Quadcopter Body Frame and Inertial Frame Kinematicsīefore delving into the physics of quadcopter motion, let us formalize the kinematics in the body and inertial frames. The body frame is defined by the orientation of the quadcopter, with the rotor axes pointing in the positive \(z\) direction and the arms pointing in the \(x\) and \(y\) directions. The inertial frame is defined by the ground, with gravity pointing in the negative \(z\) direction. We will start deriving quadcopter dynamics by introducing the two frames in which will operate. We will then test our controllers with a numerical simulation of a quadcopter in flight. We will present a very simplified model of quadcopter dynamics and design controllers for our dynamics to follow a designated trajectory. Together, these factors create a very interesting control problem. Finally, unlike ground vehicles, helicopters have very little friction to prevent their motion, so they must provide their own damping in order to stop moving and remain stable. The resulting dynamics are highly nonlinear, especially after accounting for the complicated aerodynamic effects. In order to achieve six degrees of freedom, rotational and translational motion are coupled. With six degrees of freedom (three translational and three rotational) and only four independent inputs (rotor speeds), quadcopters are severely underactuated. Quadcopter control is a fundamentally difficult and interesting problem. The decreasing cost of modern microprocessors has made electronic and even completely autonomous control of quadcopters feasible for commercial, military, and even hobbyist purposes. The development of quadcopters has stalled until very recently, because controlling four independent rotors has proven to be incredibly difficult and impossible without electronic assistance. The swashplate mechanism was needed to allow the helicopter to utilize more degrees of freedom, but the same level of control can be obtained by adding two more rotors. With four independent rotors, the need for a swashplate mechanism is alleviated. The complicated design of the rotor and swashplate mechanism presents some problems, increasing construction costs and design complexity.Ī quadrotor helicopter (quadcopter) is a helicopter which has four equally spaced rotors, usually arranged at the corners of a square body. In order to produce a torque the angle of attack is modulated by the location of each rotor in each stroke, such that more thrust is produced on one side of the rotor plane than the other. However, these configurations require complicated machinery to control the direction of motion a swashplate is used to change the angle of attack on the main rotors. The two rotors can also be arranged with one main rotor providing thrust and a smaller side rotor oriented laterally and counteracting the torque produced by the main rotor. These can be arranged as two coplanar rotors both providing upwards thrust, but spinning in opposite directions (in order to balance the torques exerted upon the body of the helicopter). Conventional helicopters have two rotors. A helicopter is a flying vehicle which uses rapidly spinning rotors to push air downwards, thus creating a thrust force keeping the helicopter aloft.
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