Lie Group Theory for Robotics (arxiv.org)

Joan Solà’s "micro Lie theory for state estimation in robotics" distills the parts of Lie-group math that are most useful for practical robotics—especially motion estimation tasks like SLAM and visual odometry—into an accessible, hands‑on reference. Rather than presenting the full abstract machinery of Lie theory, the paper walks through the minimal principles practitioners need, supplies worked application examples, and compiles a broad catalogue of formulas (including Jacobians) for the major groups used in robotics. It also ships a C++ template‑only (header‑only) library implementing the described functionality, making it easy to drop into existing estimation stacks. The significance is pragmatic: correct handling of rotations and rigid‑body poses on manifolds avoids the linearization and symmetry mistakes common when treating them as Euclidean vectors. By providing ready Jacobians, consistent exponential/log maps, and recipes for manipulating perturbations on SO(n)/SE(n) families, the work improves the numerical stability and correctness of filters and optimizers used in localization and mapping. For researchers and engineers, the micro theory lowers the barrier to using manifold-aware state representations and yields more reliable uncertainty propagation and linearization, accelerating adoption in real‑world robotics systems.