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Publications

Chapters of Books
 

  1. Rolling Maps and Nonlinear Data. In Handbook of Variational Methods for Nonlinear Geometric Data, Chapter 21. P. Grohs, M. Holler, A. Weinmann (Eds.), Springer 2020. (With K. Hüper and K. Krakowski).
     

  2. Complete Nonholonomy of the Rolling Ellipsoid - A Constructive Proof. In Modeling, Dynamics, Optimization and Bioeconomics III, Chapter 19. A. Pinto, D. Zilberman (Eds.), Springer 2018. (With F. Rüppel and R. Rodrigues).
     

  3. Sphere rolling on sphere - alternative approach to kinematics and constructive proof of controllability. In Mathematics of Planet Earth: Dynamics, Games and Science, Chapter 18. Jean Pierre Bourguignon, Rolf Jeltsch, Alberto Pinto and Marcelo Viana Eds., Springer 2015. (With F. Louro).
     

  4. Rolling maps for the Essential manifold. In Mathematics of Planet Earth: Dynamics, Games and Science, Chapter 20. Jean Pierre Bourguignon, Rolf Jeltsch, Alberto Pinto and Marcelo Viana Eds., Springer 2015. (With L. Machado and F. Pina).
     

  5. Rolling manifolds an intrinsic perspective. In Textos de Matemática, Volume 43 (J. Cardoso, K. Hueper, P. Saraiva, Eds.), Departamento de Matemática da Universidade de Coimbra, 2011, pp 71-83. (With M. Godoy, E. Grong and I. Markina).
     

  6. Rolling maps in a Riemannian framework. In Textos de Matemática, Volume 43 (J. Cardoso, K. Hueper, P. Saraiva, Eds.), Departamento de Matemática da Universidade de Coimbra, 2011, pp 15-30. (With K. Hüper and K. Krakowski).
     

  7. An exponential observer for systems on SE(3) with implicit outputs. Dynamics, Games and Science II, M.M. Peixoto et al. (eds.), Springer Proceedings in Mathematics 2, Chapter 44. Springer-Verlag Berlin Heidelberg 2011. (With S. Rodrigues, N. Crasta and A. Aguiar).
     

  8. Smooth trajectory planning for fully automated passengers vehicles: spline and Clothoid based methods and its simulation. In: Informatics in Control Automation and Robotics, Lecture Notes in Electrical Engineering, Volume 15, Parte II (May 2008), pp 169-182. (With L. Labakhua, U. Nunes and R. Rodrigues).
     

Journal Publications

  1. Rolling Stiefel Manifolds Equipped with Alpha-Metrics. Mathematics 2023, 11 (21), 3540; doi: 10.3390/math11214540. (With M. Schlarb, K. Hüper, and I. Markina).
     
  2. Endpoint geodesic formulas on Grassmannians applied to interpolation problems. Mathematics 2023, 11 (16), 3545; doi: 10.3390/math11163545. (With K. Hüper).
     
  3. Symmetric spaces rolling on flat spaces. Journal of Geometric Analysis, 33, (2023). doi: 10.1007/s12220-022-01179-5. (With V. Jurdjevic and I. Markina).
     
  4. High-Order Splines on Riemannian Manifolds. In: Proceedings of the Steklov Institute of Mathematics, 2023, Vol. 321, pp. 158–178. c© Pleiades Publishing, Ltd., 2023. DOI: 10.1134/S0081543823020128. Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Vol. 321, pp. 172–193. (With M. Camarinha and P. Crouch).
     
  5. Riemannian cubics close to geodesics at the boundaries. Journal of Geometric Mechanics, 14(4), 545-558 (2022). doi: 10.3934/jgm.2022003. (With M. Camarinha and P. Crouch).
     
  6. Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces. Journal of Geometric Mechanics, 14(1), 105-129 (2022). doi: 10.3934/jgm.2021033. (With A. Marques).
     
  7. A Lagrangian approach to extremal curves on Stiefel manifolds. Journal of Geometric Mechanics, 13(1), 55-72 (2021). doi: 10.3934/jgm.2020031. (With K. Hüper and I. Markina).
     
  8. A unifying approach for rolling symmetric spaces. Journal of Geometric Mechanics, 13(1): 145-166 (2021). doi: 10.3934/jgm.2020016 (With K. Krakowski and L. Machado).
     
  9. Uma proposta de modelagem matemática aplicada a prevenção de possíveis surtos de cólera. Brazilian Electronic Journal of Mathematics, 1(1), 105-117 (2020). https://doi.org/10.14393/BEJOM-v1-n1-2020-50097. (With B. Lima).
     
