Shannon Press · 2026 · 26 chapters
A robot never knows exactly where it is.
This book takes that fact seriously: it derives the mathematics of reasoning under uncertainty in full, makes every hard idea something you can play with in the page, and implements all of it in Rust.
Twenty-six chapters take a differential-drive rover called Rusty from its first noisy encoder tick to autonomously exploring and mapping a floorplan it has never seen — through Bayes filters, Kalman and particle filters, SLAM as least squares, planning under uncertainty, and modern factor-graph estimation.
Monte Carlo localization, running live. Nine hundred hypotheses start spread across the whole map. Each one moves with the robot and is weighted by how well its predicted range reading matches the real one. Within a few seconds, the cloud has found the robot — that collapse is what this book is about. Chapter 12 builds it properly.
The method
Three passes over every idea
Foundation
The full mathematics: definitions, assumptions stated out loud, and derivations carried through — not gestured at. Long algebra folds away for readers who want the result first.
Conceptual
Every hard idea becomes something you can manipulate. Drag the robot, turn up the noise, scrub through time, re-roll the seed, and watch what the equations were trying to tell you.
Practical
Then you build it in Rust, with the crates the field actually uses — nalgebra, faer, factrs, parry — and code you could lift into a real robot.
Contents
Seven parts, twenty-six chapters
Foundations — The Robot and Its Uncertainty
- CH.01The Robot That DoubtsWhy a single best guess is not enough, and what a belief buys you instead.
- CH.02Probability: The Language of UncertaintyBayes rule, Gaussians in one and many dimensions, moments and canonical form.
- CH.03The Geometry of MotionFrames, rotations, SE(2) and SE(3), exponential coordinates, and uncertainty on manifolds.
- CH.04Rusty, Sensors, and the SimulatorWheel odometry, LiDAR physics, and the two worlds every later chapter runs in.
The Bayes Filter Family
- CH.05The Bayes FilterThe recursion behind every estimator in the book: sensing sharpens, moving smears.
- CH.06Kalman FiltersThe linear-Gaussian world, the gain as precision-weighted trust, and the information form.
- CH.07Beyond Linearity: EKF, UKF, and ManifoldsWhere linearization lies, what sigma points fix, and how modern filters live on Lie groups.
- CH.08Nonparametric FiltersHistograms, importance sampling, particle filters, and the art of resampling.
Probabilistic Models
Localization
Mapping and SLAM
- CH.13Occupancy Grid MappingLog-odds mapping with known poses, and where per-cell independence betrays you.
- CH.14The SLAM Problem and EKF SLAMWhy correlations are the map, and the two flaws that ended the filtering era.
- CH.15SLAM as Least Squares: Factor GraphsThe modern backbone: MAP inference as sparse nonlinear least squares.
- CH.16Scan Matching and Pose-Graph SLAMICP, NDT, loop closure, and a complete 2-D SLAM system built by hand.
- CH.17FastSLAM and Rao-BlackwellizationSample the trajectory, solve the map in closed form — one particle, one universe.
- CH.18Visual and Visual-Inertial SLAMCameras as probabilistic sensors, IMU preintegration, and marginalization.
- CH.19Modern Map RepresentationsOctrees, TSDFs, and distance fields — mapping as recursive estimation in disguise.
Planning and Acting under Uncertainty
- CH.20Motion Planning: From Geometry to ProbabilityConfiguration space, A*, and sampling-based planners that are only probably complete.
- CH.21Decision Making I: MDPsFrom plans to policies, and the Bellman equation that produces them.
- CH.22Decision Making II: POMDPsPlanning in belief space, alpha-vectors, and why robots hug walls.
- CH.23Stochastic MPC: MPPI and FriendsControl by sampling: a thousand imagined futures, reweighted every frame.
- CH.24Exploration and Active SLAMWhere should the robot go in order to learn? Information gain, made concrete.
Built on the classic references — Thrun, Burgard & Fox; Lynch & Park; Craig; Niku; Choset et al.; Spong et al. — and brought up to date with factor graphs, estimation on Lie groups, and modern planning under uncertainty.