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However, unlike nav_msgs/Odometry, sensor_msgs/Imu doesn't have a separate frame_id for Twist information vs Pose information.

Yes, this is an issue that's been pointed out before. The message should really have frame_id fields for orientation, velocity, and acceleration. It makes processing IMU data awkward.

Or, should I fill the angular_velocity and linear_acceleration portions with front-left-up velocities and accelerations? In that case, which frame should be put into frame_id?

Do this. Put whatever you want in the frame_id, but then provide a static transform from base_link to that frame, and make that transform the sensor's offset w.r.t. the robot's origin.