PathSpace: Rapid continuous map approximation for efficient SLAM using B-Splines in constrained environments

Aduen Benjumea; Andrew Bradley; Alexander Rast; Matthias Rolf

cs.ROMar 3, 2026

PathSpace: Rapid continuous map approximation for efficient SLAM using B-Splines in constrained environments

Authors: Aduen Benjumea, Andrew Bradley, Alexander Rast, Matthias Rolf

Organizations: School of Engineering, Computing & Mathematics, Oxford Brookes University, Oxford, UK

Abstract

Simultaneous Localization and Mapping (SLAM) plays a crucial role in enabling autonomous vehicles to navigate previously unknown environments. Semantic SLAM mostly extends visual SLAM, leveraging the higher density information available to reason about the environment in a more human-like manner. This allows for better decision making by exploiting prior structural knowledge of the environment, usually in the form of labels. Current semantic SLAM techniques still mostly rely on a dense geometric representation of the environment, limiting their ability to apply constraints based on context. We propose PathSpace, a novel semantic SLAM framework that uses continuous B-splines to represent the environment in a compact manner, while also maintaining and reasoning through the continuous probability density functions required for probabilistic reasoning. This system applies the multiple strengths of B-splines in the context of SLAM to interpolate and fit otherwise discrete sparse environments. We test this framework in the context of autonomous racing, where we exploit pre-specified track characteristics to produce significantly reduced representations at comparable levels of accuracy to traditional landmark based methods and demonstrate its potential in limiting the resources used by a system with minimal accuracy loss.

Figures & tables

Figure 1: Example of a continuous B-spline representation of using a limited number of control points for its representation. Base map data by OpenStreetMap (available under the Open Database License)

Figure 2: Demonstration of continuous uncertainty representation from discrete control point uncertainties and how it creates a continuous distribution of splines.

Figure 3: Process of expanding the spline

S_{z}

based on new readings

\mathbf{z}

. Each reading

\mathbf{z}_{i}

are categorised as expansion points of the closest spline point is

\mathbf{S}(1)

and is beyond a threshold distance from

\mathbf{C}_{n}

and

\mathbf{C}_{n-1}

or as update points otherwise (a), the interpolation point is selected and the rest are re-categorised while the spline extends to interpolate the new point (b), and an update is performed with all remaining points (c).

Figure 4: Demonstration of $\mathbf{S}_{z}$ fitting. In (A) we find the closest point in $\mathbf{S}_{\mu}$ (green) to a new set of readings $\mathbf{z}$ (blue). In (B) we generate the sigma points $\mathbf{X}$ (red) based on the uncertainty of the reading and fit $\mathbf{S}_{\mu}$ to each one using ridge regression fitting to generate the $\mathbf{Z}$ splines (gray). in (C), the the control points in $\mathbf{Z}$ are averaged to obtain the control points and their respective covariance, defining $\mathbf{S}_{z}$ (purple). (D) shows the basis values of each control point on the closes spline point to the reading, determining how much each control point will be allowed to move to fit in (B)

Figure 5: Comparison between sample spline before and after simplification. We show a control point reduction from 100 to 32 points with minimal data loss

Figure 6: Section of the mapped simulation track, highlighting the PathSpace representations of both boundaries and examples of where CKF misses a landmark while PathSpace interpolates

Lap	PathSpace			CKF
	RMSE (m)	Size	Missed	RMSE (m)	Size	Missed
1	0.582	126	0%	0.729	158	21%
2	0.624	76	0%	0.722	166	17%
3	0.611	76	0%	0.720	169	15.5%
4	0.589	76	0%	0.710	171	15%
5	0.574	76	0%	0.710	173	14%

Table 1: Comparison of accuracy, map size, and landmark coverage: PathSpace B-spline system vs. baseline CKF on a 200 landmark circuit.

Figure 7: Scalability comparison of a traditional CKF implementation (top) against our B-spline representation (bottom) in terms of both number of landmarks in the map and number of landmarks observed per update. each point represents the average execution time of 10 update cycles.

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3D Semantic Mapping 3DGS SLAM 3D Gaussian Splatting 3D Scene Understanding

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Recently, the multi-modal fusion of RGB, depth, and semantics has shown great potential in dense Simultaneous Localization and Mapping (SLAM). However, a prerequisite for generating consistent semantic maps is the availability of dense, efficient, and scalable scene representations. Existing semantic SLAM systems based on explicit representations are often limited by resolution and an inability to predict unknown areas. Conversely, implicit representations typically rely on time-consuming ray tracing, failing to meet real-time requirements. Fortunately, 3D Gaussian Splatting (3DGS) has emerged as a promising representation that combines the efficiency of point-based methods with the continuity of geometric structures. To this end, we propose GS3LAM, a Gaussian Semantic Splatting SLAM framework that processes multimodal data to render consistent, dense semantic maps in real-time. GS3LAM models the scene as a Semantic Gaussian Field (SG-Field) and jointly optimizes camera poses and the field via multimodal error constraints. Furthermore, a Depth-adaptive Scale Regularization (DSR) scheme is introduced to resolve misalignments between scale-invariant Gaussians and geometric surfaces. To mitigate catastrophic forgetting, we propose a Random Sampling-based Keyframe Mapping (RSKM) strategy, which demonstrates superior performance over common local covisibility optimization methods. Extensive experiments on benchmark datasets show that GS3LAM achieves increased tracking robustness, superior rendering quality, and enhanced semantic precision compared to state-of-the-art methods. Source code is available at https://github.com/lif314/GS3LAM.

Abstract

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