Mapping the Unseen Ground: A Survey on Dense Mapping and Traversability Methods for Agricultural and Forestry Robots

2.2.1.1 Octree

OctoMap, an octree-based structure, is a 3D occupancy grid mapping framework designed for efficient occupancy representation in volumetric space, organizing the environment into hierarchically structured voxels, as shown in Fig. 9 to achieve memory-efficient storage by pruning unoccupied regions [92], [93], [94]. Octrees offer a memory-efficient hierarchical representation that adapts to spatial occupancy and guarantees logarithmic access time. Initially, octrees were used to store occupancy probabilities; however, voxels can also store Gaussian-based models to better represent shapes within the voxel [95], or Euclidean distances [96], [97], [98], which further aid in obstacle avoidance. OctoMap incorporates probabilistic occupancy estimation, effectively addressing sensor uncertainties and dynamic scenarios. Extensions to OctoMap have facilitated semantic 3D mapping; for example, CNN-SLAM integrates CNN-derived depth predictions with monocular SLAM within an OctoMap-based framework to generate dense semantic maps [99]. Similarly, Yang et al. employ an octree-based occupancy grid enhanced with conditional random field (CRF) optimization for semantic voxel labeling [100]. Advanced octree-based variants, such as VDB-Mapping, utilize OpenVDB for efficient sparse volumetric data representation [101], while SHINE-Mapping employs hierarchical implicit neural representations embedded in octree structures, combining traditional efficiency with neural network expressiveness [94]. OctoMap’s compactness and multi-resolution mapping capabilities enable efficient storage and rapid spatial queries, making it highly suitable for large-scale environmental modeling [102].

OctoMap applications notably include UAV and underwater robotics; however, ground vehicle applications often prefer 2.5D elevation maps for their computational advantages. Nevertheless, OctoMap demonstrates notable limitations in performance relative to contemporary neural reconstruction methods; experimental comparisons indicate significantly longer processing times and a lack of semantic segmentation for traversable objects [103]. Alternative mapping strategies, such as REAL (Rapid Exploration with Active Loop-closing), which integrate frontier-based exploration, graph planning, and active loop-closure mechanisms, have demonstrated improved performance metrics over OctoMap-based methods, particularly in exploration efficiency and pose accuracy [104].

A Gaussian Process Regression (GPR) approach with a novel inverse square law-based kernel has been developed to address data sparsity and uncertainty in radiation mapping. In this work, OctoMap serves as the underlying probabilistic octree, initially constructed by the robot using LiDAR/SLAM for spatial indexing. The Gaussian Process-predicted radiation intensities are then projected into the octree’s voxels. This approach demonstrated superior predictive accuracy in scenarios involving multiple radiation sources compared to conventional techniques [105]. Further advancements include OctoMap-RT, which leverages GPU-based massively parallel ray-shooting combined with hybrid Central Processing Unit (CPU)-GPU architectures, achieving mapping speeds up to 41.2 times faster and occupancy grid accuracy improvements of 0.52% over traditional OctoMap and SuperRay methods, addressing voxel determination bottlenecks with novel voxel and Bounding Volume Hierarch (BVH) representations [106]. Other variants of tree-based data structures have also been explored. For example, Slutsky and Dobkin introduced a Dual Inverse Sensor Model (ISM)-based approach for rapid volumetric occupancy grid generation using a Quad-Tree structure in automotive applications. Their method demonstrated a 15-fold speedup in high-resolution mode and achieved real-time frame rates between 25 and 50 FPS, effectively handling simultaneous multi-sensor integration [107].