  10. Extremal curves on Stiefel and Grassmann manifolds. The Journal of Geometric Analysis, Volume 30, 3948–3978 (2020). https://doi.org/10.1007/s12220-019-00223-1. (With V. Jurdjevic and I. Markina).
     
  11. A modified Casteljau algorithm to solve interpolation problems on Stiefel manifolds. Journal of Computational and Applied Mathematics, Volume 31 (2017), 84-99. (With K. Krakowski, L. Machado and J. Batista).
     
  12. Introduction to the intrinsic rolling with indefinite metric. Communications in Analysis and Geometry. Volume 24, Number 5 (2016), 1085–1106. (With I. Markina).
     
  13. Geometry of the rolling ellipsoid. Kybernetika, Volume 52, Number 2 (2016), 209-223. (With K. Krakowski).
     
  14. Geometric mean and geodesic regression on Grassmannians. Linear Algebra and its Applications, Volume 466 (2015), 83-101. (With E. Batzies, K. Hüper and L. Machado).
     
  15. Algebraic integrability for minimum energy curves. Kybernetika, Vol 51, N. 1 (2015), 321-334. (With I. Yudin).
     
  16. An algorithm based on rolling to generate interpolating curves on ellipsoids. Kybernetika, Vol 50, N. 4 (2014), 544-562. (With K. Krakowski).
     
  17. An intrinsic formulation of the rolling manifolds problem. Journal of Dynamical and Control Systems, Vol. 18, No.2 (2012), 181-214. (With M. Godoy, E. Grong and I. Markina). 
     
  18. High order smoothing splines versus least squares problems on Riemannian manifolds. Journal of Dynamical and Control Systems, Vol. 16, No. 1, January 2010, 121–148. (With L. Machado and K. Krakowski).  
     
  19. Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices. Journal of Computational and Applied Mathematics, Vol. 233, No. 11 (April 2010), 2867-2875. (With J. Cardoso). 
     
  20. Rolling Stiefel manifolds. International Journal of Systems Science, Vol. 39, No. 9 (September 2008), 881–887. (With K. Hüper and M. Kleinsteuber).
     
  21. On the geometry of rolling and interpolation curves on Sn, SO(n) and Graßmann manifolds. Journal of Dynamical and Control Systems, Vol. 13, No. 4 (October 2007), 467-502. (With K. Hüper).
     
  22. Fitting smooth paths on Riemannian manifolds. International Journal of Applied Mathematics & Statistics, Vol. 4, N. J06 (June 2006) 25-53. (With L. Machado).
     
  23. Padé and Gregory error estimates for the logarithm of block triangular matrices triangular matrices. Applied Numerical Mathematics, Vol. 56, No. 2 (February 2006), 253-267. (With J. Cardoso).
     
  24. Riemannian means as solutions of variational problems. LMS Journal of Computational Mathematics, 9 (2006) 86-103. (With L. Machado and K. Hüper).
      http://www.mat.uc.pt/preprints/ps/p0438.pdf
  25. A two-step algorithm of smooth spline generation on Riemannian manifolds. Journal of Computational and Applied Mathematics, Vol. 194, No. 2 (2006) 177-191. (With J. Jakubiak and R. Rodrigues).
     
  26. A new geometric algorithm to generate spline curves. LMS Journal of Computational Mathematics, 8 (2005) 251-266. (With R. Rodrigues and J. Jakubiak). 
     
    27.
  27. Discrete-time sliding-mode adaptive wheeled mobile robot control. Transactions on Automatic Control and Computer Science, Vol. 49 (63), No.1 (2004) 211-216. (With A. Filipescu and U.Nunes).
     
  28. Computing the square root and the logarithm of a real orthogonal matrix. Applied Numerical Mathematics, 46 (2003) 173-196. (With J. Cardoso and J. Kenney). 
      
  29. The Moser-Veselov equation. Linear Algebra and its Applications, 360 (2003) 237-248. (With J. Cardoso).
     
  30. L-splines - a manifestation of optimal control. IMA Journal of Mathematical Control and Information, Vol. 19, N. 3 (September 2002), 313-324. (With R. Rodrigues).
     
  31. On the geometry of Riemannian cubic polynomials. Differential Geometry and its Applications, 15 (2001) 107-135. (With M. Camarinha and P. Crouch).
      
  32. Theoretical and numerical considerations about Padé approximants for the matrix logarithm. Linear Algebra and its Applications, 330 (2001) 31-42. (With J. Cardoso).
     
  33. Almost orthogonality of a skew-symmetric matrix - solution 26-2.1 to problem 26-2. Bulletim of the International Linear Algebra Society - IMAGE, N. 27, (October 2001) 25.
     
  34. Elastic curves as solutions of Riemannian and sub-Riemannian control problems. Mathematics of Control, Signals and Systems, No. 13, 140-155 (2000). (With P. Crouch and M. Camarinha).
     
