1
00:00:00,870 --> 00:00:07,150
‫So now we know that a drone is a six degree of freedom system.

2
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‫We have three position dimensions with which we can determine where the body frame is with respect to

3
00:00:14,760 --> 00:00:15,770
‫the inertial frame.

4
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‫And we also have three orientation dimensions with which we can determine how the body frame is rotated

5
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‫with respect to the initial frame.

6
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‫So you can already see that it is a more complex system compared to the autonomous vehicle in the next

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‫section.

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‫I will show you how to represent the UVs body axis in the initial frame using oilor angles and rotation

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‫matrices.

10
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‫And by the way, this is what degree of freedom means, right?

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‫It's the number of independent variables that you need to determine your system's configuration or state,

12
00:00:58,890 --> 00:01:03,610
‫in our case to determine the drones state.

13
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‫We need three position dimensions and three orientation dimensions, because when we deal with objects

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00:01:12,030 --> 00:01:15,630
‫in 3D, we have a rigid body like a drone.

15
00:01:15,960 --> 00:01:23,730
‫Not only we need to know where the drone is with respect to the inertia frame in terms of position,

16
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‫but we also need to know what its orientation is with respect to the inertial frame.

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‫And now let's look at the oves inputs.

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‫If we think about it logically, then, since the drone has four propellers, then it would make sense

19
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‫that it has four inputs, which are the rotational velocities of its four propellers, which are measured

20
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‫in radians per second, and the rotational velocities of the drones propellers are usually denoted with

21
00:01:57,840 --> 00:01:58,890
‫a big sigma.

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00:01:59,730 --> 00:02:05,710
‫And it makes sense because that is how you physically controlled the drone, right?

23
00:02:06,150 --> 00:02:15,510
‫You manipulate the drones position and orientation by manipulating the rotational velocities of the

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00:02:15,510 --> 00:02:16,380
‫propellers.

25
00:02:16,890 --> 00:02:25,410
‫However, when we derive a mathematical model for the UVs, we will find that it is more convenient

26
00:02:25,680 --> 00:02:33,590
‫to treat the forces and moments that are created by the propellers as our system inputs.

27
00:02:34,110 --> 00:02:40,770
‫So instead of rotational velocities of the propellers, we would consider forces in moments created

28
00:02:40,770 --> 00:02:44,620
‫by those propellers as our system inputs.

29
00:02:44,820 --> 00:02:52,200
‫That is because in the mathematical model of the ovei forces in moments created by the propellers can

30
00:02:52,200 --> 00:02:56,180
‫be conveniently separated from the rest of the model.

31
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‫And that is what we need when we work with state space equations.

32
00:03:01,350 --> 00:03:10,320
‫We need to be able to extract our system inputs like that and we can do it if we consider forces and

33
00:03:10,320 --> 00:03:14,570
‫movements created by the propellers as our system inputs.

34
00:03:15,060 --> 00:03:22,050
‫And then, of course, we will also have equations that will convert the forces in moments created by

35
00:03:22,050 --> 00:03:26,110
‫the propellers to the rotational velocities of the propellers themselves.

36
00:03:26,430 --> 00:03:31,140
‫And now let's look at those forces in moments that are created by the propellers.