2.2.1.2 Voxel Grid

Algorithms, such as Voxblox and Nvblox, have established themselves as efficient methodologies for dense 3D reconstruction in robotics. These methods discretize space into voxels that encode occupancy or signed distance information, thereby explicitly representing free space and distinguishing between known and unknown regions [109], [110], [111], [112], [113]. Voxblox employs a CPU-based, two-level sparse voxel hashing scheme that enables real-time updates and querying of truncated signed distance fields (TSDFs) and Euclidean signed distance fields (ESDFs) [114]. Its spatially hashed voxel representation efficiently allocates memory to occupied regions, making it well suited for applications requiring both free space awareness and surface reconstruction [115], [116]. Nevertheless, CPU constraints limit the attainable map resolution and scale, particularly in high-detail or large-scale environments, and while recent optimizations such as Voxfield and FIESTA improve ESDF generation and runtime, these enhancements are bounded by the inherent computational load [117], [118]. In contrast, Nvblox leverages GPU acceleration to overcome these limitations. By parallelizing all aspects of the mapping pipeline, including real-time querying, Nvblox achieves up to 177× faster TSDF updates and 31× faster ESDF computations relative to its CPU-based counterpart, thereby facilitating high-resolution mapping on embedded GPU hardware [119], [120]. Although this approach necessitates GPU resources, the substantial performance gains enable higher update frequencies and improved map fidelity critical for dynamic robotic path planning and obstacle avoidance. Notably, as the desired resolution of the map increases, the memory requirements scale cubically, rendering the representation of large, detailed environments computationally intensive.

Another mapping algorithm based on voxelized spatial data is the Normal Distributions Transform (NDT), a probabilistic technique for point cloud alignment. NDT models the environment as a collection of Gaussian distributions, each defined by a mean and covariance, derived from voxelized spatial partitions. The alignment process seeks to maximize the likelihood of the observed points given the model distributions, mathematically expressed as:

\[E(R, t) = \sum_{i=1}^{M} \log P(P_i \mid R Q_i + t)\tag{1}\]

where \(P(P_i | R Q_i + t)\) is the conditional probability of observing point \(P_i\) given the transformed model point \(Q_i\) [121], [122]. NDT faces challenges including computational complexity due to voxelization and Gaussian fitting processes, potentially limiting real-time applications [123]. Furthermore, its performance is sensitive to parameter selection, such as voxel size and iteration count, influencing accuracy and convergence. Normal Distributions Transform Occupancy Map (NDT-OM) however, is a novel 3D mapping framework that extends traditional NDT methods by incorporating a recursive update scheme for Gaussian cell parameters alongside a probabilistic occupancy update, enabling efficient, memory-bounded, multi-resolution mapping in large-scale, dynamic environments [124].

NDT-OM is highly adaptable and remains robust against noise, even in dynamic, complex environments. Although, NDT-OM often outperforms grid-based approaches at coarser resolutions, updates can be slower than octree-based occupancy maps at equal discretization, potentially limiting its applicability in scenarios with extremely high sensor rates or very fine resolution requirements [125]. Building on NDT-OM’s adaptability and robustness, modern 3D mapping systems often pair it with high-resolution LiDAR hardware and optimized SLAM pipelines to balance accuracy and real-time performance. Multi-channel LiDAR configurations, such as Velodyne’s 16, 32, 64, and 128-channel models, significantly influence 3D mapping fidelity and computational complexity; higher channel counts yield denser and more detailed point clouds but impose increased computational demands, a sample point cloud map of the forest environment is presented in Fig. 6. Addressing these constraints, selective keyframe techniques have been proposed to facilitate real-time 3D reconstruction from high-density 128-channel LiDAR data, demonstrating superior detail and practicality for real-time applications [126]. Additionally, a novel 3D LiDAR reconstruction framework has been proposed, leveraging encoder-decoder neural networks to densify sparse LiDAR data with camera images, significantly improving free-space estimation by over 40% and effectively generalizing from synthetic to real-world conditions, enabling low-cost sensors to perform comparably with high-end LiDAR systems [127]. As an alternative to voxel grids planar-surface-based occupancy grids have also been proposed, reducing memory usage and erroneous artifacts by clustering stereo-vision point clouds into planar cells and combining them into efficient 3D representations [128].

2.2.1.3 Voxel hash

Both Voxblox and Nvblox frameworks utilize voxel hashing to manage memory efficiently in large-scale environments by allocating storage only to occupied regions, ensuring fast access times even in sparsely populated scenes [93]. This efficiency is crucial for real-time dense mapping, where prompt integration of sensor data is essential [129], [130]. Extensions of these voxel-based methods have also been developed for multi-robot systems. For instance, Coxgraph transforms ESDF submaps into compact mesh packs, enabling efficient inter-robot data transmission and supporting globally consistent dense mapping under limited bandwidth conditions [131].

