����

Majid Zamani is designing safer self-driving car technology with math.

An associate professor of computer science at the University of Colorado Boulder, Zamani is working on a proof-of-concept project that uses mathematical models to guide autonomous vehicles, rather than relying on testing to capture every possible crash scenario.

“Existing autonomy software are not formally proven to work all the time,” Zamani said. “Waymo taxis carry sensor suites worth hundreds of thousands of dollars and are marketed as self-driving, yet they do not always operate autonomously. At times, they become stuck and require remote operator intervention, a limitation that can undermine public trust in the system.”

The issue is edge cases. Existing autonomous driving software incorporates results from millions of miles of travel, but cars still encounter new situations regularly. While humans easily adapt to unforeseen road conditions, machines do not.

When those incidents arise, automakers update their software to address the new scenario, each time adding more lines of codes. Some vehicles now exceed 100 million lines of computer codes, Zamani said.

“One might say that 98 percent of the challenge of autonomy has been solved, leaving only 2 percent unresolved. But that remaining 2 percent is still enormous. When measured against the millions of miles driven each day, even a small fraction of failure cases translates into a significant real-world problem,” Zamani said.

What if there was a better way?

Utilizing an ERC grant awarded through his visiting-professorship at the in Germany, Zamani wants self-driving cars to rely on concrete physics and mathematical formulas rather than endless testing of scenarios.

“These are Newton’s laws. We understand the relationship between velocity and acceleration, and we can calculate how long it will take a car to stop once it detects an obstacle. The mathematics is clean, and if we succeed, we can certify the system’s effectiveness,” he said.

Zamani and his team are focused specifically on lane changes and have made significant progress. Through the grant, they plan to soon test their work on an embedded using that mimics real-world conditions.

“We have proven that our software is formally correct. Now we need to demonstrate it in practice,” he said.

Designing self-driving cars around mathematics and logic may seem like the obvious approach, but it requires substantial computation, which is one reason current systems do not fully rely on it.

“Imagine a busy intersection in a large city, with bicycles, pedestrians, traffic signals, other vehicles, and road conditions that shift with the weather. A mathematically grounded system must decide in real time how to respond, but the sheer number of interacting variables makes the problem extraordinarily complex, even though many of those interactions are ultimately governed by physics,” he said.

The team is developing methods to make its physics- and mathematics-based approaches more scalable. That includes both refining its algorithms and exploring neural networks and other machine learning techniques.

“Sometimes, a very small change in the model architecture can lead to an algorithm that scales much more effectively,” he said. “It is challenging, but we have made meaningful progress. Implementing the MORAI high-fidelity simulator is an important step toward showing that what we promise is possible and demonstrating provable safety in complex autonomous driving scenarios.”