  35. Closed forms for the exponential mapping on matrix Lie groups, based on Putzer's method. Journal of Mathematical Physics, Vol. 40, No. 7 (July 1999) 3561-3568. (With P. Crouch).
     
  36. The De Casteljau algorithm on Lie groups and spheres. Journal of Dynamical and Control Systems. Vol. 5, No. 3 (1999) 397-429. (With P. Crouch and G. Kun). 

  37. The triple cross product in IR7. Reports on Mathematical Physics, Vol. 39, No. 3 (1997) 407-424. (With P.Crouch). 

  38. Splines of class C k on non-Euclidean spaces. IMA Journal of Mathematical Control and Information, 12 (1995) 399-410. (With P.Crouch and M. Camarinha).
     
  39. The dynamic interpolation problem: on Riemannian manifolds, Lie groups and symmetric spaces. Journal of Dynamical and Control Systems, Vol l, No. 2 (1995) 177-202. (With P.Crouch).
     
  40. A matemática e o real: alguns exemplos. Boletim da Sociedade Portuguesa de Matemática, No. 29, Setembro (1994), 27-39.
     
  41. The geometry of hypercomplex matrices. Linear and Multilinear Algebra, Vol. 34, No. 2, 123-132 (1992).
     
  42. Generalized Hessenberg matrices. Linear Algebra and its Applications, Vol.170, (June 1992), 220-225.
     
  43.  Controlabilidade estrutural. Estudos de Matemática, to the honor of Professor Renato Pereira Coelho, Coimbra (1992) 39-57.
     
  44. Generalization of the De Möivre formulas for quaternions and octonions. Estudos de Matemática, to the honor of Professor Luís de Albuquerque, Coimbra (1992) 121-133. (With J. Vitória).
     
  45. Bounds on the order of generation of SO(n,R) by one-parameter subgroups. Rocky Mountain Journal of Mathematics, Vol.21, No. 2, (1991), 879-911.
     
  46. Pairs of generators for compact real forms of the classical Lie algebras. Linear Algebra and its Applications, 121 (1989), 123-133.
     
  47. On the generators of semisimple Lie algebras. Linear Algebra and its Applications, 119 (1989), 51-56. (With H. Albuquerque).
     
  48. Controllability on classical Lie groups. Mathematics of Control, Signals and Systems, 1 (1988), 31-42. (With P. Crouch).
     
  49. Uniform controllable sets of left-invariant vector fields on noncompact Lie groups. Systems & Control Letters, Vol VII, (1986), 213-216.
     
  50. Uniform controllable sets of left-invariant vector fields on compact Lie groups. Systems & Control Letters, Vol VI, (1986), 293-335.
     
  51. On the uniform finite generation of SO(n,IR). Systems & Control Letters, Vol. II, No. 4, (1983), 341-347. (With P. Crouch).
 

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Published Conference Papers

  1. K-splines on SPD manifolds. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14072. Springer, Cham. (With M. Camarinha and L. Machado). doi:10.1007/978-3-031-38299-4_64.
     
  2. Best Fitting Geodesic Going Through the Riemannian Mean. In: Brito Palma, L., Neves-Silva, R., Gomes, L. (eds) CONTROLO 2022. CONTROLO 2022. Lecture Notes in Electrical Engineering, vol 930. Springer, Cham. (With L. Machado). doi:10.1007/978-3-031-10047-5_35.
     
  3. An extrinsic approach to sub-Riemannian geodesics on the orthogonal group. Springer Lecture Notes in Electrical Engineering, Volume 695, pp. 274-283. Proc. International Conference on Automatic Control and Soft Computing (CONTROLO'2020), July 1-3, 2020, Bragança - Portugal. (With K. Hüper and I. Markina).
     
  4. Geometric algorithm to generate interpolating splines on Grassmann and Stiefel manifolds. Springer Lecture Notes in Electrical Engineering, Volume 695, pp. 180-189. Proc. International Conference on Automatic Control and Soft Computing Computing (CONTROLO'2020), July 1-3, 2020, Bragança - Portugal. (With L. Machado and E. Batzies). Best Scientific Paper award.
     
  5. Existence and uniqueness for Riemannian cubics. Springer Lecture Notes in Electrical Engineering, Volume 695, pp. 322-331. Proc. International Conference on Automatic Control and Soft Computing Computing (CONTROLO'2020), July 1-3, 2020, Bragança - Portugal. (With M. Camarinha and P. Crouch).
     
  6. Cubic splines in the Grassmann manifold. Springer Lecture Notes in Electrical Engineering, Volume 695, pp. 243-252. Proc. International Conference on Automatic Control and Soft Computing Computing (CONTROLO'2020), July 1-3, 2020, Bragança - Portugal. (With F. Pina).
     
