TERMINAL CONTROL OF QUADCOPTER SPATIAL MOTION
DOI:
https://doi.org/10.15588/1607-3274-2025-2-20Keywords:
quadcopter, quaternion, Pontryagin’s maximum principle, Hamiltonian, Lyapunov functionsAbstract
Context. Constructing quadcopter control algorithms is an area of keen interest because controlling them is fundamentally complex despite the quadcopter’s mechanical simplicity. The key problem of quadcopter control systems is to effectively couple three translational and three rotational freedom degrees of motion to perform unique target manoeuvres. In addition, these tasks are relevant due to the high demand for quadcopter in various human activities, such as cadastral aerial photography for monitoring hardto-reach areas and delivering cargo over short distances. They are also widely used in military affairs.
Objective. This work objective is to develop and substantiate novel methods for algorithms constructing the high-precision control of a quadcopter spatial motion, allowing for its autonomous operation in all main flight modes: stabilization mode, position holding mode, automatic point-to-point flight mode, automatic takeoff and landing mode.
Method. The given objective determined the use of the following research methods. Pontryagin’s maximum principle was applied to develop algorithms for calculating program trajectories for transferring a quadcopter from its current state to the given one. Lyapunov functions and modal control methods were used to synthesise and analyse quadcopter angular position control algorithms. Numerical modelling methods were used to verify and confirm the obtained theoretical results.
Results. An approach for constructing algorithms for controlling the spatial quadcopter motion is proposed. It consists of two parts. The first part solves the problem of transferring a quadcopter from its current position to a given one. The second part proposes an original method to construct algorithms for quadcopter attitude control based on a dynamic equation for a quaternion.
Conclusions. The proposed quadcopter motion mathematical model and methods for constructing control algorithms are verified by numerical modelling and can be applied to develop quadcopter control systems
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