![]() If the longitudinal and lateral axes were flown in ACAH mode, rather than TRC mode, the total motor weight of all configurations would be nearly identical, requiring about 13.5% weight fraction for motors (compared to 7–9% weight fraction from hover torque requirements). To meet handling qualities requirements, the total weight of the motors of the octocopter and hexacopter is comparable at 13.5% weight fraction, but the quadcopter’s motors are heavier, requiring 16% weight fraction. This, combined with the octocopter’s greater inertia as well as the fact that it requires 30% less current to drive its motors in hover, results in the octocopter requiring the greatest current margin, relative to hover conditions. In yaw, rotor inertia is irrelevant, as the reaction torque of the motor is the same whether the rotor is accelerating or overcoming drag. Both the quadcopter and hexacopter have maximum current margin requirements (relative to hover) during a step command in longitudinal velocity. For axes that rely on the rotor thrust (all except yaw), the increased inertia of the larger rotors on the quadcopter increase the current requirement, relative to vehicles with fewer, smaller rotors. The handling qualities and motor current requirements of a quadcopter, hexacopter and octocopter with equal gross weights (5,360N) and total disk areas (producing a 287N/mĭisk loading) are compared in hover. I will try to explain how these come together in a future post.Optimisation-based control design techniques are applied to multicopters with variable-RPM rotors. The controller design will need to account for the available sensory feedback, noise, digitization constraints (such as the zero order hold and noise amplification), and the architecture of the embedded system as well as the physical dynamics of the system. It is important to understand them however, especially when it comes to designing the controller. Summing the torques here provides the equation of motion for Yaw:ĭeriving these equations is pretty straightforward, as the quad-copter system is remarkably simple and linear. Note that motor 1 spins clockwise, which means that the counter-torque felt by the drone is counter clockwise. Below is a diagram which shows the torques created by each motor. The same equations can be applied for the pitch variable because the drone is symmetric on either side. Summing the moments about the center of mass provides: The proportionality constant represents the conversion between duty cycle to force (circuit and air dynamics are neglected). The duty cycle is a value 0-1 which is calculated by the controller and represents the minimum to maximum thrust. The thrust forces are split up into two parts, a duty cycle i n and a proportionality constant k f . Here, we have gravity acting downwards from the center of mass, and two thrust forces coming from each end of the drone. The example below illustrates the forces that effect rotation in roll from a rear view perspective. In order to derive some dynamic equations it is always helpful to use a free body diagram. Qualitatively, this seems to make sense however, in order to design a flight controller these principles need to be quantified. It also gives the controller the ability to influence position in yaw. Having two props spin in opposite directions will mostly cancel out these inflicted torques. Well, exerting a torque on the props will inflict an opposite torque on the drone. Newton’s third law is that every force exerts an equal and opposite force. ![]() The answer starts with the fact that the props are spinning in different directions. This seems intuitive, but how does it influence the position in yaw? To change pitch position, it will give more power to props 1 and 2 than props 3 and 4. The variable-pitch actuators allow the propellers to change from a full positive pitch to a full negative pitch in roughly 0. To change roll position, it will give more power to props 1 and 3 than props 2 and 4. The controller can decide how much power to give each individual propeller. Since the pitch was watered even on the eve of the Test, and because of the dew factor, there is a possibility that moisture will be in play on Day 2 morning too. In order for stable flight, all of these angles must remain as close to zero as possible. ![]() Below is a diagram of the quad-copter with some definitions.Īs you can see, the Euler angles Pitch and Roll are used to describe how the system is oriented laterally, and the Yaw angle is used to describe how it is spinning. To start, we need to define some variables to be controlled. This requires a little bit of knowledge regarding the physics of the system as well as some controller design. To get the quad-copter system to remain stable, most importantly it needs to remain level to the ground.
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