2.2.1.4 Unordered linear structures

Point clouds [132], [133], [134] provide unordered sets of spatial samples, as shown in Fig. 10. This data structure is useful for visualization, but is memory inefficient and slow while querying the selected region of the model for motion planning. Alternatively, surfels (surface elements) [135] can be used to accumulate points in a geometric structure and save memory. However, this approach does not significantly improve the query time even if the K-dimensional tree is used.

RTAB-Map is a robust dense point cloud mapping algorithm for real-time 3D mapping and navigation that integrates multiple sensor modalities, including RGB-D, stereo, and LiDAR and accommodates diverse odometry inputs. The system constructs dense point-cloud maps while employing Bayesian filtering for loop closure probability estimation, ensuring high accuracy and effective long-term online operation [136], [137]. Central to its performance is a hierarchical memory management scheme that categorizes data into Short-Term Memory (STM), Working Memory (WM), and Long-Term Memory (LTM) [13]. This structure not only retains recent observations and actively processed data but also archives less frequently accessed scans to memory, thereby optimizing RAM usage. The algorithm’s incremental appearance-based loop closure detection leverages both global and local feature extraction, often enhanced by deep learning models to reliably identify previously visited locations, generate location points with time indices and image signatures, and update corresponding weights [138], [139], [140]. Such capabilities are critical in dynamic environments.

Low-cost 3D LiDAR scanners, when combined with Extended Kalman Filter models, facilitate accurate and reliable point-cloud acquisition for precision agriculture applications. In parallel, open-source handheld mobile mapping systems have emerged as a flexible alternative for large-scale 3D mapping, offering GPU-independent operation and demonstrating effectiveness in both indoor and outdoor environments [141], [142]. In addition, novel algorithms that combine stereo camera output with ultrasonic data and perception pipelines that employ deep networks for point cloud classification have automated map cleaning and enhanced segmentation accuracy, thereby improving dense mapping outputs for autonomous navigation [134]. Additional contributions include robot-assisted mobile scanning approaches that integrate SLAM with motion control and semantic segmentation to generate high-quality dense point clouds for building interiors, and semi-automatic frameworks that align SLAM outputs with public building maps to reduce cumulative pose errors in urban environments [143], [144]. Finally, integration of Inertial Navigation System (INS)/GNSS with LiDAR Odometry and Mapping (LOAM) facilitates global georeferencing of dense point clouds with meter-level accuracy in GNSS-challenged areas, while real-time incremental manifold mesh reconstruction algorithms operating on a single CPU core significantly boost computational efficiency without sacrificing reconstruction accuracy [145], [146], [147]. A feature-by-feature comparison of the main map data structures is shown in Table 2.

2.2.2.1 Euclidean Distance Fields (ESDFs)

provide a mathematical representation of shapes by assigning each point in space a scalar value corresponding to its shortest distance to the surface of the shape. In ESDF mapping, this principle is employed to record the signed distance at every spatial point, using a convention where the distances are positive for the points outside the shape and negative for the points inside it. \[\phi(\mathbf{x}) = \operatorname{sgn}\bigl(o(\mathbf{x})\bigr)\;\min_{\mathbf{y}\in\partial O}\|\mathbf{x}-\mathbf{y}\| \quad\tag{2}\] where \[o(\mathbf{x}) = \begin{cases} +1, & \mathbf{x}\notin O\quad(\text{free space}),\\ -1, & \mathbf{x}\in O\quad(\text{inside obstacle}) \end{cases}\tag{3}\]
and \(\partial O\) is the obstacle boundary [97]. In practice, these functions are commonly implemented via voxel grids that discretize the three-dimensional space, with each voxel encapsulating the signed distance value. As new depth measurements are acquired from sensors such as LiDAR or RGB-D cameras, the ESDF is incrementally refined to enhance the fidelity of the reconstructed map. ESDF computes the precise Euclidean distance from each 3D point to the nearest surface, delivering metric fields essential for accurate motion planning and collision avoidance. ESDFs require a complete geometric reconstruction of the environment, incurring significantly higher computational overhead. The processing cost scales directly with voxel resolution; finer discretizations improve metric precision, but require increased computational resources and memory [148]. Although incremental algorithms can mitigate some of these challenges, real-time generation of high-resolution ESDF maps in large-scale environments remains a nontrivial problem. An alternative and promising avenue is the use of neural networks to implicitly represent ESDFs. These neural ESDF frameworks have the potential to offer more compact storage solutions and improved generalization to unobserved areas [149], [150], [151].

