Research

My main research area spans Control Theory, Robotics, Bayesian Methods for Machine Learning, Geometric Mechanics, and Dynamical Systems. I am particularly interested in the development of efficient control algorithms behind practical issues in robotics implementations with complex multi-robot systems.  My current research can be divided mainly into two lines: 

(1) Multi-Robot Systems: in particular, design and distributed implementations of controllers for coordination, tracking, collision avoidance of complex multi-robot systems, their applications in Unmanned Aerial and Ground Vehicles, and design of Robust Control Algorithms for fast and robust processing of data in Robotic Swarms. (2) Control-oriented by machine learning:  through the application of techniques from System Identification, Bayesian Inference, and Convex Optimization, with an emphasis on their applications to Correct-by-design Modeling and Online Learning of Complex Control Systems.

I apply my research in the fields of Automatic Control, Robotics, and Networked Nonlinear and Hybrid Systems.

Publications

Articles in Journals 

[J50] L. Colombo, M. de Leon, E. Eyrea Irazú, A. López-Gordon. Hamilton–Jacobi theory for nonholonomic and forced hybrid mechanical systems. Geometric Mechanics. Vol 1(2), 2024, To appear. 

[J49] E. Aranda Escolástico, L. Colombo, M. Guinaldo, A. Visioli. Event-triggered control of Port-Hamiltonian systems under time-delay communication. IEEE Control Systems Letters. Vol 8, 175-180, 2024. DOI: 10.1109/LCSYS.2024.3355811

[J48] A. Anahory,  L. Colombo, M. de León, M. Salgado, S. Souto. Euler-Lagrange-Herglotz equations on Lie algebroids.   Analysis and Mathematical Physics.  Vol 14 (1), 2024.

[J47] J. Goodman,  L. Colombo. Reduction by Symmetry in Obstacle Avoidance Problems on Riemannian Manifolds.   SIAM Journal of Applied Algebra and Geometry.  Vol 8 (1), 26-53, 2024.

[J46] L. Colombo, J. Giribet. Learning-Based Fault Tolerant Control for an Hexarotor with Model Uncertainties.   IEEE Transactions on Control Systems Technology,  Vol 32 (2), 672-679, 2024. 

[J45] A. Anahory Simoes, E. Stratoglou, A. Bloch, L. Colombo. Nonholonomic Virtual Constraints: A Geometric Approach. Automatica. Vol 155,  111166, 2023.

[J44] J. Goodman, T. Beckers, L. Colombo. Geometric control for load transportation with quadrotors UAVs by elastic cables.  IEEE Transactions on Control Systems Technology, Vol 31 (6), 2848-2862, 2023.

[J43] L. Colombo, E. Stratoglou. Lie-Poisson reduction for optimal control of left-invariant control systems with subgroup symmetry. Reports on Mathematical Physics. Vol 91(1), 131-141, 2023.

[J42] L. Colombo, M. Gamonal, D. Martín de Diego. Variational integrators for non-autonomous Lagrangian systems. Journal of Computational and Applied Mathematics.  424, 114966, 2023. 

[J41] A. Anahory Simoes, L. Colombo, E. Stratoglou. Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent systems on Lie groups. Communications in Analysis and Mechanics. Vol 15 (2), 1-23, 2023.

[J40] L. Colombo, M. de León, A. López-Gordón. Contact Lagrangian systems subject to impulsive constraints. Journal of Physics A: Mathematical and Theoretical.  Vol 55(42) 425203, 2022.  

[J39] T. Beckers, L. Colombo, S. Hirche. Safe trajectory tracking for underactuated vehicles with unknown dynamics. Journal of Geometric Mechanics. Vol 14 (4), 491-505, 2022.

[J38] J. Goodman, L. Colombo. Geometric Control  of two Quadrotors Carrying a Rigid Rod with Elastic Cables. Journal of Nonlinear Science. Vol 32 (5), 1-31, 2022. 

