Analyzing Multiagent Interactions in Traffic Scenes via Topological Braids

Autonomous driving is the next big thing! It has attracted enormous attention, and this interest has also grown with companies like Google and Apple entering this segment of the global market.

Image credit: Free-Photos cia Pixabay (Free Pixabay licence)

Challenge with a Self-Driving Car

Real-world traffic environments pose unique challenges due to their high dimensionality and the complexity of modeling human behavior. Also, safety is critical as these are autonomous vehicles moving at fast speeds.

Christoforos Mavrogiannis, Jonathan DeCastro, and Siddhartha S. Srinivasa have discussed this issue in their research paper titled “Analyzing Multiagent Interactions in Traffic Scenes via Topological Braids” which forms the basis of the below text.

Importance of this research

The researchers have built their research on the assumption that real-world traffic scenes exhibit significant structural features, despite existing real-world complications. In this research paper, the team have proposed a scene representation based on the formalism of topological braids that can summarize arbitrarily complex multiagent behavior in situations such that occur when going around roundabouts, or similar.

The researchers also show that the proposed framework can be extrapolated to complex scenes through a case study on real-world intersections and roundabouts. This research by the researchers could aid in algorithm design for self-driving cars, benchmarking algorithm performance against humans, and even helping to improve road design.

Research Details

Abstracting driving interactions as topological braids

This representation captures critical interaction events such as overtaking, merging & crossing in topological braids. It is done using mathematical models, as explained in the research paper.

The above image demonstrates how complex multiagent interactions (left image) can be compactly represented as topological braids (right image). Image credit: arXiv:2109.07060v1

The researchers have also shown that converting vehicle trajectories to braids offers a run-time advantage over converting them to cartesian trajectories.

Case study on traffic datasets

Researchers have demonstrated how braids may abstract traffic episodes through a case study on real-world datasets. Key features of analysis by the researchers are as below.

  • Datasets: inD and roundD datasets are considered for this. These datasets contain trajectories of vehicles, pedestrians, and bicycles from traffic scenes of the German road network
  • Methodology: Images of traffic were taken every 10 seconds. Stationary Vehicles(Vehicles moving with a speed less than 14m/s) and vehicles far from each other(distance between them > 10m) were classified and filtered out. Each vehicle trajectory was defined as a braid and Topological Complexity index (TC) was calculated for each braid representing a vehicle trajectory.
  • Analysis: Researchers observed that the complex set of real-world traffic could be mostly clustered into a small number of unique braids, describing vehicles’ interaction patterns. This demonstrates that real-world traffic tends to collapse to a small set of outcomes.


The representation proposed by the researchers was able to successfully represent different types of multiagent interactions in a compact and interpretable form. Since real-time traffic data was available, it also allowed the researchers to identify the interactions that are empirically more likely.


In the words of the researchers,

We presented a topological framework for the characterization of multiagent interactions in traffic scenes. To illustrate its value, we presented a case study demonstrating the types of behaviors that can be observed in two real-world traffic datasets. While we applied our framework to traffic scenes, it may be useful to other multiagent domains such as pedestrian tracking or sports analysis. Since our goal was to provide a proof-of-concept demonstration, specific parameters such as the projection plane for braids, the episode duration, the maximum-distance threshold between agents and the minimum moving distance threshold were empirically selected. These parameters could be further optimized or adapted to reflect the context of a particular scene (e.g., speed limits)

Source: Christoforos Mavrogiannis, Jonathan DeCastro Siddhartha S. Srinivasa, “Analyzing Multiagent Interactions in Traffic Scenes via Topological Braids”


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