‫So now we know that a drone is a six degree of freedom system.
‫We have three position dimensions with which we can determine where the body frame is with respect to
‫the inertial frame.
‫And we also have three orientation dimensions with which we can determine how the body frame is rotated
‫with respect to the initial frame.
‫So you can already see that it is a more complex system compared to the autonomous vehicle in the next
‫section.
‫I will show you how to represent the UVs body axis in the initial frame using oilor angles and rotation
‫matrices.
‫And by the way, this is what degree of freedom means, right?
‫It's the number of independent variables that you need to determine your system's configuration or state,
‫in our case to determine the drones state.
‫We need three position dimensions and three orientation dimensions, because when we deal with objects
‫in 3D, we have a rigid body like a drone.
‫Not only we need to know where the drone is with respect to the inertia frame in terms of position,
‫but we also need to know what its orientation is with respect to the inertial frame.
‫And now let's look at the oves inputs.
‫If we think about it logically, then, since the drone has four propellers, then it would make sense
‫that it has four inputs, which are the rotational velocities of its four propellers, which are measured
‫in radians per second, and the rotational velocities of the drones propellers are usually denoted with
‫a big sigma.
‫And it makes sense because that is how you physically controlled the drone, right?
‫You manipulate the drones position and orientation by manipulating the rotational velocities of the
‫propellers.
‫However, when we derive a mathematical model for the UVs, we will find that it is more convenient
‫to treat the forces and moments that are created by the propellers as our system inputs.
‫So instead of rotational velocities of the propellers, we would consider forces in moments created
‫by those propellers as our system inputs.
‫That is because in the mathematical model of the ovei forces in moments created by the propellers can
‫be conveniently separated from the rest of the model.
‫And that is what we need when we work with state space equations.
‫We need to be able to extract our system inputs like that and we can do it if we consider forces and
‫movements created by the propellers as our system inputs.
‫And then, of course, we will also have equations that will convert the forces in moments created by
‫the propellers to the rotational velocities of the propellers themselves.
‫And now let's look at those forces in moments that are created by the propellers.