[J37] J. Goodman, L. Colombo. Collision avoidance of multiagent systems on Riemannian manifolds. SIAM Journal on Control and Optimization.  Vol 60 (1), 168-188, 2022.

[J36] T. Beckers, L. Colombo, S. Hirche, G. Pappas. Online learning-based trajectory tracking for underactuated vehicles with uncertain dynamics. IEEE Control Systems Letters. Vol 6., 2090-2095, 2021.

[J35] E. Aranda-Escolástico, L. Colombo, M. Guinaldo. Distributed event-triggered flocking control of Lagrangian systems. IEEE Control Systems Letters. Vol 6., 1945-1951, 2021. 

[J34] J. Giribet, L. Colombo, P. Moreno, I. Mas, D. V. Dimarogonas. Dual Quaternion Cluster-Space Formation Control, IEEE Robotics and Automation Letters, Vol  6 (4), 6789-6796, 2021.

[J33] L. Colombo, H. García de Marina. Forced Variational Integrators for formation control of multi-agent systems. IEEE Transactions on Control of Network Systems,  8(3), 1336-1347, 2021. 

[J32] E. Aranda-Escolástico, L. Colombo, M. Guinaldo. Periodic Event-Triggered Targeted Shape Control of Lagrangian Systems with  discrete time-delay.  ISA Transactions, Vol. 117, 139-149, 2021. 

[J31] N. Raj, L. Colombo, A. Simha. Structure-Preserving Reduced Attitude Control of Gyroscopes. Automatica, Vol 125, 109471, 2021.  

[J30] A. Bloch, M. Camarinha, L. Colombo. Variational point-obstacle avoidance on Riemannian manifolds. Mathematics of Control, Signals, and Systems, 33(1), 109-121, 2021.  

[J29] V. Arroyo, M. Gamonal, P. Moreno, L. Colombo. A data-driven method based on quadratic programming for formation control of Euler-Lagrange systems. IEEE Control Systems Letters. Vol 5 (1), 313-318, 2021. 

[J28] L. Colombo and D. Dimarogonas. Symmetry reduction for optimal control of multi-agent systems. IEEE Transactions on Automatic Control.  Vol 66 (5), 2021.

[J27] A. Bloch, M. Camarinha and L. Colombo. Dynamic interpolation for obstacle avoidance on Riemannian manifolds. International Journal of Control, Vol 96 (3), 588-600, 2021. 

[J26] L. Colombo, D. Martin de Diego, A. Nayak, R. Sato de Almagro. Geometric optimal trajectory tracking of nonholonomic mechanical systems. SIAM Journal on Control and Optimization.  58(3), 1652–1675. 2020.

[J25] L. Colombo, E. Eyrea Irazú, E. García Toraño Andrés. A note on hybrid Routhian reduction for time-dependent Lagrangian hybrid systems. Journal of Geometric Mechanics. Vol 12 (2), 309-321, 2020. 

[J24] L. Colombo and E. Eyrea Irazú. Symmetries and periodic orbits in simple hybrid Routhian systems. Nonlinear Analysis: Hybrid Systems. Vol 36, 100857, 2020.

[J23] J. Goodman and L. Colombo. On the existence and uniqueness of Poincaré maps for systems with impulse effects.  IEEE Transactions on Automatic Control. Vol 65 (4), 1815-1821, 2020.

[J22] L. Colombo and D. Dimarogonas. Motion feasibility conditions for collision avoidance of multi-agent control systems on Lie groups. IEEE Transactions on Control of Network Systems,  7(1) 493-502, 2020.

[J21] W. Clark, A. Bloch, L. Colombo. A Poincaré - Bendixon Theorem for Hybrid Systems. Mathematical Control & Related Fields, Vol 10, n1, 27-45, 2020.

[J20] W. Clark, A. Bloch, L. Colombo and P. Rooney. Time minimum Quantum Purity for 2-Level Lindblad equations. Discrete and Continuous Dynamical Systems - Serie S, 2357-2372, 2019.