  7. Controllability of the kinematic equations describing pure rolling of Grassmannians. In Proc. International Conference on Automatic Control and Soft Computing, June 4-6, 2018, Azores - Portugal. IEEE Xplorer 2018, pp. 1-6. (With F. Pina).
     
  8. Controllability of rolling symmetric spaces. In Proc. International Conference on Automatic Control and Soft Computing, June 4-6, 2018, Azores - Portugal. IEEE Xplorer 2018, pp. 7-12. (With K. Krakowski).
     
  9. The geometry of quasi-geodesics on Stiefel manifolds. In Proc. International Conference on Automatic Control and Soft Computing, June 4-6, 2018, Azores - Portugal. IEEE Xplorer 2018, pp. 213-218. (With V. Jurdjeviv and K. Krakowski).
     
  10. Path planning trajectories in fluid environments. In Proc. International Conference on Automatic Control and Soft Computing, June 4-6, 2018, Azores - Portugal. IEEE Xplorer 2018, pp. 219-223. (With L. Machado and T. Monteiro).
     
  11. Constructive proof for complete controllability of a rolling pseudo-hyperbolic space. In Proc. International Conference on Automatic Control and Soft Computing, June 4-6, 2018, Azores - Portugal. IEEE Xplorer 2018, pp. 19-24. (With A. Marques).
     
  12. A Grassmannian Approach to Zero-Shot Learning for Network Intrusion Detection. In Proceedings of The 24th International Conference on Neural Information Processing (ICONIP 2017), November 14-18, 2017, Guangzhou - China. Springer International Publishing AG 2017, D. Liu et al. (Eds.): ICONIP 2017, Part I, LNCS 10634, pp. 565–575, 2017.https://doi.org/10.1007/978-3-319-70087-8_59. (With J. Rivero, B. Ribeiro and N. Chen).
     
  13. Exploring Quasi-Geodesics on Stiefel Manifolds in Order to Smooth Interpolate between Domains. In Proceedings of IEEE Conference on Decision and Control (CDC 2017), December 12-15, 2017, Melbourne - Australia. (With J. Batista and K. Krakowski).
     
  14. Multi-source domain adaptation using C1-smooth subspaces interpolation. In 2016 IEEE International Conference on Image Processing (ICIP), pages 2846–2850. IEEE, September 2016. (With J. Batista, K. Krakowski, L. Machado and P. Martins).
     
  15. Wheels for staircases. Lecture Notes in Electrical Engineering, Volume 402, pp 361-371, Springer 2016. (With J. Batista, K. Krakowski, A. Carvalho, T. Cruz, E. Domingues, A. Lizardo and G. Saraiva).
     
  16. Rolling symmetric spaces. In Geometric Science of Information, Lecture Notes in Computer Science, Vol 9389, pp 550-557, 2015. (With K. Krakowski and L. Machado).
     
  17. Controllability for the constrained rolling motion of symplectic groups. Lecture Notes in Electrical Engineering, Volume 321. António Paulo Moreira, Aníbal Matos, Germano Veiga Editors, pp 3-12, Springer 2014. (With A. Marques).
     
  18. Interpolation and polynomial fitting in the SPD manifold. Proc. 52nd IEEE Conference on Decision and Control, pp 1150-1155, 10-13 December, 2013. Florence, Italy. (With L. Machado).
     
  19. Rolling riemannian manifolds to solve the multi-class classification problem. Proc. 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2013, pp 41-48, 23-28 June 2013. Portland, Oregon, USA. (With R. Caseiro, P. Martins, J. Henriques, J. Batista)..
     
  20. Smooth interpolation on ellipsoids via rolling motions. Proc. PHYSCON 2013, 26–29 August, 2013, San Luis Potosí - Mexico. (With K. Krakowski).
     
  21. Approximating sets of symmetric and positive-definite matrices by geodesics. Conference Papers in Mathematics, Volume 2013 (2013), Article ID 425608, 7 pages. (With L. Machado). http://dx.doi.org/10.1155/2013/425608.
     
  22. Rolling motions of pseudo-orthogonal groups. Proc. IEEE-CDC 2012, 10-13 December 2012, Hawai'i - USA (With P. Crouch).
     
  23. Why controllability of rolling motions may fail. Proc. CONTROLO 2012, pp 197-203, 16-18 July 2012, Madeira - Portugal.  (With K. Krakowski).
     
  24. Rolling a pseudohyperbolic space over the affine tangent space at a point. Proc. CONTROLO 2012, pp  123-128, 16-18 July 2012, Madeira - Portugal. (With A. Marques).
     
