Motion planning in velocity affine mechanical systems

References

• Allgower , EL and Georg , K . 1990 . Numerical Continuation Methods , Berlin : Springer-Verlag .
   Google Scholar
• Alouges, F., Chitour, Y., and Long, R. (2009), ‘A Motion Planning Algorithm for the Rolling-body Problem’, in Proceedings of the 48th IEEE Conference on Decision and Control, December 16–18, Shanghai, pp. 2112–2116.
   Google Scholar
• Arnold , VI . 1989 . Mathematical Methods of Classical Mechanics , Berlin : Springer-Verlag .
   Google Scholar
• Ben-Horin , P and Thomas , F . 2008 . “ A Nonholonomic 3-DOF Parallel Robot ” . In Advances in Robot Kinematics , Edited by: Lenarčič , J and Wenger , P . 111 – 118 . Berlin : Springer Science+Business Media B.V. .
   Google Scholar
• Ben-Israel , A and Greville , TNE . 2003 . Generalized Inverses. Theory and Applications , New York : Springer-Verlag .
   Google Scholar
• Brockett , RW and Dai , L . 1993 . “ Non-holonomic Kinematics and the Role of Elliptic Functions in Constructive Controllability ” . In Nonholonomic Motion Planning , Edited by: Li , Z and Canny , JF . 1 – 21 . Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Chitour , Y . 2006 . A Continuation Method for Motion Planning Problems . ESAIM: Control, Optimization and Calculus of Variations , 12 : 139 – 168 .
   Web of Science ®Google Scholar
• Davidenko , DF . 1953 . On a New Method of Numerically Integrating a System of Nonlinear Equations . Doklady Akademii Nauk , 88 : 601 – 603 .
   Google Scholar
• Divelbiss , AW and Wen , JT . 1997 . A Path Space Approach to Nonholonomic Motion Planning in the Presence of Obstacles . IEEE Transactions on Robotics and Automation , 13 : 443 – 451 .
   Google Scholar
• Grosch , P , Di Gregorio , R and Thomas , F . 2010 . Generation of Under-actuated Manipulators With Nonholonomic Joints From Ordinary Manipulators . Journal of Mechanisms and Robotics , 2 : 011005
   Google Scholar
• Jakubiak, J., and Tchoń, K. (2004), ‘Fourier vs. Non-Fourier Band-limited Jacobian Inverse Kinematics Algorithms for Mobile Manipulators’, in Proceedings of the 10th IEEE International Conference Methods and Models in Automation and Robotics, August 30–September 2, Międzyzdroje, Poland, pp. 1005–1010.
   Google Scholar
• Jurdjevic , V . 1993 . The Geometry of the Plate-Ball Problem . Archive for Rational Mechanics Analysis , 124 : 305 – 328 .
   Web of Science ®Google Scholar
• Mazur , A . 2010 . Trajectory Tracking Control in Workspace-defined Tasks for Nonholonomic Mobile Manipulators . Robotica , 28 : 57 – 68 .
   Google Scholar
• Nakamura , Y , Chung , Y and Sordalen , OJ . 2001 . Design and Control of the Nonholonomic Manipulator . IEEE Transactions on Robotics and Automation , 17 : 48 – 59 .
   Google Scholar
• Selig , JM . 2005 . Geometric Fundamentals of Robotics , Berlin : Springer Science+Business Media B. V .
   Google Scholar
• Sussmann , HJ . 1993 . “ A Continuation Method for Nonholonomic Path Finding Problems ” . In in Proceedings of 32nd IEEE CDC , 2718 – 2723 . TX : San Antonio .
   Google Scholar
• Tchoń, K. (2007), ‘Continuation Method in Robotics’, in Proceedingso of the 7th Conference on Computer Methods and Systems, AGH University of Science and Technology, Cracow, PL, pp. 17–24.
   Google Scholar
• Tchoń , K and Jakubiak , J . 2003 . Endogenous Configuration Space Approach to Mobile Manipulators: A Derivation and Performance Assessment of Jacobian Inverse Kinematics Algorithms . International Journal of Control , 76 : 1387 – 1419 .
   Web of Science ®Google Scholar
• Tchoń , K and Małek , Ł . 2009 . On Dynamic Properties of Singularity Robust Jacobian Inverse Kinematics . IEEE Transactions on Automation and Control , 54 : 1402 – 1406 .
   Google Scholar
• Ważewski , T . 1947 . Sur l'évaluation Du Domaine d'Existence Des Fonctions Implicites Réelles ou Complexes . Annales Societatis Mathematicae Polonae , 20 : 81 – 120 .
   Google Scholar