On Lie Group IMU and Linear Velocity Preintegration for Autonomous Navigation Considering the Earth Rotation Compensation

Robot localization is a fundamental task in achieving true autonomy. Recently, many graph-based navigators have been proposed that combine an inertial measurement unit (IMU) with an exteroceptive sensor applying IMU preintegration to synchronize both sensors. IMUs are affected by biases that also have to be estimated. To increase the navigator robustness when faults appear on the perception system, IMU preintegration can be complemented with linear velocity measurements obtained from visual odometry, leg odometry, or a Doppler Velocity Log (DVL), depending on the robotic application. Moreover, higher grade IMUs are sensitive to the Earth rotation rate, which must be compensated in the preintegrated measurements. In this article, we propose a general purpose preintegration methodology formulated on a compact Lie group to set motion constraints on graph simultaneous localization and mapping problems considering the Earth rotation effect. We introduce the SE$_{N}(3)$ group to jointly preintegrate IMU data and linear velocity measurements to preserve all the existing correlation within the preintegrated quantity. Field experiments using an autonomous underwater vehicle equipped with a DVL and a navigational grade IMU are provided and results are benchmarked against a commercial filter-based inertial navigation system to prove the effectiveness of our methodology.