  25. Kinematics for rolling a Lorentzian sphere. Proc. IEEE-CDC-ECC 2011, pp 6522-6528, 12- 15 December 2011, Orlando, USA. (With A. Korolko ).
     
  26. An overview of geometric nonlinear control through rolling motions. Proc. 9th Portuguese Conference on Automatic Control (CONTROLO'2010).
      
  27. Intrinsic rolling of manifolds. Proc. 9th Portuguese Conference on Automatic Control (CONTROLO'2010) (With M. Godoy, E. Grong and I. Markina).
     
  28. Rolling maps in Riemannian manifolds. Proc. 9th Portuguese Conference on Automatic Control (CONTROLO'2010) (With K. Krakowski)
     
  29. State estimation for systems on SE(3) with implicit outputs: An application to visual servoing. MTNS 2010. (With S. Rodrigues, N. Crasta, A. Aguiar).
       
  30. The geometry of rolling. Proc. XVII International Fall Workshop on Geometry and Physics (IFWGP'08), American Institute of Physics, N. 1130, 101-109, 3-6 September 2008, Castro Urdiales, Spain.
     
  31. Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices. Proc. Conference on Numerical Analysis (NumAn, 2008), 1-5 September 2008, Kalamata, Greece, pp. 54-57 (with J. Cardoso).
     
  32. A variational approach for high order least squares problems on Riemannian manifolds. Proc. 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), 28 July - 1 August, 2008, Virginia Tech, USA (with L. Machado and K. Krakowski).
     
  33. Riemannian mean as a limiting process. Proc. 8th Portuguese Conference on Automatic Control (CONTROLO'2008), 21-23 July 2008, Vila Real, Portugal (with L. Machado and K. Krakowski).
     
  34. Interpolation problems on Riemannian manifolds - a geometric approach. Proc. 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), 22-24 August, 2007, Pretoria, South Africa (with R. Rodrigues).
     
  35. On the analogy between mathematical problems of nonlinear control and option pricing theory. Proc. Workshop on Mathematical Control Theory and Finance, 10-14 April, 2007, Lisbon, Portugal (with P. Saraiva and H. Sebastião).
     
  36. On the geometry of rolling maps and applications to robotics. Proc. Workshop on Robotics and Mathematics (RoboMat 2007). 17-19 September, 2007, Coimbra, Portugal (with K. Hüper and M. Kleinsteuber).
     
  37. Generalized least squares problems on riemannian manifolds. Proc. Workshop on Robotics and Mathematics (RoboMat 2007). 17-19 September, 2007, Coimbra, Portugal (with L. Machado and K. Hüper).
     
  38. Geometric Splines and Interpolation on S2: Numerical Experiments. Proc. 45th IEEE Conference on Decision and Control. San Diego, CA, USA, 13-15 December, 2006. (With Yueshi Shen and Knut Hüper).
     
  39. Smooth trajectory planning for fully automated passenger’s vehicles - spline and clothoid based methods and its simulation. Proc. 3rd International Conference on Informatics in Control, Automation and Robotics (ICINCO 2006). Setúbal - Portugal, 1-5 August, 2006. (With Larissa Labakhua, Urbano Nunes and Rui Rodrigues).
     
  40. Interpolation curves on the sphere by rolling and wrapping. Proc. 7th Portuguese Conference on Automatic control (CONTROLO'2006), Lisbon - Portugal, 11-13 September 2006. (With Knut Hüper).
     
  41. L-splines and optimal control. Proc. 7th Portuguese Conference on Automatic control (CONTROLO'2006), Lisbon - Portugal, 11-13 September 2006. (With R. Rodrigues).
     
  42. An extension of the classical least squares method to non-Euclidean spaces. Proc. 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto - Japan, 24-28 July, 2006. (With L. Machado and K. Hüper).
     
  43. Complete controllability of the N-sphere - a constructive proof. Proc. 3rd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNLC'06). Nagoya - Japan, 19-21 July, 2006. (With M. Kleinsteuber and K. Hüper).
     
  44. Smooth interpolation of orientation by rolling and wrapping for robot motion planning. Proc. IEEE International Conference on Robotics and Automation (ICRA 2006), Orlando - Florida, USA, 15-19 May, 2006, 113-118. (With Yueshi Shen and K. Hüper).
     
  45. Trajectory planning methods for a car-like vehicle. Proc. International Symposium on System Theory, Automation, Robotics, Computers, Informatics, Electronics and Instrumentation (SINTES 2005). 20-22 October, 2005, Craiova - Roménia. (With L. Labakhua, U. Nunes and R. Rodrigues).
     
  46. Interpolation on Manifolds by Rolling and Wrapping to appear: Oberwolfach Reports, OWR, ISSN 1660-8933, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach-Walke, Germany, 2005.
     
