Four-rotor dynamics, simulation and control

Translator Note: This article: http://andrew.gibiansky.com/blog/physics/quadcopter-dynamics/

This paper introduces the dynamics and control model of four rotor, and simulates it in MATLAB, which is helpful to understand the working principle of the four rotor blades. The translator studied at the College of Aeronautical Science and Engineering, Beihang University, please specify the source.

Only part of the code is given in the original text, and some configurations are not indicated. The translator has partially perfected it. The perfect section is marked with a gray font. In addition, due to my knowledge level and English proficiency is limited, the translation process inevitably error, please correct me.

Introduced

A helicopter is an aircraft that uses a high-speed rotating motor to press the airflow downward to provide thrust and remain in the air. A conventional helicopter has two motors. They can both be configured to provide lift together on the same plane and turn opposite (this is to balance the torque generated on the aircraft). Two motors can also be configured as a main motor to provide lift while the smaller one is configured to balance the torque generated by the main motor paddle. However, both configurations require a complex mechanical structure to control the direction of movement of the aircraft, and an automatic tilt is required on the main motor to change the angle of attack of the main propeller. In order to produce a torque this angle of attack is mainly determined by the position of two motors at each stage, so there will be more lift on one side of the motor. This complex motor and automatic tilt design is prone to mechanical failure, resulting in increased structural cost and design complexity.

The four-rotor helicopter (four-rotor) has four identical motors separated by a total of four motors, typically arranged in four corners of the aircraft. With these four independent motors, the need for an automatic tilt is reduced. The automatic tilt is designed to allow the motor to have more degrees of freedom on the angle, while the same level of control requirements can be met by an additional two motors.

The development of the four rotors was once stalled, because it was difficult to control four separate motors at the same time without using electronic equipment. With the reduction of microprocessor cost, the four rotors can be controlled by electronic devices or even fully automatic control becomes feasible, so that the four rotors may be used in commercial, military or even just because of people's interest.

Four-rotor control is a difficult and interesting problem. It has six degrees of freedom (three position coordinates and three angular coordinates) but only four inputs (four motors), which is a statically indeterminate system. In order to achieve the motion in six directions, the rotational and moving movement in the horizontal direction must appear in pairs. Therefore, the dynamics model of the four rotors is strongly nonlinear, especially after the complicated aerodynamic effects are calculated. Finally, unlike robots on the ground, the four rotors have very little frictional resistance, so they must be provided with damping so that they can stop movement and remain stable. To sum up, these factors together form an interesting control puzzle. We will build a simplified four rotor dynamics model and design a controller for the model to allow our four rotors to fly in the specified orbit while testing our controllers using a numerical simulation system.

The dynamics of four rotor blades

Four-rotor dynamics, simulation and control