[J19] A. Bloch, L. Colombo and F. Jimenez. The variational discretization of the constrained higher-order Lagrange-Poincare equations. Discrete and Continuous Dynamical Systems - Serie A, Vol 39, n1, 309-344, 2019.

[J18] L. Colombo. A variational-geometric approach for the optimal control of nonholonomic systems. International Journal of Dynamics and Control. Vol 6 (2), 652-662, 2018.

[J17]  L. Abrunheiro and L. Colombo. Lagrangian Lie subalgebroids generating dynamics for second-order mechanical systems on Lie algebroids. Mediterranean Journal of Mathematics. 15 (2), 57, 2018.

[J16] A. Bloch, L. Colombo, R. Gupta and T. Ohsawa. Optimal control problems with symmetries breaking cost functions.   SIAM Journal on Applied Algebra and Geometry, 1-1, pp. 626-646, 2017.

[J15] L. Colombo. Second-order constrained variational problems on Lie algebroids: Applications to optimal control. Journal of Geometric Mechanics. Vol 9, n1, 2017, 1-45.

[J14] L. Colombo, S. Ferraro and D. Martín de Diego. Geometric Integrators for Higher-Order Variational Systems and their applications to Optimal Control . Journal of Nonlinear Science. 26 - 6, pp. 1615 - 1650, 2016.

[J13] L. Colombo and D. Martín de Diego. Higher-order variational problems on Lie groupoids and optimal control applications. Discrete and Continuous Dynamical Systems, Serie A. Vol 36 (11), 6023-6064, 2016.

[J12] L. Colombo and P. Prieto Martínez. Regularity properties of fiber derivatives associated with higher-order mechanical systems. Journal of Mathematical Physics, 57 (8), 2016.

[J11] L. Colombo, F. Jimenez and D. Martín de Diego. Variational Integrators for Mechanical Control Systems with Symmetries. Journal of Computational Dynamics. Vol 2, n. 2, 193-225, 2015.

[J10] L. Colombo and H. Jacobs. Lagrangian Mechanics on centered semi-direct products. Geometry, mechanics, and dynamics: the legacy of Jerry Marsden, Fields Institute Communications, Vol. 73,167-184, 2015.

[J9] A. Bloch, L. Colombo, R. Gupta and D. Martín de Diego. A Geometric Approach to the Optimal Control of Nonholonomic Mechanical Systems. Analysis and Geometry in Control Theory and its Applications. INdAM series. Vol 12. 2015.

[J8] L. Colombo and D. Martín de Diego. On the geometry of higher-order variational problems on Lie groups. Journal of Geometric Mechanics, Vol. 6, number 4, 451-478, 2014.

[J7] L. Colombo and P. Prieto-Martínez. Unified formalism for higher-order variational problems and its applications in optimal control. International Journal of Geometric Methods in Modern Physics. Vol 11, n4, 2014.

[J6] L. Colombo, M. de Leon, P. Prieto Martínez and N. Roman-Roy. Geometric Hamilton-Jacobi theory for higher-order autonomous systems. Journal of Physics A: Math. Theor. 47, 235203, 2014.

[J5] L. Colombo, M. de Leon, P. Prieto Martínez and N. Roman-Roy. Unified formalism for higher-order geometric Hamilton-Jacobi theory. International Journal of Geometric Methods in Modern Physics. Vol 11, n6, 2014.

[J4] L. Colombo, D. Martín de Diego and M. Zuccalli. Discrete higher-order variational problems with constraints. Journal of Mathematical Physics. Vol 54, 093507, 2013.

[J3] L. Colombo, F. Jimenez and D. Martín de Diego. Discrete second-order Euler-Poincare equations. Applications to optimal control. International Journal of Geometric methods in Modern Physics. Vol 9, N4, 2012.

[J2] L. Colombo, D. Martín de Diego and Marcela Zuccalli. On Variational Integrators for Optimal Control of Mechanical Control Systems. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas (Journal of Spanish Royal Academy of Science) Volume 106, Issue 1, Page 161-171, 2012.

