. Bibliographie, Abramowitz 65] Milton Abramowitz, Irene A Stegunet al. Handbook of mathematical functions, 1965.

A. Andrei and Y. Sachkov, Control theory from the geometric viewpoint, 2004.

N. M. Amato, O. Burchan-bayazit, L. K. Dale, and C. Vallejo, OBPRM : An Obstacle-based PRM for 3D Workspaces, Proceedings of the Third Workshop on the Algorithmic Foundations of Robotics on Robotics : The Algorithmic Perspective., WAFR '98, pp.155-168, 1998.

O. Burhcan-bayazit, &. Jyh-ming-lien, M. Nancy, and . Amato, Probabilistic roadmap motion planning for deformable objects, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292), pp.2126-2133, 2002.
DOI : 10.1109/ROBOT.2002.1014854

. Dmitry-berenson, S. Siddhartha, D. Srinivasa, &. Ferguson, J. James et al., Manipulation planning on constraint manifolds, Robotics and Automation, 2009. ICRA'09. IEEE International Conference on, pp.625-632, 2009.

J. Biggs, W. Holderbaum, and &. Velimir-jurdjevic, Singularities of optimal control problems on some 6-D Lie groups. Automatic Control, IEEE Transactions on, vol.52, issue.6, pp.1027-1038, 2007.

R. Bohlin, &. Lydia, and E. Kavraki, Path planning using lazy PRM, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065), pp.521-528, 2000.
DOI : 10.1109/ROBOT.2000.844107

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.1989

R. Bohlin, &. Lydia, and E. Kavraki, A randomized algorithm for robot path planning based on lazy evaluation, Handbook on Randomized Computing, pp.221-249, 2001.

A. Borum, Optimal control problems on lie groups with symmetry breaking cost functions, 2015.

A. Borum and &. Bretl, The free configuration space of a Kirchhoff elastic rod is path-connected, 2015 IEEE International Conference on Robotics and Automation (ICRA), pp.2958-2964, 2015.
DOI : 10.1109/ICRA.2015.7139604

T. Bretl and &. Mccarthy, Quasi-static manipulation of a Kirchhoff elastic rod based on a geometric analysis of equilibrium configurations, The International Journal of Robotics Research, vol.29, issue.13, pp.48-68, 2014.
DOI : 10.1017/CBO9780511546877

A. Earl-bryson, Applied optimal control : optimization, estimation and control, 1975.

J. Canny, The complexity of robot motion planning, 1988.

M. Howie and . Choset, Principles of robot motion : theory, algorithms, and implementation, 2005.

A. Khoury, F. Lamiraux, and &. Michel-taix, Optimal motion planning for humanoid robots, 2013 IEEE International Conference on Robotics and Automation, pp.3136-3141, 2013.
DOI : 10.1109/ICRA.2013.6631013

URL : https://hal.archives-ouvertes.fr/hal-00715419

D. Flavigne and &. M. Taix, Improving motion planning in weakly connected configuration spaces, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.5900-5905, 2010.
DOI : 10.1109/IROS.2010.5650612

B. Frank, M. Becker, C. Stachniss, M. Teschner, and W. Burgard, Efficient path planning for mobile robots in environments with deformable objects, 2008 IEEE International Conference on Robotics and Automation, 2008.
DOI : 10.1109/ROBOT.2008.4543784

B. Frank, C. Stachniss, N. Abdo, and W. Burgard, Efficient motion planning for manipulation robots in environments with deformable objects, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2011.
DOI : 10.1109/IROS.2011.6094946

H. Jerome, J. L. Friedman, &. Bentley, and . Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Transactions on Mathematical Software (TOMS), vol.3, issue.3, pp.209-226, 1977.

