A series of reflections on the physical and philosophical nature of power electronics, where the transformation of energy reveals the fundamental rules of the world.
A robot dropped into an unmapped room faces a chicken-and-egg problem: to know where it is, it needs a map; to build a map, it needs to know where it is. Simultaneous Localization and Mapping refuses to solve these one after another. It solves them at once, as a single joint estimate that gets less wrong with every new measurement.
The classical approach, EKF-SLAM, keeps one large state vector holding the robot's pose and every landmark's position, wrapped in a covariance matrix that records how uncertain each belief is and how those uncertainties are correlated. See a landmark twice from two different poses and the correlation between "where was I" and "where was it" tightens for both, even though neither was measured directly against ground truth. Certainty is manufactured entirely from consistency between guesses.
Graph-SLAM reframes the same problem spatially instead of statistically: poses become nodes, relative measurements between them become edges, and the whole graph is optimized at once by nonlinear least squares — Gauss-Newton or Levenberg-Marquardt — walking Lie groups like SE(3) and SO(3) because rotations do not add, they compose. Loop closure — recognizing a place revisited — adds one edge that ties the far end of a long drift back to somewhere it belongs, and the correction ripples backward through the whole trajectory at once, not just the last few poses.
Bundle adjustment does the same thing with cameras instead of wheels: thousands of pixel observations across thousands of frames, refined by marginalizing the 3D landmark variables via a Schur complement so the update cost scales with the number of poses, not the number of points. What the robot believes about the world and what it believes about itself are never separable quantities. They are solved as one.
Seed: Autonomous Navigation, SLAM & Sensor Fusion (EKF-SLAM, Graph-SLAM, Factor Graphs, Bundle Adjustment)