Research | GRaDS Lab

The GRaDS Lab studies how the geometry of a dynamical system can be turned into better control. A rotating body, a wheeled robot, a quadrotor — each lives on a curved state space, and respecting that structure yields controllers that are simpler, provably correct, and robust. Our work spans three connected thrusts, from deterministic path following to safety guarantees to stochastic control and learning on Lie groups.

Geometric Path Following & Feedback Linearization

Make a robot converge to — and stay on — a geometric path, rather than chase a clock. We exploit the geometry of a system's motion through transverse feedback linearization and quadratic-program reformulations that eliminate the singularities of classical designs, with demonstrations on unicycle robots, quadrotors, and aircraft.

Path Following for Quadrotors

Quasi-static transverse feedback linearization (QSTFL) that makes a quadrotor follow a geometric path with no extra controller states.

Singularity-Free Tracking of Unicycle Robots

A relaxed quadratic-program reformulation of dynamic feedback linearization that stays well-defined even at zero velocity — enabling stop-and-reverse maneuvers.

Acceleration Feedback for Reduced-Gravity Flight

Acceleration-feedback control for atmospheric reduced-gravity (parabolic) flights, in collaboration with Georgia Tech and KAUST.

Safe & Resilient Autonomy

Convergence is not enough: a safe system must never leave its path once it reaches it — even amid obstacles, sensor noise, or adversarial cyber-attacks. We build control-barrier-function and hybrid controllers that certify forward path invariance and robustness for car-like robots and quadrotors.

Safe Hybrid Control with Barrier Functions

A hybrid framework for car-like robots that combines global convergence with guaranteed path invariance and obstacle avoidance, using control barrier functions.

Path Invariance under Cyber-Attacks

A transverse-feedback-linearization controller that keeps a quadrotor on its path with provable forward invariance, even when an adversary hijacks a rotor.

Geometric Stochastic Control & Learning on Lie Groups

Real robots evolve on curved state spaces — rotation groups like SO(2) and SO(3) — where Euclidean tools break down. We develop coordinate-free methods to steer probability densities (Schrödinger bridges) and to learn certificates of stability (neural Lyapunov functions) directly on Lie groups.

Schrödinger Bridges on SO(2)

A coordinate-free solution to the Schrödinger bridge problem on the circle — steering probability densities on SO(2) with minimum control effort.

Schrödinger Bridges over Compact Lie Groups

Generalizing coordinate-free density steering from SO(2) to any compact connected Lie group, with numerical examples on SO(2) and SO(3).

Learning Neural Lyapunov Functions on SO(n)

A physics-informed neural framework that learns maximal Lyapunov functions — and estimates regions of attraction — for dynamical systems evolving on the rotation group SO(n).