Autonomous mobile robot
navigation

Before You StartHow This Book Is Laid Out

This book covers the full navigation stack the way you would actually build one: math first, then estimation, then maps, then decisions — with the infrastructure and outdoor hardening before the learning-based finale. The phases stack deliberately: Phase 5’s planners consume Phase 3’s maps, which consume Phase 2’s odometry, which stands entirely on Phase 1’s optimization machinery.

Everything here is deliberately ROS-free. Every library named runs as a standalone C++ dependency, so you learn the actual algorithms and systems rather than a middleware’s wrappers around them. Each phase brief below says what the phase covers, why it sits where it does, and the specific state-of-the-art tools worth knowing by name.

This page is the map; the chapters are the territory. Every phase below links to its deep dive — same format as the SLAM field book: equations, diagrams, runnable C++ setups, papers, and interview questions.

ContentsThe Eight Phases

1. 01Mathematical Foundations & OptimizationPoses, Lie theory, and the nonlinear least-squares machinery every later phase reuses.Start here
2. 02State Estimation & OdometryFilters, wheel/IMU kinematics, and the LiDAR-inertial and visual-inertial odometry SOTA.Estimation
3. 03Mapping & SLAM SystemsMap representations, loop closure, pose graphs, and the SLAM systems that matter.Mapping
4. 04Global Localization & RelocalizationThe kidnapped robot problem: particle filters, scan matching, and place recognition.Localization
5. 05Path Planning & Motion ControlFrom A* and sampling planners to MPPI and nonlinear MPC: deciding and steering.Planning
6. 06Calibration & ROS-Free InfrastructureSensor calibration, time sync, and zero-copy IPC — the plumbing, without ROS.Infrastructure
7. 07Outdoor & Large-Scale NavigationGNSS fusion, elevation maps, dynamic obstacles, and surviving the real world at scale.Outdoors
8. 08Learning-Based Methods (AI Navigation)Learned odometry, Gaussian splatting SLAM, DRL policies, neural planners, and VLA navigation.AI Nav

Phase 1Mathematical Foundations & Optimization

Every later phase speaks one language — pose — and this phase teaches it properly: rigid transformations in SE(2) and SE(3) for where things sit, and Lie theory (so(3), se(3)) for doing calculus on rotations without singularities or slowly-corrupting matrices. On top comes the estimation machinery the whole stack reuses: the Bayes filter as the master recipe for reasoning under uncertainty, and Gauss-Newton and Levenberg-Marquardt as the workhorses of the nonlinear least-squares problems that SLAM backends, calibration, and planners all eventually reduce to. Get this phase right and phases 2–8 become applications, not mysteries.

Deep dive available: Phase 1 · Mathematical Foundations & Optimization → — equations, diagrams, Sophus/manif/Ceres code, papers, and interview questions.

Phase 2State Estimation & Odometry

The robot’s first continuous job is a running estimate of where it is and how it is moving, fused from sensors that each lie a little in their own way. The classical tools come first: EKF/UKF fusion, wheel and IMU kinematics, visual odometry in both feature-based and direct flavors, and point cloud registration with ICP and NDT. Then the systems defining today’s state of the art: tightly-coupled LiDAR-inertial odometry (FAST-LIO2, DLIO, Point-LIO) and the visual-inertial pipelines (ORB-SLAM3, VINS-Fusion, OKVIS2, SVO 2.0). Everything in this phase drifts without bound — fixing that is Phase 3’s job.

Deep dive available: Phase 2 · State Estimation & Odometry → — IMU and wheel models, EKF/ESKF, visual odometry, ICP/NDT, the LIO and VIO SOTA, plus two runnable C++ setups.

Phase 3Mapping & SLAM Systems

Odometry drifts; SLAM caps the drift by building a map and recognizing when the robot returns somewhere it has already been. This phase covers the map representations — occupancy grids, 3D octrees (OctoMap), and the TSDF/SDF distance fields that replaced them for dense work — plus the correction machinery of loop closure detection and pose graph optimization. On the systems side: Cartographer’s standalone C++ core and the GPU-accelerated GLIM for LiDAR, ORB-SLAM3 across monocular, stereo, and RGB-D with IMU, and Voxblox / NVBlox for modern dense TSDF and ESDF mapping.

Deep dive available: Phase 3 · Mapping & SLAM Systems → — occupancy grids, octrees, TSDF/ESDF, loop closure, pose graphs, the Cartographer/GLIM/ORB-SLAM3 tour, plus two runnable C++ setups.