[J1] L. Colombo, D. Martín de Diego and Marcela Zuccalli. Optimal Control of Underactuated Mechanical Systems: A Geometric Approach. Journal of Mathematical Physics. Vol 51, 083519, 2010.

Articles in Conference (Refereed) Proceedings

[C49] A. Roca, G. Torre, J. Giribet, G. Castro, L. Colombo, I. Mas, J. Pereira. Detección Automática de Ciervos de los Pantanos Utilizando Imágenes Aéreas de UAV.  Actas de las Jornadas Argentinas de Robótica, 2024. To appear. 

[C48] W. Clark, L. Colombo, A. Bloch. The interplay bewteen symmetries and impact effects on hybrid mechanical systems.  2024 European Control Conference (ECC 24). To appear, 2024. 

[C47] E. Stratoglou, A. Anahory Simoes, L. Colombo. Virtual constraints on Riemannian homogeneous spaces.  8th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2024 (LHMNC 24). To appear, 2024. 

[C46] G. Torre, O. Yago Nieto, A. Anahory Simoes, J. Giribet, L. Colombo. Learning Cost Functions for Reinforced Learned Controllers in a Quadrupedal Robot.  8th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2024 (LHMNC 24). To appear, 2024. 

[C45] O. Yago Nieto, L. Colombo. Learning-Based Control for an Aerial Robot with Manipulator Arms.  8th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2024 (LHMNC 24). To appear, 2024. 

[C44] A. López-Gordon, L. Colombo. On the integrability of hybrid Hamiltonian systems.  8th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2024 (LHMNC 24). To appear, 2024. 

[C43] A. Rodriguez Abella, L. Colombo. Implicit Nonholonomic Mechanics with Collisions.  8th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2024 (LHMNC 24). To appear, 2024. 

[C42] J. Goodman, L. Colombo.  Reduction of Sufficient Conditions in Variational Obstacle Avoidance Problems. 8th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2024 (LHMNC 24). To appear, 2024. 

[C41] J. Goodman, L. Colombo. Reduction of Necessary Conditions for the Variational Collision Avoidance Problem. 8th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2024 (LHMNC 24). To appear, 2024. 

[C40] A. Anahory Simoes, L. Colombo. Hamel equations and quasivelocities for nonholonomic systems with inequality constraints. Proceedings of the 62th  Conference on Decision and Control, 2023. To appear.

[C39] A. Anahory Simoes, M. Barbero Liñan, L. Colombo, D. Martín de Diego. Higher-order retraction maps and construction of numerical methods for optimal control of mechanical systems.  Proceedings of the 62th  Conference on Decision and Control, 2023. To appear.

[C38] E. Stratoglou, A. Anahory Simoes, A. Bloch, L. Colombo. Virtual Affine Nonholonomic Constraints. Proceedings of the 6th International Conference on Geometric Science of Information, 89-96, 2023.

[C37] A. Anahory Simoes, L. Colombo. Nonholonomic systems with inequality constraints. Proceedings of the 6th International Conference on Geometric Science of Information, 97-104, 2023.

[C36] L. Colombo, J. Goodman. Existence of global minimizer for elastic variational obstacle avoidance problems on Riemannian manifolds.  Proceedings of the 6th International Conference on Geometric Science of Information, 81-88,  2023.

[C35] L. Colombo, E. Eyrea Irazù, D. Sánchez, M. Zuccalli. Lagrangian mechanics and Routh reduction for an ASV-UAV system based on cluster-space formulation. Proceedings of the IX Conference on Applied, Computational and  Industrial Mathematics, Vol 9, 127-130, 2023.  

[C34] A. Anahory Simoes, A. López Gordón, A. Bloch, L. Colombo. Discrete mechanics and optimal control for passive walking with foot slippage. Proceedings of the 2023 American Control Conference (ACC), 4587-4592.  

[C33] A. López Gordón, L. Colombo, M. de León.  Nonsmooth Herglotz variational principle. Proceedings of the 2023 American Control Conference (ACC), 3376-3381, 2023. 