Despite these advancements, several limitations persist. One significant issue is the approximation error incurred when integrating new measurements. Many implementations rely on projective distances along sensor rays for ESDF updates, a method that can result in inaccuracies, particularly for surfaces viewed at oblique angles [152].

To counteract this, some researchers have proposed normal-guided sampling techniques that compute distances along the surface normals rather than along the sensor rays as shown in Fig. 11. Additionally, the computational cost associated with high-resolution voxel data access and map updates can become a bottleneck for real-time applications, prompting further research into hardware acceleration and more efficient data structures [93]. For neural ESDF representations, the issue of catastrophic forgetting during incremental mapping remains a concern; as neural networks update with new observations, there is a risk of losing information from previously mapped regions. Techniques such as robot-centric mapping and bundle supervision have been proposed to mitigate this problem by maintaining an accurate local map and constraining network training with historical data [153].

2.2.2.2 Truncated Signed Distance Function (TSDF)

Truncated Signed Distance Functions (TSDFs) extend the conventional ESDF approach by truncating distance values beyond a predefined threshold. This modification yields a more tractable representation of the environment, particularly in real-time applications, by preserving the smooth surface characteristics of ESDFs while reducing both memory footprint and computational overhead. However, TSDFs exhibit limitations, notably in their diminished capacity to represent distant points accurately, which can lead to drift in tracking scenarios. Moreover, the resolution constraints inherent to TSDF representations may impair data association during depth image processing, especially when utilizing high-resolution sensors [154].

A principal advantage of TSDFs lies in their ability to produce high-quality, smooth surface reconstructions [110]. This is typically achieved through trilinear interpolation methods during surface extraction, often implemented via the Marching Cubes algorithm. The zero-crossing of the signed distance field accurately delineates surface boundaries, facilitating the extraction of meshes or point clouds, and generally yielding three-dimensional models with superior fidelity compared to alternative mapping techniques [109], [135].

Notwithstanding these benefits, TSDF mapping faces substantial challenges in terms of memory efficiency. The storage of dense voxel grids can be prohibitively expensive for large-scale environments. To mitigate this, many implementations have adopted sparse voxel representations, such as voxel hashing, which allocate memory only to voxels proximal to observed surfaces [109]. Additionally, the truncation process itself may impede the accurate representation of thin structures that are smaller than the truncation threshold, potentially resulting in a loss of fine geometric detail.

Despite these limitations, TSDF mapping remains a widely adopted and effective approach for three-dimensional reconstruction in applications that demand real-time performance and high-quality surface detail. Its robustness has been demonstrated in various domains, ranging from autonomous navigation to augmented reality. Recent research efforts have further enhanced TSDF capabilities by integrating semantic information into the mapping process, thereby enriching environmental representations with contextual understanding [155].

Real-time TSDF implementations often leverage GPU acceleration to address the computational demands associated with updating large voxel grids. For instance, the KinectFusion [156] algorithm showcased the feasibility of real-time, GPU-accelerated TSDF mapping for three-dimensional reconstruction. More recent frameworks, such as Voxblox [96], have improved both efficiency and scalability by incrementally constructing the TSDF and dynamically expanding the map without prior knowledge of the dimensions of the environment [157].

Finally, TSDF mapping exhibits challenges when applied to dynamic environments. The presence of moving objects can introduce persistent artifacts in the reconstructed model, and while techniques like ray tracing have been proposed to mitigate this issue, they typically incur additional computational costs. Furthermore, TSDFs have occasionally been observed to overestimate Euclidean distances, which may further impact the accuracy of the mapping process [102], [158].

2.2.2.3 Fast Iterative Euclidean Signed Distance Transform Algorithm (FIESTA)

Computes ESDFs to rapidly determine obstacle proximities, enabling efficient, real-time map generation in cluttered environments. The algorithm’s iterative framework continuously refines the ESDF, enhancing spatial accuracy while accommodating environmental changes. However, its performance is contingent on high-quality input data; noisy or incomplete measurements can propagate errors, and its static environment optimization limits effectiveness in highly dynamic scenes. This requires the integration of auxiliary modules (e.g. semantic segmentation, dynamic object tracking) to increase robustness [97].

