to eliminate the singularity at the target point, the problem is solved in the formulation of weak terminal control. Before the target point hits the given neighborhood, the velocity of the moving object is calculated based on the remaining distance and time of movement. When a given neighborhood of the target point is reached, the speed of movement becomes constant. The analysis of the closed-loop system is carried out, as a result of which the asymptotic stability of the desired trajectory and the hit of a moving object in a finite given neighborhood of the target point at a finite time are shown. The results of numerical modeling, confirming the performance of the proposed algorithms in the example of hexacopter, are presented.

terminal control, mobile object, multi-copter, position control, path control

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