IMU preintegration for 2D SLAM problems using Lie Groups

2D SLAM is useful for mobile robots that are constrained to a 2D plane, for example in a warehouse, simplifying calculations in respect to the 3D case. The use of an IMU in such a context can enrich the estimation and make it more robust. In this paper we reformulate the IMU preintegration widely used in 3D problems for the 2D case, making use of Lie Theory. The Lie theory based formalization, first derived for a perfectly horizontal plane, allows us to easily extend it to problems where the plane is not orthogonal to the gravity vector. We implement the theory in a factor graph based estimation library, and carry out experiments to validate it on a mobile platform. Two experiments are carried out; on a horizontal and a sloped environment, and the sensor data is processed using our two 2D methods and a state-of-the-art 3D method.