Phase 4Global Localization & Relocalization

A robot switched on inside an already-mapped building has a map but no idea where it stands in it — the kidnapped robot problem. Monte Carlo Localization answers it with a cloud of particle hypotheses, whittled down by scan matching against the known map until one survives. The modern accelerant is place recognition: compressing what the robot currently sees into a fingerprint it can look up in the map — DBoW3, NetVLAD, and CosPlace for cameras; Scan Context++, OverlapNet, and LiDAR-Iris for LiDAR. The same machinery is what rescues a SLAM system after tracking loss.

Deep dive available: Phase 4 · Global Localization & Relocalization → — Monte Carlo localization with kidnap recovery, scan matching, visual and LiDAR place recognition, plus two zero-dependency C++ setups.

Phase 5Path Planning & Motion Control

With a pose and a map in hand, the robot can finally decide where to go and how to steer. Global planners search the map, either on a graph (A*, D* Lite, Jump Point Search) or by sampling (RRT*, PRM, Informed RRT*, LazyPRM*), while the local layer turns the chosen route into motor commands: the Dynamic Window Approach, Pure Pursuit, the Stanley controller, and model predictive control. The state-of-the-art local stack is GPU-accelerated MPPI, the standalone Time-Elastic-Band optimizer, and nonlinear MPC built on ACADO or CasADi.

Deep dive available: Phase 5 · Path Planning & Motion Control → — A*/D* Lite/JPS, RRT* and the informed trick, DWA/TEB/MPPI, pure pursuit and Stanley, plus runnable A* and pure-pursuit setups.

Phase 6Calibration & ROS-Free System Infrastructure

None of the earlier math survives contact with a rig whose sensors disagree about where they are mounted and when they measured. This phase covers intrinsic and extrinsic sensor calibration — Kalibr for camera–IMU, LiDAR-Align for LiDAR–IMU, BIFROST — and the systems plumbing a ROS-free stack must supply for itself: zero-copy shared-memory IPC with Iceoryx, messaging with ZeroMQ, standalone eProsima Fast-DDS, and the multi-threading and time-synchronization discipline that keeps a multi-sensor pipeline honest. Unglamorous, and the difference between a demo and a product.

Deep dive available: Phase 6 · Calibration & ROS-Free Infrastructure → — intrinsics, Allan variance, Kalibr and hand-eye, time sync, zero-copy IPC, plus runnable Allan-variance and ZeroMQ benchmarks.

Phase 7Outdoor & Large-Scale Navigation

Outdoors, the tidy indoor assumptions collapse: no flat floor, kilometres of scale, moving people and vehicles, and lighting and weather that change what every sensor sees. The additions this phase brings: RTK-GNSS fusion with correct WGS84 → ENU frame handling, 2.5D elevation mapping with ETH Zurich’s Grid Map library, dynamic obstacle removal so a car that parked and left doesn’t haunt the map forever, and robustness to appearance change. Graph-based GNSS–LiDAR–inertial fusion ties the global and local estimates together at scale.

Deep dive available: Phase 7 · Outdoor & Large-Scale Navigation → — RTK-GNSS, exact WGS84→ENU math, GNSS factor graphs, elevation mapping and traversability, dynamic removal, plus two zero-dependency setups.

Phase 8Learning-Based Methods (AI Navigation)

The final phase asks, for every module built so far, whether a neural network does the job better — and the honest answer is sometimes, and the list grows every year. Learned front-ends replace hand-designed features and ICP, NeRFs and 3D Gaussian Splatting replace voxel grids with continuous photorealistic scenes, reinforcement-learned policies trained sim-to-real replace local planners in dynamic crowds, and vision-language models let you state the goal in plain English (“find the office coffee machine”). Five tracks, each enhancing or replacing a classical phase from earlier in the book:

Deep dive available: Phase 8 · Learning-Based Methods → — SuperPoint/LightGlue/DROID-SLAM, NeRF and Gaussian-splatting SLAM, DRL with PPO, neural planners, VLA navigation, plus value-iteration and REINFORCE setups.

NextThe Deep Dives

All eight phases now have their chapters — the intuition, the real machinery, the SOTA systems compared honestly, worked C++ setups you can reproduce, linked papers, and interview questions with answers. Start at Phase 1 and read in order, or jump from any brief above; the prev/next navigation chains them end to end.

Compiled July 2026 · Complete edition — all eight deep dives live · Classical & SOTA, ROS-free throughout.