. Gayle, . Gayle, C. Ming, &. Lin, and . Manocha, Constraint-Based Motion Planning of Deformable Robots, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp.1046-1053, 2005.
DOI : 10.1109/ROBOT.2005.1570254

. Gayle, P. Gayle, . Segars, C. Ming, &. Lin et al., Path Planning for Deformable Robots in Complex Environments, Robotics: Science and Systems I, pp.225-232, 2005.
DOI : 10.15607/RSS.2005.I.030

D. Hsu, L. E. Kavraki, J. Latombe, R. Motwani, and &. Stephen-sorkin, On Finding Narrow Passages with Probabilistic Roadmap Planners, Proceedings of the Third Workshop on the Algorithmic Foundations of Robotics on Robotics : The Algorithmic Perspective., WAFR '98, pp.141-153

C. Thomas, . Hudson, C. Ming, J. Lin, S. Cohen et al., V-COLLIDE : accelerated collision detection for VRML, Proceedings of the second symposium on Virtual reality modeling language, p.117, 1997.

]. I. Jolliffe, Principal component analysis, 2002.
DOI : 10.1007/978-1-4757-1904-8

I. Kabul, R. Gayle, &. Ming, and C. Lin, Cable route planning in complex environments using constrained sampling, Proceedings of the 2007 ACM symposium on Solid and physical modeling , SPM '07, pp.395-402, 2007.
DOI : 10.1145/1236246.1236303

I. Kamon and &. Ehud-rivlin, Sensory-based motion planning with global proofs Robotics and Automation, IEEE Transactions on, vol.13, issue.6, pp.814-822, 1997.
DOI : 10.1109/70.650160

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.1821

I. Kamon, E. Rimon, and &. Ehud-rivlin, Range-sensor based navigation in three dimensions, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C), pp.163-169, 1999.
DOI : 10.1109/ROBOT.1999.769955

S. Karaman and &. Frazzoli, Sampling-based algorithms for optimal motion planning, The International Journal of Robotics Research, vol.23, issue.7, pp.846-894, 2011.
DOI : 10.1017/CBO9780511546877

E. Lydia, P. Kavraki, J. Svestka, &. Latombe, H. Mark et al., Probabilistic roadmaps for path planning in highdimensional configuration spaces. Robotics and Automation, IEEE Transactions on, vol.12, issue.4, pp.566-580, 1996.

W. Khalil, G. Gallot, and &. F. Boyer, Dynamic Modeling and Simulation of a 3-D Serial Eel-Like Robot. Systems, Man, and Cybernetics , Part C : Applications and Reviews, IEEE Transactions on, vol.37, issue.6, pp.1259-1268, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00630752

J. James, &. Kuffner, M. Steven, and . Lavalle, RRT-connect : An efficient approach to single-query path planning, Robotics and Automation Proceedings. ICRA'00. IEEE International Conference on, pp.995-1001, 2000.

F. Lamiraux and &. L. Kavraki, Planning Paths for Elastic Objects under Manipulation Constraints, The International Journal of Robotics Research, vol.20, issue.3, pp.188-208, 2001.
DOI : 10.1177/02783640122067354

J. Langer, A. David, and . Singer, The total squared curvature of closed curves, Journal of Differential Geometry, vol.20, issue.1, pp.1-22, 1984.
DOI : 10.4310/jdg/1214438990

J. Langer, &. David, and A. Singer, Lagrangian Aspects of the Kirchhoff Elastic Rod, SIAM Review, vol.38, issue.4, pp.605-618, 1996.
DOI : 10.1137/S0036144593253290

E. Larsen, S. Gottschalk, C. Ming, &. Lin, and . Manocha, Fast distance queries with rectangular swept sphere volumes, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065), pp.3719-3726, 2000.
DOI : 10.1109/ROBOT.2000.845311

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.9259

J. Latombe, Robot motion planning, 1991.
DOI : 10.1007/978-1-4615-4022-9

M. Steven and . Lavalle, Rapidly-Exploring Random Trees : A New Tool for Path Planning, 1998.

M. Steven, &. Lavalle, J. James, and . Kuffner-jr, Rapidly-exploring random trees : Progress and prospects, 2000.

M. Steven, &. Lavalle, J. James, and . Kuffner, Randomized kinodynamic planning, The International Journal of Robotics Research, vol.20, issue.5, pp.378-400, 2001.

