The Score Kalman Filter: Non-Gaussian Estimation Through Linear Algebra
Connecting score matching with probability theory to estimate nonlinear systems beyond Gaussian approximations.
Featured Research
Explore how geometry connects dynamics, control, uncertainty, and artificial intelligence. These articles introduce the mathematical ideas, computational methods, and experiments behind our research in robotics and aerospace engineering.
Research
Return to top
Robot Maps That Remember Motion and Revise Their Understanding
PIMS-SLAM and REVISE connect persistent object tracking, revisable 3D mapping, and language-based scene understanding.
Tracking Uncertainty Through Impacts and Changing Dynamics
Geometric uncertainty propagation on a torus, extended to dimension-changing resets through merging and splitting particles.
Relative Navigation Through Geometry: Estimating Motion Between Robots
A geometric foundation for relative-state estimation, connecting invariant Kalman filtering to experiments with independently moving aerial and ground vehicles.
Vision-Based Maritime Flight: From Deep Perception to UAV Experiments
Combining transformer networks, geometric estimation, and flight testing to navigate relative to a ship.
Brownian Motion on Curved Spaces: The Geometry Behind Randomness
Connecting differential geometry and stochastic analysis to model uncertainty in rotations, constrained motion, and manifold-based AI.
Equivariant Reinforcement Learning Frameworks for Quadrotor Low-Level Control
This study explores how Equivariant Reinforcement Learning uses geometric symmetry to dramatically improve the training efficiency, safety, and precision of autonomous quadrotor drones.
Learning to Control a Flying Inverted Pendulum
Using geometric control and real flight data to improve the transfer of reinforcement learning from simulation to hardware.
Ship-Relative UAV Pose Estimation with 3D LiDAR
Learning ship geometry from synthetic LiDAR scans to estimate UAV position and orientation from sparse, partial measurements.
Data-driven Controls of a Flapping Wing UAV
This post is about my PhD thesis on the dynamical modeling, stability analysis, optimal controls, and data-driven control policies for a flapping wing unmanned aerial vehicle, inspired by Monarch butterflies.
Modular Reinforcement Learning for a Quadrotor UAV
This study addresses the limitations of traditional RL approaches for quadrotor control by decomposing the quadrotor dynamics into translational and yaw subsystems, resulting in more efficient training and enhanced yaw control performance.
Variational Integrators: Preserving Geometry in Simulation
From rotating bodies and elastic tethers to optimization and stochastic impacts, discrete mechanics turns physical structure into reliable numerical methods.
Matrix Fisher Distributions: Uncertainty and Estimation on SO(3)
A geometric probability framework for uncertain rotations, correlated sensor biases, and navigation with large attitude errors.
Fourier Analysis on SO(3): Global Uncertainty Propagation
Noncommutative harmonic analysis connects the geometry of rotations with computational methods for evolving non-Gaussian probability distributions.
Low-Thrust Space Missions: Geometry, Reachability, and Optimization
From low-thrust transfers to autonomous asteroid exploration, geometry connects mission design, shape reconstruction, and optimal guidance.
Geometric Quadrotor Control and Aerial Transportation
From agile flight on SE(3) to suspended loads and cooperative transport, geometric control connects coupled dynamics, stability analysis, and UAV experiments.
Attitude Control: Geometry, Topology, and Stability
From large-angle attitude tracking to hybrid and memory-based control, geometric methods connect mathematical stability guarantees with rigid-body experiments.