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Suppose I have a satellite which has 3 reaction wheels, one for rotating the satellite about each of it's axes and an IMU. Can anyone give me an intuitive explanation of how gimbal lock can occur in this system if I am trying to control the attitude?

Edit : The sensor I plan to use is this. https://invensense.tdk.com/wp-content/uploads/2015/02/MPU-6000-Datasheet1.pdf

As far as I understand I can read the rotation rates from the triple axis gyro and fuse it with the accelerometer readings for understanding my orientation.

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I think I realized where I will run into a singularity. enter image description here In my algorithm i will be knowing the initial orientation and hence the matrix inv(S). I will also be knowing the angular velocities from my sensor hence the w vector. I can then solve to get my new orientation, which will be impossible when S becomes singular.

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  • $\begingroup$ Gimbal lock is when two of your 3 reaction wheels are aligned giving you 0 authority in some axis. Imagine a roll, pitch yaw system where the pitch is pointed up or down, making any effect of roll redundant with the yaw. $\endgroup$ Commented Aug 9 at 11:33
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    $\begingroup$ Your question needs to be edited for more information. Please edit your question to explain why you think you may experience gimbal lock, with citations if you're reading this in some source or another. If you're using rate gyros with fixed axes (i.e., an even vaguely modern IMU) and reaction wheels with fixed axes, then mechanical gimbal lock cannot happen. There's a mathematical behavior around the attitude determination that can run into singularities. It is called gimbal lock, but there's a number of different ways that it can be avoided. $\endgroup$ Commented Aug 9 at 13:47

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Reaction wheels have their spin (and torque) axis fixed with respect to the spacecraft body. When they are installed in the spacecraft body, the directions of the (say 3) reaction wheel spin axes are kept sufficiently different from each other (e.g. three orthogonal directions if three wheels are used) so that singularity doesn't occur; control authority is present in all three axes. Since the axes are fixed with respect to spacecraft body, this situation doesn't change throughout the operation.

For IMU hardware, unless it is a stabilised platform IMU (which has gimbal inside gimbal inside gimbal construction), the rotating / vibrating / oscillating elements are, again, fixed with respect to the spacecraft body during installation.

For IMU software, there are different algorithms; some of which are susceptible to singularity (e.g. Euler angles); and some which are not susceptible (e.g. Quaternions, DCMs).

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For a sensor / IMU which gives Euler angles as output, singularity manifests as wild and sudden variations of angle #1 and angle #3 even for slow rotations, when angle #2 is near +-90 deg.

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  • $\begingroup$ Yeah it's the software part that I am interested in. If I'm using a MEMS gyro sensor which will always give me three axis rotations (physical gimbal lock can never happen) how will Euler angles throw a singularity in software? $\endgroup$ Commented Aug 10 at 12:13
  • $\begingroup$ I saw a clip that showed the importance of the intelligent sequencing of commands to "pitch," "roll," and "yaw" to prevent gimbal lock. I look for it! $\endgroup$ Commented Aug 10 at 17:24
  • $\begingroup$ Please include the details of the sensor in the question by editing it (not as a comment). If it gives three angles as output, its datasheet / application note / user manual will indicate if it suffers the problem of singularity or not. Without detailed knowledge of the sensor, it is not possible to answer. $\endgroup$ Commented Aug 11 at 12:16

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