[C32] A. Anahory Simoes, L. Colombo.  Contracting forced Lagrangian and contact Lagrangian systems: applications to nonholonomic systems with symmetries. Proceedings of the 2023 American Control Conference (ACC), 909-916, 2023.

[C31] T. Beckers, G. Pappas, and L. Colombo.  Learning rigidity-based flocking control using Gaussian Processes with probabilistic stability guarantees. Proceedings of the 61st  Conference on Decision and Control, 7254-7259, 2022. 

[C30] T. Beckers, L. Colombo, M. Morari and G. Pappas.  Learning-based balancing of model-based and feedback control for second-order mechanical systems. Proceedings of the 61st  Conference on Decision and Control, 4667-4673, 2022. 

[C29] E. Eyrea Irazú, A. Lopez-Gordon, M. de Leon, L. Colombo. Hybrid Routhian reduction for simple hybrid forced Lagrangian systems. Proceedings of the 2022 European Control Conference (ECC),  345-350, 2022 .

[C28] A. Anahory Simoes,  L. Colombo.  Variational problems on Riemannian manifolds with constrained accelerations. Proceedings of  the 15th International Conference on Automatic Control and Soft Computing, 375-384, 2022.

[C27] T. Beckers, S. Hirche, and L. Colombo.  Safe Online Learning-based Formation Control of Multi-Agent Systems with Gaussian Processes”. Proceedings of the 60th  Conference on Decision and Control, 2021.  

[C26] J. Goodman, L. Colombo. Variational Obstacle Avoidance with Applications to Interpolation Problems in Hybrid Systems. 7th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2021 (LHMNC 21). IFAC Papers Online 54 (19), 82-87.

[C25] L. Colombo, D. Martín de Diego. Noether Symmetries and Decay Laws in Formation Control of Multi-agent Systems.  7th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2021 (LHMNC 21). IFAC Papers Online 54 (19), 76-81.

[C24] M. E. Eyrea Irazú, L. Colombo, A. Bloch.  Reduction by Symmetries of Simple Hybrid Mechanical Systems.  7th IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control,  2021 (LHMNC 21). IFAC Papers Online 54 (19), 94-99.

[C23] M. Gamonal, P. Moreno, L. Colombo. Learning Shape Control of Multi-Agent Systems with Lagrangian Neural Networks.  2021 Proceedings of the SIAM Conference on Control and Its Applications (CT21) , 40-47, 2021.

[C22] O. Yago Nieto, L. Colombo. A geometric path planning strategy based on variational calculus for the shape control of multi-agent Lagrangian systems.  29th Mediterranean Conference on Control and Automation. 1092-1099, 2021. 

[C21] L. Colombo, M. E. Eyrea Irazú. M. Zuccalli. Reduction by symmetries and higher-order magnetic systems. VIII Congress of Applied, Computational, and Industrial Mathematics (MACI), La Plata, Argentina. Vol 8, 163-166, 2021.

[C20] L. Colombo, J. Goodman. A decentralized strategy for variational collision avoidance on complete Riemannian manifolds. Proceedings of  the 14th International Conference on Automatic Control and Soft Computing, 363-372, 2020.

[C19] L. Colombo, P. Moreno, M. Ye, H. Garcia de Marina, M. Cao. Forced variational integrators for distance based shape control with flocking behavior for multi-agent systems. 21st IFAC World Congress, 2020, Berlin, Germany.

[C18] R. Seshan Chandrasekaran, L. Colombo, M. Camarinha, R. Banavar, A. Bloch. Variational collision and obstacle avoidance of multi-agent systems on Riemannian manifolds. Proceedings of the 2020 European Control Conference (ECC), Saint Petersburg, Russia, 1689-1694, 2020.

[C17] E. Aranda Escolástico, L. Colombo, M. Guinaldo. Distributed targeted distance-based formation control for mechanical systems. Proceedings of the 2020 European Control Conference (ECC), Saint Petersburg, Russia, 172-177, 2020.