FIESTA consists of two core components: a feature extraction module and a tracking module. The feature extraction stage employs a multilayer FEAST network, comprising a Fast Adapting Network (FAN) and a Slow Adapting Network (SAN) arranged in a feedforward configuration, to isolate and consolidate salient events from the data stream, effectively filtering out noise. Subsequently, a modified asynchronous Probabilistic Data Association (PDA) tracker processes these events, achieving sub-pixel localization with processing times below 40 \(\mu\)s. Although the unsupervised learning strategy facilitates rapid adaptation to new targets with minimal prior modeling, the current reliance on a point target model constrains its applicability to extended or high-intensity targets. Moreover, while performance has been validated in single-target tracking scenarios, the algorithm’s scalability to multi-target environments and its behavior under low-motion, low-contrast conditions (e.g., geostationary orbits in leap-frog observations) remain open challenges [159].

2.2.2.4 Implicit Signed Distance Functions (ISDFs)

integrate neural implicit representations with traditional SDF frameworks to model complex, dynamic surfaces under noisy conditions. In ISDF, a multi-layer perceptron (MLP) maps 3D coordinates to signed distance values. The network is trained in real time using a self-supervised loss that constrains the predicted distance by the minimum distance from a batch of query points. Active sampling from a sparse set of keyframes is employed to counteract catastrophic forgetting, while batch sampling along back-projected rays enables simultaneous supervision of the signed distance and its spatial gradient.

The approach provides adaptive resolution and effective denoising through a neural field that dynamically allocates memory based on local data density. However, its implementation introduces significant complexity. The use of low-frequency positional embeddings, optimized for free, space SDFs can oversmooth surfaces, and the regularized enforcement of the Eikonal constraint inadequately handles singularities, limiting the method to room-scale environments [149].

In comparison to other SDF variants, ISDFs offer enhanced flexibility and adaptability at the cost of increased algorithmic complexity. Alternative strategies include Gaussian Process Distance Fields (GPDF) for probabilistic, continuous representations [158], and data structures such as octrees [160] and VDB for efficient memory and query performance. Multi-resolution and submap-based techniques further address scalability in large environments [118], [161].

Recent developments, such as the AiSDF framework, leverage the Atlanta World assumption to process streams of posed depth images. AiSDF achieves superior mesh reconstruction quality compared to methods like Voxblox and ISDF, generating an explicit 3D planar map composed of Atlanta-aware surfels for downstream processing [162]. However, per-keyframe surfel extraction precludes the formation of a unified global map, and integration of Atlanta priors into the implicit representation remains an open challenge.

DeepSDF mapping algorithms leverage neural network architectures to parameterize signed distance functions over 3D space. These methods employ CNNs or MLPs to extract hierarchical features directly from raw sensor data, facilitating robust reconstruction and shape completion by inferring missing regions based on learned latent representations [150], [151]. However, the training and inferencing process for these high-dimensional models is computationally intensive, often necessitating extended training periods and high-performance computing resources [163]. Moreover, while deep SDFs generalize over diverse shape classes, they may exhibit degraded performance on highly intricate geometries, leading to representation inaccuracies. The requirement for large, annotated datasets further constrains their applicability in domains where data acquisition is challenging [164].

Recent advances in 3D LiDAR mapping have increasingly leveraged implicit neural representations combined with spatial hashing and submapping techniques to achieve high-fidelity, scalable reconstructions while dramatically reducing memory consumption. These approaches converge to deliver robust dense mapping, precise localization, and improved semantic segmentation in diverse environments. A notable contribution in this domain is the introduction of compact map representations, exemplified by the Tri-Pyramid method, which significantly reduces memory requirements without compromising mapping quality. Using an implicit neural framework, the Tri-Pyramid scales seamlessly from room-scale to city-scale environments while providing localization performance on par with state-of-the-art systems [165]. Building on this, the integration of hierarchical hash encoders with spatial hash grids has further optimized the implicit mapping process. This approach not only minimizes memory overhead by mitigating hash collisions but also enhances reconstruction accuracy through real-time, accurate signed distance function (SDF) labeling. As a result, these methods achieve state-of-the-art 3D mapping performance using less than half the memory compared to previous techniques [166]. Complementing these implicit representations, the Voxgraph framework introduces a submap-based strategy for volumetric mapping. By partitioning the environment into overlapping SDF submaps and maintaining global consistency through optimal alignment, Voxgraph operates efficiently even on computationally constrained platforms. Its performance is underscored by trajectory RMSEs of less than 1 m over extensive paths, thereby outperforming traditional visual SLAM and LiDAR systems in challenging real-world scenarios [118]. Finally, advances in domain transfer for semantic segmentation have further broadened the applicability of these mapping systems. By generating semi-synthetic scans from source datasets, recent methods enable deep learning models to generalize across various LiDAR sensor configurations without the need for additional labeled data. This strategy effectively bridges domain gaps, significantly improving segmentation performance, and facilitating dense semantic annotation propagation [167].