M. Steven and . Lavalle, Planning algorithms, 2006.

P. Leven and &. S. Hutchinson, Using manipulability to bias sampling during the construction of probabilistic roadmaps, IEEE Transactions on Robotics and Automation, vol.19, issue.6, pp.1020-1026, 2003.
DOI : 10.1109/TRA.2003.819732

D. Liberzon, Calculus of variations and optimal control theory : a concise introduction, 2012.

[. Lozano-perez, Spatial planning : A configuration space approach. Computers, IEEE Transactions on, vol.100, issue.2, pp.108-120, 1983.
DOI : 10.1109/tc.1983.1676196

URL : http://dspace.mit.edu/handle/1721.1/5684#files-area

J. Vladimir, &. Lumelsky, A. Alexander, and . Stepanov, Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape, Algorithmica, vol.2, issue.1-4, pp.403-430, 1987.

A. Mahoney, J. Bross, and &. Johnson, Deformable robot motion planning in a reduced-dimension configuration space, 2010 IEEE International Conference on Robotics and Automation, pp.5133-5138, 2010.
DOI : 10.1109/ROBOT.2010.5509649

E. Jerrold, T. Marsden, and . Ratiu, Introduction to mechanics and symmetry : a basic exposition of classical mechanical systems, 2013.

X. Merlhiot, J. L. Garrec, G. Saupin, and C. Andriot, The XDE Mechanical Kernel : Efficient and Robust Simulation of Multibody Dynamics with Intermittent Nonsmooth Contacts, Proceedings of the Second Joint International Conference on Multibody System Dynamics -IMSD 2012, 2012.

B. Mirtich and . V-clip, V-Clip: fast and robust polyhedral collision detection, ACM Transactions on Graphics, vol.17, issue.3, pp.177-208, 1998.
DOI : 10.1145/285857.285860

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.128.6538

E. Lydia and . Kavraki, Path planning for deformable linear objects, Robotics IEEE Transactions on, vol.22, issue.4, pp.625-636, 2006.

M. Richard, Z. Murray, &. Li, and . Sastry, A mathematical introduction to robotic manipulation, 1994.

J. Nocedal and &. Wright, Numerical optimization, 2006.
DOI : 10.1007/b98874

A. Orthey, O. Roussel, O. Stasse, and &. Michel-taix, Irreducible Motion Planning by Exploiting Linear Linkage Structures, In Transactions on Robotics, vol.15
URL : https://hal.archives-ouvertes.fr/hal-01163259

C. Frank and . Park, Distance metrics on the rigid-body motions with applications to mechanism design, Journal of Mechanical Design, vol.117, issue.1, pp.48-54, 1995.

A. Perez, R. Platt, G. Konidaris, L. Kaelbling, and &. T. Lozano-perez, LQR-RRT*: Optimal sampling-based motion planning with automatically derived extension heuristics, 2012 IEEE International Conference on Robotics and Automation, pp.2537-2542, 2012.
DOI : 10.1109/ICRA.2012.6225177

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.856

S. Redon, &. Ming, and C. Lin, Practical Local Planning in the Contact Space, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp.4200-4205, 2005.
DOI : 10.1109/ROBOT.2005.1570765

URL : https://hal.archives-ouvertes.fr/hal-01148126

H. John and . Reif, Complexity of the mover's problem and generalizations, Proceedings of the 20th Annual IEEE Conference on Foundations of Computer Science, pp.421-427, 1979.

M. Renaud, Les intégrales et fonctions elliptiques, 2014.

M. Renaud, ´ Etude des groupes et algèbre de Lie Théorème de réduction de Lie-Poisson. Application au groupe spécial euclidien SE(3) etàetà son algèbre se(3) Rapport technique, LAAS-CNRS, 2015.

E. Rimon, &. Daniel, and E. Koditschek, Exact robot navigation using artificial potential functions Robotics and Automation, IEEE Transactions on, vol.8, issue.5, pp.501-518, 1992.
DOI : 10.1109/70.163777

URL : http://repository.upenn.edu/cgi/viewcontent.cgi?article=1364&context=ese_papers

G. Robinson and &. J. Davies, Continuum robots - a state of the art, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C), pp.2849-2854, 1999.
DOI : 10.1109/ROBOT.1999.774029

S. Rodriguez, J. Lien, &. Nancy, and M. Amato, Planning motion in completely deformable environments, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., pp.2466-2471, 2006.
DOI : 10.1109/ROBOT.2006.1642072

A. Roussel-15a-]-olivier-roussel and M. Borum, Manipulation planning with contacts for an extensible elastic rod by sampling on the submanifold of static equilibrium configurations, Robotics and Automation (ICRA), 2015 IEEE International Conference on, pp.3116-3121, 2015.

