SLAM simultaneously estimates an agent trajectory and a map of an initially unknown or changing environment. SLAM enables robot and drone navigation, AR anchors, autonomous systems, surveying, inspection, warehouses, mines, construction, and mapping where external positioning is unavailable or insufficient. The problem couples localization and mapping: pose is needed to place landmarks, while landmarks are needed to correct pose. Gauge freedom, scale, coordinate frame, observability, data association, calibration, synchronization, and loop closure define the solution. An engineering definition states variables, units, assumptions, domains, initial and boundary conditions, sampling or update rate, uncertainty, stability or error objective, and implementation constraints. Mathematical guarantees apply to the stated model; they do not automatically cover unmodeled dynamics, finite precision, sensor faults, saturation, delay, concurrency, or hostile inputs.

Architecture, representation, and operating mechanism. A front end extracts and tracks visual features or scan geometry, estimates relative motion, and proposes loop candidates. A back end optimizes a pose graph, factor graph, bundle adjustment, or filter. The map may contain sparse landmarks, dense depth, surfels, voxels, meshes, semantics, or neural fields. Each sensor observation is time-aligned and associated with prior features or map elements; odometry predicts motion; optimization/f filtering updates states; keyframes bound compute; place recognition detects revisits; loop constraints correct accumulated drift and propagate changes through the map. Absolute and relative trajectory error, drift per distance/time, loop precision/recall, relocalization, map accuracy/completeness, consistency, initialization time, tracking loss, recovery, latency, update rate, memory, power, and long-run stability matter. Sensors, actuators, sampling clocks, quantizers, communication, memory, processors, power, thermal behavior, software scheduling, safety interlocks, and operators affect the delivered result. End-to-end design allocates error and latency budgets to named components instead of assuming ideal data and unlimited compute. Results report accuracy or error, stability and robustness margins where applicable, convergence, latency, throughput, memory, numerical conditioning, precision, energy, coverage, false alarms, and behavior at operating limits. Reference models, analytic cases, independent implementations, and confidence bounds make numerical or test evidence interpretable.

Implementation, hardware, and failure modes. ORB-SLAM uses visual features and bundle adjustment, VINS-Mono tightly couples monocular camera and IMU, LIO-SAM uses lidar-inertial smoothing and mapping, RTAB-Map emphasizes graph-based real-time appearance mapping, and direct methods optimize image intensity. Cameras, lidars, IMUs, GNSS, timestamp units, ISPs, feature accelerators, CPUs/GPUs, memory, and storage cooperate. Front-end feature/scan processing is high-rate; back-end sparse optimization can spike; embedded systems use keyframe and map pruning. Textureless/repeated scenes, motion blur, dynamic objects, lidar degeneracy, IMU bias, rolling shutter, clock/extrinsic error, loop perceptual aliasing, scale ambiguity, long corridors, weather, sensor dropout, and map changes cause drift or catastrophic correction. Engineering must include data movement, finite precision, resource contention, numerical or physical limits, error propagation, and deterministic behavior when assumptions are violated. Requirements, mathematical model, discretization, algorithm, numerical format, implementation, calibration, verification, deployment, monitoring, update, and incident response form one lifecycle. Versions of coefficients, transforms, test corpora, compiler settings, hardware kernels, tolerances, and assumptions remain linked to measurements.

Evaluation, verification, and deployment. Use sequence-separated datasets and real routes, surveyed ground truth, indoor/outdoor and dynamic scenes, high speed, loops, long duration, sensor failures, calibration/time perturbations, relocalization, map updates, compute overload, and replay determinism. SLAM feeds planning and AR but depends on calibration, sensor health, frame transforms, map version, localization confidence, storage, fleet merging, and safe fallback. A visually attractive map can still have unsafe local metric errors. Maps can reveal homes, facilities, people, security layouts, and locations. Capture permission, redaction, access, encryption, retention, sharing, geofencing, update authority, and deletion apply. Verification uses analytic identities, invariants, dimensional checks, deterministic unit cases, randomized and property tests, Monte Carlo uncertainty, worst-case boundaries, high-precision references, formal reasoning where tractable, extracted or hardware models, fault injection, and closed-loop or production replay. Independent evidence is essential when one model is used to validate itself. Requirements, mathematical model, discretization, algorithm, numerical format, implementation, calibration, verification, deployment, monitoring, update, and incident response form one lifecycle. Versions of coefficients, transforms, test corpora, compiler settings, hardware kernels, tolerances, and assumptions remain linked to measurements. Results report accuracy or error, stability and robustness margins where applicable, convergence, latency, throughput, memory, numerical conditioning, precision, energy, coverage, false alarms, and behavior at operating limits. Reference models, analytic cases, independent implementations, and confidence bounds make numerical or test evidence interpretable.

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    <text x="75" y="19" fill="#93c5fd" font-size="7.8" font-weight="700" text-anchor="middle">ESTIMATE → OBSERVE → CORRECT</text>
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    <tspan fill="#fbbf24" font-weight="700">LOOP CLOSURE</tspan><tspan fill="#8b98a5"> recognizes a previously seen place and redistributes pose error across the trajectory.</tspan>
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Selection and practical application. Use visual SLAM for low sensor cost and rich appearance, lidar SLAM for robust metric geometry, visual-inertial for high-rate motion and scale, and multi-sensor factor graphs for demanding robustness at greater complexity. ARKit/ARCore-like tracking, robot vacuums, warehouse AMRs, drones, vehicles, underground mapping, construction progress, and inspection use SLAM. Sensors, actuators, sampling clocks, quantizers, communication, memory, processors, power, thermal behavior, software scheduling, safety interlocks, and operators affect the delivered result. End-to-end design allocates error and latency budgets to named components instead of assuming ideal data and unlimited compute. An engineering definition states variables, units, assumptions, domains, initial and boundary conditions, sampling or update rate, uncertainty, stability or error objective, and implementation constraints. Mathematical guarantees apply to the stated model; they do not automatically cover unmodeled dynamics, finite precision, sensor faults, saturation, delay, concurrency, or hostile inputs. CFS connects this topic to semiconductor architecture, implementation, verification, manufacturing, packaging, test, and deployed AI-system tradeoffs across the platform.