Current Research

My research lies at the intersection of Machine Learning, Control Theory, and Robotics. I am particularly interested in

  • Combining machine learning and control theory tools to develop data-efficient methods for controlling autonomous systems in unknown environments

  • Developing tools for the performance analysis, e.g., safety and robustness analysis, of data-driven models.

Other than robotics, I am also interested in the Hamilton-Jacobi Reachability theory and its application to multi-agent autonomous systems.

Machine Learning and Control Theory

Real-world autonomous systems are becoming increasingly complex and commonly act in poorly understood environments where it is extremely challenging to model their true dynamics. While machine learning and AI have the potential to transform autonomous systems, this transformation requires systems which are robust, resilient and safe. Repeated experiments to gain realistic data is typically not a possibility, and models and analysis must be used in a principled way to enable this transformation. Motivated by this, my research focuses on learning data-efficient models from the learning perspective, and on designing efficient control/analysis schemes for these data-driven models from the control theory perspective.

Apart from control, an important lingering question for the autonomous systems is that of their safety and performance analysis. In order to verify a system, the control community analyzes a validated system model, using Hamilton-Jacobi reachability for instance, and provide formal performance and safety guarantees on that system model. In theory, the same tools can be used to verify a data-driven model, except that one first needs to validate that model to make sure that the analysis conducted on it holds for the actual system. We are currently developing some sampling and machine learning based methods to validate a data-driven system model.

Hamilton-Jacobi Reachability

Hamilton-Jacobi (HJ) reachability is a useful tool for guaranteeing goal satisfaction and safety, and has been used in various safety-critical scenarios including aircraft auto-landing, automated aerial refueling, large-scale multiple-vehicle path planning, etc. In reachability theory, one is interested in computing the Backward Reachable Set (BRS), the set of states such that the trajectories that start from this set can reach some given target set. If the target set consists of those states that are known to be unsafe, then the BRS contains states which are potentially unsafe and should therefore be avoided.

Traditionally, reachable set computations involve solving an HJ partial differential equation on a grid representing a discretization of the state space, resulting in an exponential scaling of computational complexity with respect to system dimensionality; this is often referred to as the “curse of dimensionality.” My research focuses on how we can overcome this curse by exploiting system structures.

SPP 

One particular problem that we have addressed is how a group of vehicles, such as unmanned aerial vehicles (UAVs), in the same vicinity can safely reach their destinations while avoiding collision with each other, despite external disturbances. Such multi-UAV systems have several applications, including package delivery (see Amazon Prime Air and Google Project Wing for instance), fire-fighting, aerial surveillance, and fast disaster response. HJ reachability is ideal for such systems, except that the reachability analysis is intractable for large-scale systems due to the “curse of dimensionality.” We solve this large-scale path planning problem under a mild structural assumption. In particular, we assign priorities to vehicles; path-planning problem is then solved sequentially starting from the highest priority vehicle, effectively alleviating the curse of dimensionality. Using HJ reachability, we focus on designing the sequential path-planning algorithms that are robust to disturbances and intruders, and thus guarantee collision avoidance. In other works, we propose methods to decompose the computation of reachable set into several small dimensional computations for general nonlinear systems.

(Image credits: NASA)