Some Applications of Gröbner Bases in Robotics and Engineering

Grobner bases in polynomial rings have numerous applications in geometry, applied mathematics, and engineering. We show a few applications of Grobner bases in robotics, formulated in the language of Clifford algebras, and in engineering to the theory of curves, including Fermat and Bezier cubics, and interpolation functions used in finite element theory.

[1]  Gordon R. Pennock,et al.  Theory of Machines and Mechanisms , 1965 .

[2]  B. Buchberger.  Gröbner Bases and Applications: Introduction to Gröbner Bases , 1998 .

[3]  D. Eisenbud.  Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .

[4]  Joseph L. Awange,et al.  Solving Algebraic Computaitonal problems in Geodesy and Geoinformatics : The Answer to Modern Challenges , 2005 .

[5]  L. Meister,et al.  A concise quaternion geometry of rotations , 2005 .

[6]  Craig Huneke,et al.  Commutative Algebra I , 2012 .

[7]  Robin Hartshorne,et al.  Algebraic geometry , 1977, Graduate texts in mathematics.

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

[9]  J. Reddy.  An introduction to the finite element method , 1989 .

[10]  Erich Kaltofen,et al.  Computer Algebra Handbook : Foundations · Applications · Systems , 2003 .

[11]  Andreas Koch,et al.  Efficient Inverse Kinematics Algorithm Based on Conformal Geometric Algebra - Using Reconfigurable Hardware , 2008, GRAPP.

[12]  B. Buchberger,et al.  Gröbner bases and applications , 1998 .

[13]  Dietmar Hildenbrand,et al.  Analysis of Point Clouds - Using Conformal Geometric Algebra , 2008, GRAPP.

[14]  Nirmal K. Bose.  Multidimensional systems theory and applications (2. ed.) , 2003 .

[15]  임종인,et al.  Gröbner Bases와 응용 , 1995 .

[16]  Erich Kaltofen,et al.  Computer algebra handbook , 2002 .

[17]  Robert L. Norton,et al.  Design of machinery : an introduction to the synthesis and analysis of mechanisms and machines , 1999 .

[18]  Quaternion Optimization Problems in Engineering , 2001 .

[19]  G. Greuel,et al.  A Singular Introduction to Commutative Algebra , 2002 .

[20]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[21]  Donal O'Shea,et al.  Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.

[22]  Jane Liu,et al.  On the parallel lines for nondegenerate conics , 2006, math/0602248.

[23]  Eduardo Bayro Corrochano,et al.  Geometric Algebra with Applications in Science and Engineering , 2012 .

[24]  N. Bose.  Multidimensional Systems Theory , 1985 .

[25]  Wave Fronts and Caustics of Vector Fields. , 2002 .