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Assuming a drone is in two dimension, it has to predict its future position by calculating its future displacement:

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For a real quad-rotor, why should we not only estimate the displacement of a robot in three dimensions but also the change of orientation of the robot, its linear velocity and its angular velocity?

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  • $\begingroup$ Why would you think anything to the contrary? If you never update angular/pose information, then the linear displacement doesn't mean anything. $\endgroup$
    – Chuck
    May 23 '16 at 18:04
  • $\begingroup$ @Chuck but isn't estimating the displacement of the robot sufficient? What necessary information do I get with the change of orientation of the robot, its linear velocity and its angular velocity? $\endgroup$ May 23 '16 at 19:13
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If the robot's orientation is fixed, then determining its linear displacement is sufficient to determine its location in the world. This is because one unit of "forward" on the robot is equivalent to one unit of "forward" in the world.

However, when the robot is allowed to rotate, one unit of "forward" for the robot now corresponds to a partial unit "forward" and a partial unit "sideways".

The clearest way to imagine this is to imagine that the robot has rotated 180 degrees, such that it is looking in the direction opposite to that which it had when it started. Now one unit of "forward" for the robot actually translate to one unit of "backward" in the world. Similarly, one unit of "left" now corresponds to one unit of "right" and vice-versa.

In this manner, local coordinates, as established relative to the robot, are only useful when the orientation of the robot is known relative to the world. If you don't know which way you're pointed, you can't know which way you're moving.

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By assuming that the drone is 2D as you have done, you are fixing the vertical axis (e.g. height from the ground). For a real drone operating in 3D, there are six degrees of freedom corresponding to the x,y, and z position of the robot in space as well as the roll,pitch, and yaw of the drone.

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