NeuralBlox advances volumetric mapping robustness through incremental neural implicit updates from partial sequential observations, outperforming traditional TSDF methods in handling pose estimation errors and sensor noise. This approach supports real-time execution on CPUs, exhibits flexibility with diverse sensor inputs without retraining, and substantially enhances scene completeness and recall, facilitating safer robotic operation in dynamic environments [168]. Complementing this, the Depth-Visual-Inertial (DVI) mapping system integrates time-of-flight, RGB cameras, and IMU data through an error-state iterative Kalman filter, demonstrating exceptional precision and trajectory estimation robustness under complex, real-world conditions, particularly validated through the Bunker DVI Dataset [169]. Other neural models such as Neural Radiation fields (NeRFs) [170] are also still limited to small areas.

2.2.2.5 Semantic Mapping

Semantic Fusion leverages ElasticFusion for precise camera pose estimation and globally consistent surfel-based 3D reconstruction of environments [171]. It integrates CNN-based semantic segmentation on RGB-D frames to assign pixel-level class labels that are aggregated onto surfels via a Bayesian update scheme. A moving average continuously refines the semantic labels, while the inclusion of a CRF model enforces spatial regularity, which is essential for complex indoor settings. Real-time performance ensures robust pose estimation and mapping in dynamic scenarios, yet limitations persist in distinguishing individual instances within the same category [172]. Moreover, CNN dependency may compromise performance in cluttered or occluded environments [173], and high computational demands can restrict deployment [174].

Complementary to SemanticFusion, SemSegMap extends the SegMap framework by incorporating semantic and color information from RGB cameras into LiDAR-based mapping. This early sensor fusion enriches point clouds with geometric, visual, and semantic cues, enhancing segmentation consistency through an adapted Euclidean distance metric and a PointNet++-based descriptor network [175]. The multi-modal approach not only improves localization accuracy and robustness under varying environmental conditions but also facilitates detailed 3D reconstruction and semantic extraction [176]. In parallel, complementary approaches such as Volume-DROID, which integrates volumetric mapping with DROID-SLAM through real-time fusion of point cloud registration, semantic segmentation, and Convolutional Bayesian Kernel Inference, demonstrate the efficacy of dense representations in enhancing 3D semantic mapping for autonomous navigation [177]. Table 3 compares these different cell-content variants.

