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I think I agree on all your points, but let's use an example to test: consider the case where we roll the IMU in the positive direction (so roll is +90 degrees), and then, while it is on its side, rotate it counter-clockwise 90 degrees. In other words, I want to do an extrinsic rotation of the IMU of +90 degrees of roll, then +90 degrees of yaw (with the intrinsic, IMU-frame rotation being +90 degrees roll, +90 degrees pitch). What do you expect the IMU to read for (a) orientation and (b) rotation rate? For (a), I expect the IMU to read +90 degrees roll, and +90 degrees yaw. For (b), while we are rolling it, I expect to see positive roll rate, and then when we carry out the second rotation, I expect to see positive pitch rate.