M. Roussel-15b-]-olivier-roussel, &. Renaud, and . Michel-ta¨?xta¨?x, Inverse geometry for Kirchhoff elastic rods, IMA Conference on Mathematics of Robotics, 2015.

M. Roussel-15c-]-olivier-roussel, B. Ta¨?xta¨?x, E. Michel, and . Ferré, Calcul automatique de trajectoires pour l'assemblage d'objets déformables, 14ème Colloque national AIP-Primeca, 2015.

T. Sam, &. Roweis, K. Lawrence, and . Saul, Nonlinear dimensionality reduction by locally linear embedding, Science, vol.290, issue.5500, pp.2323-2326, 2000.

M. Saha, J. Latombe, and Y. Prinz, Finding Narrow Passages with Probabilistic Roadmaps: The Small-Step Retraction Method, Autonomous Robots, vol.20, issue.5, pp.301-319, 2005.
DOI : 10.1007/s10514-005-4748-1

M. Saha and &. Isto, Manipulation Planning for Deformable Linear Objects, IEEE Transactions on Robotics, vol.23, issue.6, pp.1141-1150, 2007.
DOI : 10.1109/TRO.2007.907486

J. Salençon, Mécanique des milieux continus : Concepts généraux, Editions Ecole Polytechnique, vol.1, 2005.

J. Salençon, Mécanique des milieux continus : Milieux curvilignes, Editions Ecole Polytechnique, vol.3, 2005.

G. Saupin, O. Roussel, and &. Garrec, Robust and Scalable Navmesh Generation with multiple levels and stairs support, International Conference in Central Europe on Computer Graphics and Visualization (WSCG), 2013.

F. Schwarzer, M. Saha, and &. Jean-claude-latombe, Adaptive dynamic collision checking for single and multiple articulated robots in complex environments, IEEE Transactions on Robotics, vol.21, issue.3, pp.338-353, 2005.
DOI : 10.1109/TRO.2004.838012

J. Simo, A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Computer methods in applied mechanics and engineering, pp.55-70, 1985.

A. David, . Singer, J. Oscar, E. Garay, &. Garcia-rio et al., Lectures on elastic curves and rods, AIP Conference Proceedings, p.3, 2008.

P. Soueres and &. Boissonnat, Optimal trajectories for nonholonomic mobile robots, Robot motion planning and control, pp.93-170, 1998.
DOI : 10.1007/BFb0036072

I. Sucan, M. Moll, E. Lydia, and . Kavraki, The Open Motion Planning Library, IEEE Robotics & Automation Magazine, vol.19, issue.4, pp.72-82, 2005.
DOI : 10.1109/MRA.2012.2205651

B. Joshua, V. D. Tenenbaum, &. Silva, C. John, and . Langford, A global geometric framework for nonlinear dimensionality reduction, Science, vol.290, issue.5500, pp.2319-2323, 2000.

A. Yershova, L. Jaillet, T. Simeon, and &. S. Lavalle, Dynamic-Domain RRTs: Efficient Exploration by Controlling the Sampling Domain, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp.3856-3861, 2005.
DOI : 10.1109/ROBOT.2005.1570709

A. Yershova, S. Jain, M. Steven, &. Lavalle, C. Julie et al., Generating uniform incremental grids on SO (3) using the Hopf fibration. The International journal of robotics research, 2009.

L. Zhang and &. D. Manocha, An efficient retraction-based RRT planner, Robotics and Automation ICRA 2008. IEEE International Conference on, pp.3743-3750, 2008.

J. Kuffner and &. Michael-branicky, Multipartite RRTs for rapid replanning in dynamic environments, Robotics and Automation IEEE International Conference on, pp.1603-1609, 2007.