2.2.3.1 Graph-based mapping

methods have gained prominence due to their ability to efficiently represent and optimize robot trajectories and environment structures. The ART-SLAM [178] employs a pose graph framework, with robot poses as nodes interconnected by edges representing spatial constraints derived from sensor measurements or environmental elements such as floor coefficients. This system integrates diverse constraint information, including odometry, sensor alignment, and loop closures, using the g2o framework to achieve optimized trajectory estimations capable of handling extensive datasets like KITTI and underground mine scenarios, demonstrating both accuracy and real-time performance. Addressing scalability in graph-based SLAM, the c-blox system developed by Millane et al. [109] utilizes overlapping TSDF subvolumes for environmental representation. Camera tracking and bundle adjustment localize these subvolumes, with global trajectory optimization managed via pose graph optimization [109]. The method proposed in [179] utilizes local NDT-OM maps connected with pose graph that are optimized after loop closure detection to improve the global map. Similarly, the D3VIL-SLAM system by Frosi and Matteucci integrates LiDAR, visual, and inertial sensor data within a factor graph optimization framework, combining LiDAR localization, trajectory loop closure, and inter-frame constraints to enhance robustness [180]. Hierarchical approaches combining deep learning and graph optimization have been proposed in visual-LiDAR SLAM, incorporating modules for odometry, loop closure detection, and 3D mapping, further optimized through g2o [181]. RGB-D SLAM frameworks similarly leverage frontier-based exploration and pose graph optimization, refining trajectories through strategically selected exploration goals [182]. Continuous-time SLAM methods, particularly suitable for aerial mapping, represent trajectories as continuous temporal functions optimized via robust iterative least squares methods, incorporating sensor data, inertial measurements, and motion models for global consistency [183]. Graph-based methods further enhance mapping through explicit modeling of spatial correlations, as demonstrated by MRFMap’s use of Markov Random Fields and loopy belief propagation to address occlusions and noisy sensor data [184]. Multi-robot collaborative mapping is efficiently handled by systems like Coxgraph, achieving global consistency through joint trajectory and submap optimization across multiple agents [131]. Similarly, CAOM utilizes dense pose graph structures and factor graphs integrating local coherence and heterogeneous sensor fusion to mitigate drift [132]. In exploration contexts, methods like Volume-DROID utilize factor graphs for fusing LiDAR and inertial data, applying improved loop closure detection algorithms inspired by Cartographer to mitigate drift in trajectory estimates [177]. Systems employing multi-layered graph representations further demonstrate efficiency by combining XML-based metadata structures and optimized point cloud storage, facilitating large-scale dataset management [185].

Recent advances in graph-based mapping have yielded significant improvements across diverse applications. Deep learning applied to ground-based LiDAR point clouds now surpasses traditional methods in semantic segmentation, individual tree delineation, and species classification, although standardization and data sharing remain critical issues with emerging opportunities in Graph Neural Networks [133]. In urban navigation, novel techniques summarize large-scale 3D maps by leveraging augmented spherical RGB-D images that integrate geometric, photometric, and semantic data to construct navigability graphs, thus achieving efficient data compression without sacrificing localization performance [186]. Complementarily, graph-based SLAM approaches have been developed that obviate the need for odometry by employing scan matching and weighted motion averaging to optimize pose graphs, thereby producing robust, consistent 3D reconstructions of outdoor environments [187]. Further, innovative map merging strategies utilize deformable pose graph models to correct distortions inherent in SLAM-generated maps, enhancing global consistency and reducing cumulative errors [188]. Additionally, mesh optimization algorithms based on region-growing techniques have been shown to reduce polygon complexity by up to 75% in planar environments without significant loss of geometric precision, despite limited effectiveness for curved surfaces [189]. Finally, mapping systems tailored for non-uniform density 3D point clouds acquired by micro aerial vehicles integrate an extended Generalized-ICP algorithm with multi-edge pose graph optimization, effectively compensating for sparse data and yielding globally consistent maps [190].

RTAB-Map’s graph-based mapping framework underpins its scalability and efficiency, facilitating incremental data integration essential for large-scale applications [191], [192]. However, the memory management strategy can incur potential data loss in environments that undergo substantial changes [139], [193], and high levels of dynamic objects can challenge its loop closure detection, resulting in mapping inaccuracies [194]. Additionally, the considerable computational resources required may restrict its deployment in resource-constrained systems [136], [195]. Complementing this, approaches based on handheld LiDAR SLAM integrated within a factor graph framework have demonstrated centimeter-level mapping accuracy and efficient 3D reconstruction through LiDAR point cloud fusion, even under GNSS constraints [196].

The Robot-centric Implicit Mapping (RIM) method addresses efficiency and memory constraints in large-scale dense mapping by utilizing a hybrid representation comprising implicit features and shallow MLP networks. RIM maintains both local and scalable global maps, effectively mitigating catastrophic forgetting and handling noisy inputs via robust outlier removal, resulting in superior performance metrics, such as improved accuracy, completeness, and adaptability across extensive spatial scales [153].

The hierarchical SLAM method by Estrada, Neira, and Tardós presents a two-level mapping architecture in which independent local stochastic maps are maintained in constant time, while a sparse global adjacency graph encodes inter-map relations and enables a near-optimal, loop-closing optimization whose cost scales linearly with loop size [197]. In contrast, Folkesson and Christensen’s graphical SLAM formulates the entire mapping problem as energy minimization on a pose–feature graph, using nonlinear energy nodes and coarse-to-fine fitting to impose multiple loop constraints automatically, thereby reducing linearization errors and achieving scalable, consistent map building. Together, these approaches demonstrate that choosing an appropriate map data structure, whether a hierarchical submap graph or a globally optimized pose graph, is critical for balancing SLAM accuracy, robustness, and real-time performance [198].