  47. Fitting geodesics to data on SO(n). Proc. Third Junior European Meeting on Control, Computation and Optimization. Aveiro - Portugal, 6-8 September 2004. (With  L. Machado and K. Hüper).
     
  48. Spin systems and minimal switching decompositions. Proc. International Conference Physics and Control (PhysCon 2003). Saint Petersburg - Russia, 20-22 August 2003, 855-860. (With J. Clemente-Gallardo).
     
  49. On the generation of a trigonometric interpolating curve in R3. Proc. 11th International Conference on Advanced Robotics (ICAR 2003). Coimbra - Portugal, 30 June - 3 July 2003, 1629-1634. (With R. Rodrigues and S. Rosa).
     
  50. Spin systems, time optimality  and minimal switching decompositions. Proc. 11th International Conference on Advanced Robotics (ICAR 2003), Coimbra - Portugal, 30 June - 3 July 2003, 783-790. (With J. Clemente-Gallardo).
     
  51. The generalized Brockett's function and optimization problems. CD-Rom Proc. CONTROLO'2002, Universidade de Aveiro, 4-7 September, 2002. (With L. Machado).
     
  52. Smoothing interpolation curves on manifolds with applications to path planning. CD-Rom Proc.  MED'2002, Instituto Superior Técnico, Lisboa, 9-12 Julho, 2002. (With K. Hüeper ).
     
  53. Computing the inverse matrix hyperbolic sine. Proc. of the Second Conference on Numerical Analysis and Applications. July 2000, Rousse - Bulgaria. In Lecture Notes in Computer Science, No. 1988, Springer-Verlag, 2001. (With J. Cardoso).
     
  54. Hamiltonian structure of generalized cubic polynomials. Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, 16-18 March 2000, Princeton University, USA. (With P. Crouch and M. Camarinha).
     
  55. On the generation of smooth splines and optimal control. Proc. Nonlinear Control Network Pedagogical School, 6-10 September 1999, Athens, Greece, 365-380.
     
  56. Generalized splines and optimal control. Proc. European Control Conference - ECC'99, 31 August-3 September 1999, Karlsruhe, Germany. (With R. Rodrigues and C. Simões).
     
  57. Geometric splines. Proc. 14th World Congress of IFAC-International Federation of Automatic Control, Volume D, 533-538, 5-9 July 1999, Beijing, China. (With P. Crouch and G. Kun).
     
  58. Generalization of spline curves on the sphere: a numerical comparison. Proc. Third Portuguese Conference on Automatic Control, Vol II, 447-451, Coimbra, Portugal, 9-11 September 1998. (With P. Crouch and G. Kun).
     
  59. Hamiltonian formulation for a higher order variational problem on a Riemannian manifold. Proc. Third Portuguese Conference on Automatic Control, Vol. I, 321-327, Coimbra - Portugal, 9-11 September 1998. (With M. Camarinha and P. Crouch).
     
  60. Control systems on matrix lie groups. Proc. Meeting on Matrix Analysis and Applications, 295-306, Seville, Spain, 10-12 September 1997.
     
  61. An alternative proof for the generalized Euler's formula. Proc. Meeting on Matrix Analysis and Applications, 307-312, Seville, Spain, 10-12 September 1997. (With P. Saraiva)
     
  62. Geometric polynomials in Riemannian manifolds. Proc. European Control Conference ECC 97, July 1-4 1997, Brussels, Belgium. (With P. Crouch and M. Camarinha).
     
  63. De Casteljau algorithm for cubic polynomials on the rotation group. Proc. Portuguese Control Conference - CONTROLO-96, Vol II, 547-552, Porto, Portugal, 11-13 September 1996. (With P. Crouch and G. Kun).
     
  64. Second order optimality conditions for a higher order variational problem on a Riemannian manifold. Proc. 35th IEEE CDC, Kobe, Japan, 11-13 December 1996. (With P. Crouch and M. Camarinha).
     
  65. Sufficient conditions for an optimization problem on a Riemannian manifold. Proc. Portuguese Control Conference - CONTROLO-96, 127-131, Porto, Portugal, 11-13 September 1996. (With P. Crouch and M. Camarinha).
      
  66. Spline elements on spheres. Mathematical Methods for Curves and Surfaces, 49-54, M. Daehlen, T.Lych and L.Schumaker Edts. Vanderbilt Univ. Press, Nashville, TN. 1995. (With P. Crouch and G. Bunnett).
      
  67. Two higher order variational problems on Riemannian manifolds and the interpolation problem. Proc. Third European Control Conference, Vol. IV, 1131-1137. Roma, 1995. (With P.Crouch and M. Camarinha).
      
