Visual-Inertial Odometry, LiDAR SLAM, and 3D Mapping: IMU Preintegration, Bundle Adjustment, Point-Cloud ICP, Loop Closure, and GPS-Denied Navigation

Deep End Era. Engineering with Sankalp · Oct 29, 2026 · 1h 7m

A quadrotor flying down a wet rock penstock six hundred metres underground has no GPS, a magnetic field twisted by steel rebar, and an inertial sensor whose position error grows with the square of time. Then the rock wall turns to smooth concrete, one camera frame drops in the driver queue, and the drone pitches violently into an oscillation. To understand why, we open up visual-inertial odometry and LiDAR SLAM from first principles: dead reckoning, IMU preintegration on manifolds, bundle adjustment, the four unobservable degrees of freedom, point-cloud ICP, tunnel degeneracy, loop closure…