2.2.3.2 Dense Object Nets (DON)

Employs deep learning architectures, predominantly convolutional neural networks, to derive dense object representations from visual data, extracting features that yield comprehensive spatial maps of object presence, arrangement, and interrelationships. This process is enhanced through instance segmentation, enabling the differentiation of overlapping instances via mask prediction and bounding box regression [199], [200], [201], while integrated attention mechanisms further refine detection by emphasizing pertinent features amid background noise [202].

The resulting dense representations provide superior environmental context compared to traditional sparse methods, facilitating accurate object localization and recognition in applications such as autonomous driving and robotic manipulation. However, the inherent computational complexity of processing dense maps can induce latency in object-dense scenarios, and reliance on extensive annotated datasets can impede generalization in novel environments [203].

Additionally, challenges such as overfitting, despite mitigation via data augmentation and transfer learning, persist when training data lacks diversity [173], [204], [205].

Google’s Cartographer, introduced by Hess et al. in “Real-Time Loop Closure in 2D LIDAR SLAM” combines local scan matching into submaps – probability grids refined via a Ceres-based nonlinear least-squares optimizer and a sparse pose graph with branch-and-bound loop closure detection and robust optimization to achieve accurate real-time 2D SLAM on modest hardware [91]. Sobczak et al. then examined how different sensor suites affect Cartographer’s performance in simulation, finding that three 2D LiDARs plus IMU and odometry yields the lowest errors in cluttered rooms while a single 3D Velodyne LiDAR with IMU excels in long hallway scenarios [206]. finally, Nüchter et al. demonstrated that applying a continuous-time, spline-based 6-DoF trajectory optimization atop Cartographer’s pose graph further refines maps into globally consistent, high-fidelity 3D reconstructions even without inertial measurements [207].

2.2.3.3 Elastic mapping

This mapping technique constitute advanced methodologies, integrating elasticity to dynamically adapt environmental representations based on real-time sensor data. These maps effectively address challenges posed by complex and unstructured environments where rigid mapping approaches may falter. Typically implemented via parametric models such as spline-based representations, elastic maps exhibit smooth deformation capabilities enhanced by mathematical methods like Laplacian regularization to preserve spatial continuity and feature accuracy [208]. Elastic maps are inherently designed for robust multisensor integration, incorporating data from LiDAR, vision sensors, and inertial measurement units (IMUs). Probabilistic algorithms, notably Bayesian inference techniques, manage sensor uncertainties and noise, thus ensuring comprehensive and precise environmental modeling [209]. A significant advantage of elastic maps is their dynamic responsiveness to environmental changes, proving particularly beneficial in non-static contexts such as urban areas or natural terrains. Real-time adaptability facilitates continuous localization and navigation without necessitating complete re-mapping procedures [210]. To maintain computational efficiency, elastic mapping systems frequently employ hierarchical voxel block hashing methods, optimizing the data structures and scaling effectively for extensive environments [211]. This inherent flexibility allows for the seamless incorporation of incoming data, vital for robotic applications characterized by unpredictability [212]. By continuously updating and refining environmental representations, elastic maps significantly enhance autonomous navigation strategies, enabling informed decision-making and obstacle avoidance in dynamic conditions.

Despite their clear advantages, elastic mapping approaches can incur considerable computational overhead due to the complexity and continuous nature of map updating processes. Furthermore, the performance of elastic maps is closely tied to sensor data quality; thus, noisy or inaccurate sensor inputs pose risks of deteriorated map accuracy and compromised robotic operations. Consequently, successful implementation necessitates sophisticated algorithms and an in-depth comprehension of both underlying mathematical frameworks and specific application contexts.

A subset of the sensors reviewed in the literature, including stereo and depth cameras as well as LiDAR, was integrated into established mapping frameworks to generate sample maps of a landmark. Fig. 12 presents these maps, illustrating the visual differences that arise when various sensors and algorithms are applied.