Lane Detection using Graph Search and Geometric Constraints for Formula Student Driverless

TL;DR

The paper tackles lane detection when boundaries are sparsely marked by 2D points with many false positives, as encountered in Formula Student Driverless. It introduces Cone Lane Connector (CLC), a deterministic, backtracking graph-search that enforces geometric constraints to yield geometrically sound lanes, paired with a neural network for ranking candidate lanes. The approach achieves long prediction horizons (up to ~100 m) with low failure rates (0.6% critical at moderate FP rates) and real-time CPU latency (<15 ms), validated on real racetrack data and released as an open dataset. This combination of exhaustive, constraint-driven search and learned ranking enables robust lane estimation on unknown tracks, supporting high-speed autonomous racing. Future work includes learning search heuristics and using boundary-point features directly in the ranking model.

Abstract

Lane detection is a fundamental task in autonomous driving. While the problem is typically formulated as the detection of continuous boundaries, we study the problem of detecting lane boundaries that are sparsely marked by 2D points with many false positives. This problem arises in the Formula Student Driverless (FSD) competition and is challenging due to its inherent ambiguity. Previous methods are inefficient and unable to find long-horizon solutions. We propose a deterministic algorithm called CLC that uses backtracking graph search with a learned likelihood function to overcome these limitations. We impose geometric constraints on the lane candidates to guarantee a geometrically sound lane. Our exhaustive search leads to finding the global optimum in 45% of instances, and the algorithm is overall robust to up to 50% false positives. Our algorithm runs in less than 15 ms on a single CPU core, meeting the low latency requirements of autonomous racing. We extensively evaluate our method on real data and realistic racetrack layouts, and show that it outperforms the state-of-the-art by detecting long lanes over 100 m with few (0.6%) critical failures. This allows our autonomous racecar to drive close to its physical limits on a previously unknown racetrack without being limited by perception. We release our dataset with realistic Formula Student racetracks to enable further research.

Figures (21)

• Figure 1: The autonomous race car of the team StarkStrom Augsburg at the Formula Student Germany competition 2023 on the race track marked by blue and yellow traffic cones. (Copyright FSG Lodholz).
• Figure 2: Detecting the driving lane (outlined in gray) on race tracks where the boundaries are marked only sparsely by points and with many false-positives (empty circles) introduces ambiguity: On the left is the correct prediction, but given only the partial observation of the boundary points, it may be detected incorrectly as shown on the right, taking a shortcut.
• Figure 3: Proposed search graph construction
• Figure 4: Search graph construction using the Delaunay-triangulation
• Figure 6: Next-vertex decider: For the last point $p_n$ of either the left or right boundary we choose an adjacent vertex ($v_1, ..., v_4$) to visit next. In this example, $v_3$ is chosen as the next vertex adjacent to $p_n$ since the absolute angle between the line segments $\overline{p_{n-1} p_n}$ and $\overline{p_n v_3}$ is the smallest from all segments to possible adjacent vertices.

Theorems & Definitions (9)

• Definition 1: Solution set of path pairs
• Lemma 1: Backtracking criterion for $C_{seg}$-constraint
• proof
• Lemma 2: Backtracking criterion $C_{poly}$-constraint
• proof
• Lemma 3: Backtracking criterion $C_{width}$-constraint
• proof
• Theorem 4: Backtracking does not exclude valid solutions \ref{['alg:enumerate_path_pairs_rec']}
• proof