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My research is driven by the goal of making robotic systems safer, more capable, and deployable in the real world. I combine applied mathematics, data analysis, and modern learning methods to design and analyze robotic controllers and understand their global dynamics, supporting safe deployment and more effective hybrid solutions. I work on flow matching and diffusion-based methods for robotic applications, robotic arm imitation learning from wearable human motion data, and sim-to-real pipelines for transferring control policies from simulation to physical platforms such as the UR5e and Baxter. I also investigate decentralized multi-agent task allocation for autonomous underwater vehicle swarms, and architect sensing, sensor fusion, and embedded-system processing pipelines grounded in mathematical and statistical modeling with Gaussian processes.

Dynamics, Data Analysis, and Robotic Control:

Data-Efficient RoA Verification of Black-box Controllers via Flow Matching and Conformal Inference.
D. Ramesh, S. Tangirala, M. Ying, E. R. Vieira, Y. Hung and K. E. Bekris.
Submitted. website

MORALS: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space
E. R. Vieira , A. Sivaramakrishnan, S. Tangirala, E. Granados, K. Mischaikow and K. E. Bekris.
2024 International Conference on Robotics and Automation (ICRA).
Best Paper Award in Automation finalist. paper

Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees.
E. R. Vieira , A. Sivaramakrishnan, Y. Song, E. Granados, M. Gameiro, K. Mischaikow, Y. Hung and K. E. Bekris.
International Conference on Robotics and Automation (ICRA) 2023. paper

Persistent Homology Guided Monte-Carlo Tree Search for Effective Non-Prehensile Manipulation.
E. R. Vieira , K. Gao, D. Nakhimovich, K. E. Bekris and J. Yu.
International Symposium on Experimental Robotics (ISER 2023), Chiang Mai, Thailand. paper

Identifying Nonlinear Dynamics with High Confidence from Sparse Data
B. Batko, M. Gameiro, Y. Hung, W. Kalies, K. Mischaikow and E. R. Vieira
SIAM Journal on Applied Dynamical Systems paper

Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers.
E. R. Vieira , E. Granados, A. Sivaramakrishnan, M. Gameiro, K. Mischaikow and K. E. Bekris.
Workshop on the Algorithmic Foundations of Robotics 2022, WAFR-22.. paper

Persistent Homology for Effective Non-Prehensile Manipulation.
E. R. Vieira , D. Nakhimovich, K. Gao, R. Wang, J. Yu and K. E. Bekris.
International Conference on Robotics and Automation (ICRA) 2022, pp. 1918–1924. paper

This work explores the use of topological tools - persistent Homology for achieving effective non-prehensile manipulation in cluttered and constrained workspaces.

Theoretical Math - Topology and Dynamics:

D. Lima, M. Silveira, E. R. Vieira. Covering action on Conley index theory. Ergodic Theory and Dynamical Systems, 1-33, 2022. doi:10.1017/etds.2022.13.

R. Bastos, N.R. Rocco, E. R. Vieira. Finiteness of homotopy groups related to the non-abelian tensor product. Annali di Matematica Pura ed Applicata (2019), No 1, 1–11.

R. Franzosa, E. R. Vieira. Transition Matrix Theory. Transactions of the American Mathematical Society, 369 (2017) 11, 7737–7764.

R. Franzosa, K. A. de Rezende, E. R. Vieira. Generalized topological transition matrix. Topological Methods in Nonlinear Analysis 48, No 1 (2016), 183–212.