Neural networks have had a seismic impact on how engineers design controllers for robots, catalyzing more adaptive and efficient machines. Still, these brain-like machine learning systems are a double-edged sword: Their complexity makes them powerful, but also makes it difficult to guarantee that a neural network-powered robot will perform its task safely.
A traditional way of verifying security and stability are techniques called Lyapunov functions. If you find a Lyapunov function whose value keeps decreasing, then you can know that dangerous or unstable situations associated with higher values will never occur. However, for robots controlled by neural networks, previous approaches to verify Lyapunov conditions were not suitable for complex machines.
Researchers at MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL) and elsewhere have now developed new techniques that rigorously certify Lyapunov calculations in more sophisticated systems. Their algorithm efficiently finds and verifies the Lyapunov function, thereby providing a stability guarantee to the system. This approach could potentially enable safer deployment of robots and autonomous vehicles, including aircraft and spacecraft.
To outperform previous algorithms, the researchers found a modest shortcut to the training and validation process. They created cheaper counterexamples—for example, unfavorable sensor data that could throw off the controller—and then optimized the robotic system to account for them. Understanding these edge cases has helped machines learn how to handle challenging circumstances, allowing them to operate safely in a wider range of conditions than previously possible. They then developed a new verification formulation that allows the use of a scalable neural network verifier, α,β-CROWN, to provide strict worst-case guarantees beyond counterexamples.
“We’ve seen some impressive empirical performances in AI-controlled machines such as humanoids and robot dogs, but these AI controllers lack formal guarantees that are essential for safety-critical systems,” says Lujie Yang, MIT Electrical Engineering and Computer Science (EECS ) PhD student and CSAIL affiliate who co-authored a new paper on the project with Toyota Research Institute researcher Hongkai Dai SM ’12, PhD ’16. “Our work bridges the gap between the performance level of neural network controllers and the security guarantees needed to deploy more complex neural network controllers in the real world,” notes Yang.
For the digital demonstration, the team simulated how a quadrotor drone with lidar sensors would stabilize in a two-dimensional environment. Their algorithm successfully guided the drone into a stable hover position using only the limited environmental information provided by the lidar sensors. In two other experiments, their approach enabled stable operation of two simulated robotic systems over a wider range of conditions: an inverted pendulum and a trajectory tracking vehicle. These experiments, while modest, are relatively more complex than what the neural network validation community has been able to do before, especially since they involved sensor models.
“Unlike conventional machine learning problems, the consistent use of neural networks as Lyapunov functions requires solving challenging global optimization problems, so scalability is a key bottleneck,” says Sicun Gao, associate professor of computer science and engineering at the University of California, San. Diego, who did not participate in this work. “The current work makes a significant contribution by developing algorithmic approaches that are much better suited to the specific use of neural networks as Lyapunov functions in control problems. Compared to existing approaches, it achieves an impressive improvement in the scalability and quality of the solution. The work opens up exciting directions for further development of optimization algorithms for neural Lyapunov methods and consistent use of deep learning in control and robotics in general.
Yang and her colleagues’ stability approach has the potential for widespread application where guaranteeing safety is critical. It could help provide a smoother ride for autonomous vehicles like airplanes and spacecraft. Likewise, a drone delivering items or mapping various terrains could benefit from such security guarantees.
The techniques developed here are very general and not specific to robotics; the same techniques could potentially help with other applications in the future, such as biomedicine and industrial processing.
While the technique is an upgrade from previous work in terms of scalability, the researchers are exploring how it can perform better in higher-dimensional systems. They would also like to consider data outside of the lidar readings, such as images and point clouds.
As a future research direction, the team would like to provide the same stability guarantees for systems that are in uncertain environments and subject to disturbances. For example, if the drone faces strong winds, Yang and her colleagues want to ensure that it will still fly continuously and complete the required task.
They also intend to apply their method to optimization problems where the objective would be to minimize the time and distance a robot needs to complete a task while remaining stable. They plan to extend their technique to humanoids and other machines in the real world, where the robot needs to remain stable while making contact with its surroundings.
Russ Tedrake, MIT professor of EECS, aeronautics, aerospace, and mechanical engineering at Toyota, vice president of robotics research at TRI, and fellow at CSAIL, is the lead author of the research. The work also credits University of California, Los Angeles doctoral student Zhouxing Shi and associate professor Cho-Jui Hsieh, as well as University of Illinois Urbana-Champaign assistant professor Huan Zhang. Their work was supported in part by Amazon, the National Science Foundation, the Office of Naval Research, and the AI2050 program at Schmidt Sciences. The researchers’ contribution will be presented at the 2024 International Conference on Machine Learning.