Research Projects

The design of reliable control systems in the real world remains a cornerstone challenge in robotics, automation, and cyber-physical systems, particularly due to the persistent gap between theoretical models and real-world behavior. While traditional control theory assumes access to precise mathematical models, real-world systems often involve uncertainties, unmodeled dynamics, and stochastic perturbations. Simultaneously, learning-based and data-driven approaches, although promising, are frequently data-intensive and lack strong formal guarantees for safety and performance-critical requirements in domains such as defense, healthcare, autonomous systems, and environmental monitoring. There have been notable incidents such as the autonomous Tesla car crash and the chess playing robot injuring a child, where controllers derived from simulator models failed to ensure safe real-world behavior. In contrast, controllers designed using known mathematical models offer formal performance and safety guarantees. Also, studies show that at least 8.8 billion miles of test driving are needed to demonstrate, with 95% confidence, that an autonomous vehicle’s failure rate is lower than that of a human driver [1, 2]. This equates to more than 400 years of continuous driving, making real-world validation of self-driving cars impractical. This highlights the urgent need for robust testing and validation frameworks based on simulators and mathematical models. It also motivates a deeper investigation into the math-to-sim-to-real gap the discrepancy in system behavior across the mathematical model, the simulator, and the real-world system. This project proposes a unified, model based framework to quantify and mitigate this gap across three key platforms: (1) the mathematical model derived from first principles, (2) high-fidelity simulation environments, and (3) the real-world system. By introducing novel constructs, namely, the stochastic simulation gap function and the reality gap function, the framework enables precise characterization of the deviation between models and implementation platforms. These gaps will then be addressed using a combination of control-theoretic techniques (e.g., incremental stability, adaptive control barrier functions) and formal verification tools (e.g., behavioral relations, SMT solvers, counterexample-guided synthesis). Finally, the proposed techniques will be experimentally validated on a diverse set of platforms, including a wheeled ground vehicle, a 6-DOF manipulator (Piper), and a drone, thereby showcasing the generality and robustness of the solution across control-affine and underactuated systems. By bridging the math-to-sim-to-real gap without resorting to data-intensive retraining, the project aims to significantly reduce development cost and time, while offering formal performance and safety guarantees. This will enable faster, more dependable deployment of controllers in real-world applications where precision and reliability are non-negotiable.