[C16] L. Colombo, H. Garcia de Marina, M. Barbero Liñán, D. Martin de Diego. On the observability of relative positions in left-invariant multi-agent control systems and its application to formation control. Proceedings of the 58th. IEEE Conference on Decision and Control (CDC) Nice, France, 7333-7338, 2019.

[C15] A. Nayak, R. Sato de Almagro, L. Colombo, D. Martín de Diego. Trajectory tracking of nonholonomic mechanical systems: a geometric approach. 2019 American Control Conference (ACC), Philadelphia, USA, 1924-1929, 2019.

[C14] M. Asif, R. Banavar, L. Colombo, M. Camarinha and A. Bloch. Collision avoidance on Riemannian manifolds. Proc. 57th. IEEE Conference on Decision and Control (CDC), Miami, FL, USA, 2791-2796, 2018.

[C13] L. Colombo and H. García de Marina. A Variational Integrator for the formation control of multi-agent systems. Proc. 7th IFAC Workshop on Distributed Estimation and Control in Networked Systems, Groningen, the Netherlands, 2018 (NecSys). IFACPapersOnLine 51 (23), 76-81.

[C12] L. Colombo and D. Dimarogonas. Optimal control of left-invariant multi-agent systems with asymmetric formation constraints. 17th annual European Control Conference (ECC), Limassol, Cyprus, 1728-1733, 2018.

[C11] L. Colombo, W. Clark, A. Bloch. Time reversal symmetries and zero dynamics for simple hybrid Hamiltonian control systems. 2018 American Control Conference (ACC), Milwaukee, 2218-2223, 2018.

[C10] L. Colombo, A. Bloch, W. Clark. Quasivelocities and symmetries in simple hybrid systems. Proc. 56th. IEEE Conference on Decision and Control (CDC), Melbourne, Australia. 1529-1534, 2017.

[C9] A. Bloch, M. Camarinha and L. Colombo, Variational obstacle avoidance problem on Riemannian manifolds. Proc. 56th. IEEE Conference on Decision and Control (CDC), Melbourne, Australia, 145-150, 2017.

[C8] W. Clark, A. Bloch, L. Colombo and P. Rooney. Optimal Control of Quantum Purity for n = 2 Systems. Proc. 56th. IEEE Conference on Decision and Control (CDC), Melbourne, Australia 1317-1322, 2017.

[C7] L. Colombo, A. Bloch, R. Gupta and D. Martín de Diego. Variational discretization for optimal control problems of nonholonomic mechanical systems. Proc. 54th. IEEE Conference on Decision and Control (CDC), Osaka, Japan, 4047-4052, 2015.

[C6] L. Colombo, A. Bloch and R. Gupta. Higher-Order Constrained Variational Problems on Principal Bundles with Applications to Optimal Control of Underactuated Systems. IFAC Conference Proceedings. 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non-Linear Control, p.87-92, 2015.

[C5] L. Colombo, D. Martín de Diego and Marcela Zuccalli. On the construction of structure preserving algorithms for optimal control problems of nonholonomic mechanical systems. Actas del XII Congreso Monteiro, 135-147, 2014.

[C4] L. Colombo. On the plate ball optimal control problem.  IV Congress of Applied, Computational, and Industrial Mathematics (MACI), Buenos Aires, Argentina,  2013, pp. 698-701.

[C3] L. Colombo and D. Martín de Diego. Optimal control of underactuated mechanical systems with symmetries. Dynamical Systems and Differential Equations, Discrete and Continuous Dynamical Systems, November 2013. Proceedings of the 9th AIMS international conference, Orlando, Florida, USA. 149-158.

[C2] L. Colombo, F. Jimenez and D. Martín de Diego. Second-order Euler-Poincaré equations for trivial principal bundles. Proceedings of the American Institute of Physics, Geometry and Physics, 1460, 185-191 2012.

[C1] L. Colombo and D. Martín de Diego. Quasivelocities and optimal control of underactuated mechanical systems. Proceedings of the American Institute of Physics, Geometry and Physics, 1260, 133-140, 2011.