A Quadcopter study is a fun challenge. It’s a busy area of interest, so there are papers and materials to use as a guide and many hardware and software platform options to work with.
We visit optimal control, estimation, classical and state-space design techniques, applied math, and forays into underlying mechanics, electronics, software, etc.
What is a “quad-rotor”? Well you probably know it’s a thing with four rotors. We buy it as a, “drone” and we fly it with a remote control or via a phone app acting like one. I’ll probably bounce between the terms quad-rotor and quadcopter throughout. I mean the same thing. It is incredible what …
Ultimately we’ll buy Electronic Speed Controllers (ESCs) for our Quad motors. They take PWM in and produce drive voltages for brushless DC motors. Let’s jump in to understand the motor-propeller subsystem on a quadrotor. DC Motor Modelling You’ll find basic DC motor equations in any undergraduate dynamics textbook. I add the Bouabdallah model for the …
In the last post we arrived at a mathematical model for the combination brushless DC motor (BLDC), gearbox, and propeller model. A small quadrotor motor will not have a gearbox. It will have the propeller mounted directly to the shaft of a small hobby motor. In larger craft a gearbox helps match the motor to …
It’s been fun to mess with the motor-propeller differential equation and linearization in an post. However, when I got into looking-up some rough parameter estimates and performing dimensional analysis (seeing if the units worked-out right for me in the equations) I ran into some problems. I realized I was not only needing numbers, but I …
In the last quadcopter post we clarified the load torque of the propeller applied through the gearbox to the motor shaft. We won’t even have a gearbox but the terms in the equation needed clarification. We haven’t yet covered the main point of the propeller: LIFT! A propeller blade is just a spinning wing at each …
Here we’ll derive the equations of motion for copter attitude: it’s roll, pitch, and yaw or orientation in the sky relative to an observer on the ground. The X,Y,Z position of the craft relative to the same observer comprise the other degrees-of freedom. We’ll later see how thrust and attitude drive to the X,Y,Z position, …
The equations below are from the last post, where we see we matched our Bouabdallah paper‘s equations for rotational motion. We know some propeller input is going to be a part of the applied torque. There is going to be a set of equations for linear motion too, but let’s clarify what is going on …
This post explains how we determine propeller thrust and drag factors for our quadcopter project. The last couple of posts have been working out the sum of torque on our quadcopter. A few weeks ago, we covered the gyroscopic effect of the total airframe in the “equations of motion” post. Next, we looked at the …
The last few posts covered each of three dynamic details separately: Gyroscopic effect of the rigid body (the entire quadcopter). Gyroscopic effect of the spinning propellers. Propeller thrust and drag effects. We’re going to use all of this information as we look at controlling the flight of a quadcopter, but first we’re going to make …
In the last post I simplified the model to arrive at a transfer function representing the roll and pitch axes independently for our ‘+’ shaped quadrotor. The following video explains how we stabilize this inherently unstable system. The PDF that follows is produced from the Maple document I review in the video. This, “lead-compensator” design …