  68. The dynamic interpolation problem: on Riemannian manifolds, Lie groups and symmetric spaces. Journal of Dynamical and Control Systems, Vol 1, No. 2 (1995) 177-202. (With  P. Crouch).
     
  69. Elastic curves and optimal control of nonlinear systems. Proc. First Portuguese Control Conference, Lisbon, Portugal, 14-16 September, 1994. (With M. Camarinha).
      
  70. On the construction of spline elements on spheres. Proc. Second European Control Conference, Groningen, June 28-July 1, Vol. 4 (1993) 1930-1934. (With P. Crouch, Y. Yan and G. Brunnett).
      
  71. On the finite generation of Lie algebras . Proc. XIII Jornadas Espano-Lusas de Matemática. Valladolid, Spain. (With H. Albuquerque).
      
  72. Geometry and the dynamic interpolation problem. Proc. 1991 American Control Conference, Boston, 26-29 June (1991), 1131-1136. (With P. Crouch).
      
  73. Controllability and graphs. Progress in Systems and Control Theory, Vol.7, Birkäuser, (1991), 668-675. (With P. Crouch).
      
  74. On the generation of classical Lie groups and Lie algebras. Proc. 26.th IEEE Conference on Decision and Control, Los Angeles, (1987), 489-504. (With P. Crouch).
      
  75. Hypercomplex numbers and rotations. Proceedings XII Jornadas Luso-Espanholas de Matemática, Braga, 4-10 May (1987), Vol. II, 636-643. (With J. Vitória and C. Simões).
      
  76. Complexos, quaterniões e octoniões: um caso exemplar em investigação pedagógico-científica. Actas do Simpósio Pedagogia na Universidade, 23-24 March, UTL, (1985), 212-215. (With J. Vitória and P. Macedo).
      
  77. Geração uniforme dos grupos clássicos. Actas do Congresso do Grupo de Matemáticos de Expressão Latina, 10-14 September, Coimbra, (1985), Vol.1, 441-445.
      
  78. The uniform finite generation problem of Lie groups and its application to control problems. Contemporary Mathematics, Vol. 47 (1985), 273-285.
      
  79. The use of permutation matrices in the generation of the rotation group. Actas do Encuentro Internacional de Algebra Lineal y Aplicaciones, 28-30 September, Vitoria, Spain, (1983), 289-306.
 

Posters

  1. Generalizing Euclidean splines to SPD manifolds.
 

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Preprints

  1. Endpoint geodesic formulas on Grassmannians applied to interpolation problems. Pré-Publicações do Departamento de Matemática, N. 23-22 (2023), University of Coimbra. (With Knut Hüeper).
      
  2. k-Splines on SPD manifolds. Pré-Publicações do Departamento de Matemática, N. 23-14 (2023), University of Coimbra. (With M. Camarinha and L. Machado).
      
  3. Riemannian high-order splines. Pré-Publicações do Departamento de Matemática, N. 22-37 (2023), University of Coimbra. (With M. Camarinha and P. Crouch).
      
  4. Symmetric spaces rolling on flat spaces. Pré-Publicações do Departamento de Matemática, N. 22-13 (2022), University of Coimbra. (With V. Jurdjevic and Irina Markina).
      
  5. Cubic splines in the Grassmann manifold generated by the De Casteljau algorithm. Pré-Publicações do Departamento de Matemática, N. 20-07 (2020), University of Coimbra. (With F. Pina).
      
  6. Extremal curves on Stiefel and Grassmann manifolds. Pré-Publicações do Departamento de Matemática, N. 18-36 (2018), University of Coimbra. (With V. Jurdjevic and Irina Markina).
      
  7. Pure rolling motion of pseudo-Riemannian manifolds: an extrinsic perspective. Pré-Publicações do Departamento de Matemática, N. 18-18 (2018), University of Coimbra. (With A. Marques).
      
  8. Complete controllability of the kinematic equations describing pure rolling of Grassmannians. Pré-Publicações do Departamento de Matemática, N. 17-38 (2017), University of Coimbra. (With F. Pina).
      
  9. Solving interpolations problems on Stiefel manifolds using quasi-geodesics. Pré-Publicações do Departamento de Matemática, N. 15-36 (2015), University of Coimbra. (With K. Krakowski, L. Machado and J. Batista).
      
  10. The significance of Lie theory in the geometry of rolling motions. Pré-Publicações do Departamento de Matemática, N. 15-30 (2015), University of Coimbra. (With K. Krakowski and L. Machado).
      
  11. A note on the rolling ellipsoid and the C. Neumann problem. Pré-Publicações do Departamento de Matemática, N. 14-46 (2014), University of Coimbra. (With K. Krakowski).
      
  12. Algebraic integrability for minimum energy curves. Pré-Publicações do Departamento de Matemática, N. 14-30 (2014), University of Coimbra. (With I. Yudin).
      
