Triangularizing kinematic constraint equations using Gröbner bases for real-time dynamic simulation

[1]  Akira Suzuki,et al.  Computing Gröbner Bases within Linear Algebra , 2009, CASC.

[2]  O. Bauchau,et al.  Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems , 2008 .

[3]  O. Bauchau,et al.  Review of Classical Approaches for Constraint Enforcement in Multibody Systems , 2008 .

[4]  H. Stetter,et al.  Numerical computation of Gröbner bases , 2008 .

[5]  Tateaki Sasaki,et al.  Floating-Point Gröbner Basis Computation with Ill-conditionedness Estimation , 2007, ASCM.

[6]  Klaus Lamberg,et al.  Automated Real-Time Testing of Electronic Control Units , 2007 .

[7]  Yoshihiro Suda,et al.  Evaluation of driver’s behavior with multibody-based driving simulator , 2007 .

[8]  Martin Arnold,et al.  Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs , 2007 .

[9]  Fabrice Rouillier,et al.  On solving the direct kinematics problem for parallel robots , 2006 .

[10]  Torsten Butz,et al.  Simulation of Vehicle-Trailer Combinations by Real-Time Capable DAE Solvers , 2006 .

[11]  Bruno Buchberger,et al.  Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal , 2006, J. Symb. Comput..

[12]  M. A. Akanbi,et al.  Numerical solution of initial value problems in differential - algebraic equations , 2005 .

[13]  John McPhee,et al.  Dynamic Modelling of Mechatronic Multibody Systems With Symbolic Computing and Linear Graph Theory , 2004 .

[14]  A. Gorshkov Stabilization of Linear Parabolic Equations Defined in an Exterior of a Bounded Domain by a Boundary Control , 2004 .

[15]  Jean-Claude Samin,et al.  Symbolic Modeling of Multibody Systems , 2003 .

[16]  John McPhee,et al.  Inverse dynamic analysis of parallel manipulators with full mobility , 2003 .

[17]  John McPhee,et al.  Dynamics of Multibody Systems Using Virtual Work and Symbolic Programming , 2002 .

[18]  Li Cheng,et al.  Modeling and Simulation of Robotic Systems with Closed Kinematic Chains Using the Virtual Spring Approach , 2002 .

[19]  Bruno Buchberger,et al.  Gröbner Bases and Systems Theory , 2001, Multidimens. Syst. Signal Process..

[20]  Anoop K. Dhingra,et al.  Closed-form displacement and coupler curve analysis of planar multi-loop mechanisms using Gröbner bases , 2001 .

[21]  L. Tsai Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work , 2000 .

[22]  Michael W. Sayers,et al.  VEHICLE MODELS FOR RTS APPLICATIONS , 1999 .

[23]  J. Faugère A new efficient algorithm for computing Gröbner bases (F4) , 1999 .

[24]  J. McPhee Automatic generation of motion equations for planar mechanical systems using the new set of “branch coordinates” , 1998 .

[25]  Ralf Fröberg,et al.  An introduction to Gröbner bases , 1997, Pure and applied mathematics.

[26]  Michael Kalkbrener,et al.  Converting Bases with the Gröbner Walk , 1997, J. Symb. Comput..

[27]  Manfred Hiller,et al.  Symbolic Processing of Multiloop Mechanism Dynamics Using Closed-Form Kinematics Solutions , 1997 .

[28]  Jean-Claude Samin,et al.  Symbolic generation of a multibody formalism of order N - Extension to closed-loop systems using the coordinate partitioning method , 1996 .

[29]  M. Husty An algorithm for solving the direct kinematics of general Stewart-Gough platforms , 1996 .

[30]  Kiyoshi Shirayanagi Floating point Gro¨bner bases , 1996 .

[31]  B. Roth,et al.  Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators , 1995 .

[32]  Jadran Lenarčič,et al.  Advances in Robot Kinematics and Computational Geometry , 1994 .

[33]  Bernard Roth Computational Advances in Robot Kinematics , 1994 .

[34]  Jean-Charles Faugère,et al.  Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering , 1993, J. Symb. Comput..

[35]  André Heck,et al.  Introduction to Maple , 1993 .

[36]  Andrés Kecskeméthy,et al.  On Closed Form Solutions of Multiple-Loop Mechanisms , 1993 .

[37]  Keith O. Geddes,et al.  Algorithms for computer algebra , 1992 .

[38]  Leo Joskowicz,et al.  Computational Kinematics , 1991, Artif. Intell..

[39]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[40]  M. A. Serna,et al.  A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems , 1988 .

[41]  Pietro Fanghella,et al.  Kinematics of spatial linkages by group algebra: A structure-based approach , 1988 .

[42]  C. W. Gear,et al.  Automatic integration of Euler-Lagrange equations with constraints , 1985 .

[43]  J. Baumgarte Stabilization of constraints and integrals of motion in dynamical systems , 1972 .