  13. The geometric mean and the geodesic fitting problem on the Grassmann manifold. Pré-Publicações do Departamento de Matemática, N. 13-22 (2014), University of Coimbra. (With E. Batzies and L. Machado).
      
  14. An intrinsic formulation for rolling pseudo-Riemannian manifolds. Pré-Publicações do Departamento de Matemática, N. 12-26 (2012), University of Coimbra. (With I. Markina).
      
  15. Why controllability of rolling may fail: a few illustrative examples. Pré-Publicações do Departamento de Matemática, N. 12-26 (2012), University of Coimbra. (With K. Krakowski).
      
  16. Sphere rolling on sphere - alternative approach to kinematics and constructive proof of controllability. Pré-Publicações do Departamento de Matemática, N. 12-25 (2012), University of Coimbra. (With F. Louro).
      
  17. An intrinsic formulation to the rolling manifolds problem. Preprint NCTS (2010), Taiwan. (With M. Godoy, E. Grong and I. Markina).
      
  18. High order smoothing splines versus least squares problems on Riemannian manifolds. Pré-Publicações do Departamento de Matemática, N. 08-39 (2008), University of Coimbra. (With L. Machado and K. Krakowski).
      
  19. Covariant differentiation under rolling maps. Pré-Publicações do Departamento de Matemática, N. 08-22 (2008), University of Coimbra. (With K. Krakowski).
      
  20. On the geometry of rolling and interpolation curves on Sn, SO(n), and Grassmann manifolds. SISSA Report 56/2005/M, (July 2005). (With Knut Hüeper).
      
  21. On a one-step spline generation algorithm on Lie groups and spheres. Pré-Publicações do Departamento de Matemática, N. 04-38 (2004), University of Coimbra. (With  J. Jakubiak and  R. Rodrigues).
      
  22. A new geometric algorithm to generate spline curves. Pré-Publicações do Departamento de Matemática, N. 04-37 (2004), University of Coimbra. (With R. Rodrigues and J. Jakubiak).
      
  23. Fitting Smooth paths on Riemannian manifolds. Pré-Publicações do Departamento de Matemática, N. 04-31 (2004), University of Coimbra. (With L. Machado).
      
  24. Optimization problems on quadratic matrix Lie groups. Pré-Publicações do Departamento de Matemática, N. 02-21 (2001), University of Coimbra. (With L. Machado).
      
  25. A multi-input/multi-output systems representation of generalized splines in Rn. Pré-Publicações do Departamento de Matemática, N. 02-13 (2002), University of Coimbra. (With R. Rodrigues).
      
  26. The Moser-Veselov equation, Pré-Publicações do Departamento de Matemática, N. 01-12 (2001), University of Coimbra. (With J. Cardoso).
      
  27. L- splines - a manifestation of optimal control. Pré-Publicações do Departamento de Matemática, N. 99-17 (1999), University of Coimbra. (With R. Rodrigues).
      
  28. On computing real logarithms for matrices in the Lie group of special Euclidean motions in Rn, Pré-Publicações do Departamento de Matemática, N. 99-01 (1999), University of Coimbra. (With J. Cardoso).
      
  29. A second order Riemannian variational problem from a Hamiltonian perspective. Pré-Publicações do Departamento de Matemática, N. 98-17 (1998), University of Coimbra. (With P. Crouch and M. Camarinha).
      
  30. A remarkable example of simple r-Lie algebras. Pré-Publicações do Departamento de Matemática, N. 97-02 (1997), University of Coimbra. (With P. Saraiva).
     
  31. Generalized De Casteljau algorithm for polynomial curves on Lie groups and symmetric spaces. Pré-Publicações do Departamento de Matemática, N. 96-13 (October 1996), University of Coimbra. (With P. Crouch and G. Kun).
           
  32. Introdução às álgebras de Lie e aos Grupos de Lie (Mini-Course). Proc. VI Encontro Regional do Centro da Sociedade Portuguesa de Matemática, Vol. 3, 20-23 September (1983), Coimbra.

 

Thesis, Reports

  1. Interpolação Dinâmica em Variedades Riemanianas: Fundamentos e Aplicações. (Lição Síntese). University of Coimbra (2003). (15 pages, in portuguese).
           
  2. Introdução à Teoria Geométrica dos Sistemas de Controlo Não Lineares. (Programa de disciplina). University of Coimbra (2003). (35 pages, in portuguese).
           
  3. Álgebras de Lie. Programa de disciplina. University of Coimbra (1988). (15 pages, in portuguese).
           
  4. Uniform finite generation of the orthogonal group and applications to control theory. Ph.D. Thesis, Warwick University, England (January 1983).
     

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