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Robot's finger and expansions in non-integer bases
| 1. | Sapienza Università di Roma, Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sezione Matematica, Via A. Scarpa n.16 00161 Roma, Italy |
| 2. | Sapienza Università di Roma, Sapienza Università di Roma, Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sezione Matematica, Via A. Scarpa n.16 00161 Roma, Italy |
References:
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A. Bicchi, Robotic grasping and contact: A review, Proc. IEEE Int. Conf. on Robotics and Automation, (2000), 348-353. |
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Y. Chitour and B. Piccoli, Controllability for discrete systems with a finite control set, Mathematics of Control Signals and Systems, 14 (2001), 173-193.
doi: 10.1007/PL00009881. |
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P. Erd\Hos and V. Komornik, Developments in non-integer bases, Acta Math. Hungar., 79 (1998), 57-83.
doi: 10.1023/A:1006557705401. |
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K. J. Falconer, "Fractal Geometry," Mathematical Foundations and Applications, John Wiley & Sons, Ltd., Chichester, 1990. |
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W. J. Gilbert, Geometry of radix representations, in "The Geometric Vein," Springer, New York-Berlin, (1981), 129-139.
doi: 10.1007/978-1-4612-5648-9_7. |
| [6] |
W. J. Gilbert, The fractal dimension of sets derived from complex bases, Canad. Math. Bull., 29 (1986), 495-500.
doi: 10.4153/CMB-1986-078-1. |
| [7] |
W. J. Gilbert, Complex bases and fractal similarity, Ann. Sci. Math. Québec, 11 (1987), 65-77. |
| [8] |
P. S. Heckbert, ed., "Graphics Gems IV," Academic Press, 1994. |
| [9] |
J. Easudes C. J. H. Moravec and F. Dellaert, Fractal branching ultra-dexterous robots (bush robots), Technical report, NASA Advanced Concepts Research Project, 1996. |
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J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), 713-747.
doi: 10.1512/iumj.1981.30.30055. |
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K.-H. Indlekofer, I. Kátai and P. Racskó, Number systems and fractal geometry, in "Probability Theory and Applications," Math. Appl., 80, Kluwer Acad. Publ., Dordrecht, (1992), 319-334. |
| [12] |
A. C. Lai, "On Expansions in Non-Integer Base," Ph.D thesis, Sapienza Università di Roma and Université Paris Diderot, 2010. |
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W. Parry, On the $\beta $-expansions of real numbers, Acta Math. Acad. Sci. Hungar., 11 (1960), 401-416.
doi: 10.1007/BF02020954. |
| [14] |
J. Pineda, A parallel algorithm for polygon rasterization, Proceedings of the 15th annual conference on Computer graphics and interactive techniques, 22 (1988), 17-20. |
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A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar, 8 (1957), 477-493.
doi: 10.1007/BF02020331. |
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B. Siciliano and O. Khatib, "Springer Handbook of Robotics," 2008. |
show all references
References:
| [1] |
A. Bicchi, Robotic grasping and contact: A review, Proc. IEEE Int. Conf. on Robotics and Automation, (2000), 348-353. |
| [2] |
Y. Chitour and B. Piccoli, Controllability for discrete systems with a finite control set, Mathematics of Control Signals and Systems, 14 (2001), 173-193.
doi: 10.1007/PL00009881. |
| [3] |
P. Erd\Hos and V. Komornik, Developments in non-integer bases, Acta Math. Hungar., 79 (1998), 57-83.
doi: 10.1023/A:1006557705401. |
| [4] |
K. J. Falconer, "Fractal Geometry," Mathematical Foundations and Applications, John Wiley & Sons, Ltd., Chichester, 1990. |
| [5] |
W. J. Gilbert, Geometry of radix representations, in "The Geometric Vein," Springer, New York-Berlin, (1981), 129-139.
doi: 10.1007/978-1-4612-5648-9_7. |
| [6] |
W. J. Gilbert, The fractal dimension of sets derived from complex bases, Canad. Math. Bull., 29 (1986), 495-500.
doi: 10.4153/CMB-1986-078-1. |
| [7] |
W. J. Gilbert, Complex bases and fractal similarity, Ann. Sci. Math. Québec, 11 (1987), 65-77. |
| [8] |
P. S. Heckbert, ed., "Graphics Gems IV," Academic Press, 1994. |
| [9] |
J. Easudes C. J. H. Moravec and F. Dellaert, Fractal branching ultra-dexterous robots (bush robots), Technical report, NASA Advanced Concepts Research Project, 1996. |
| [10] |
J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), 713-747.
doi: 10.1512/iumj.1981.30.30055. |
| [11] |
K.-H. Indlekofer, I. Kátai and P. Racskó, Number systems and fractal geometry, in "Probability Theory and Applications," Math. Appl., 80, Kluwer Acad. Publ., Dordrecht, (1992), 319-334. |
| [12] |
A. C. Lai, "On Expansions in Non-Integer Base," Ph.D thesis, Sapienza Università di Roma and Université Paris Diderot, 2010. |
| [13] |
W. Parry, On the $\beta $-expansions of real numbers, Acta Math. Acad. Sci. Hungar., 11 (1960), 401-416.
doi: 10.1007/BF02020954. |
| [14] |
J. Pineda, A parallel algorithm for polygon rasterization, Proceedings of the 15th annual conference on Computer graphics and interactive techniques, 22 (1988), 17-20. |
| [15] |
A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar, 8 (1957), 477-493.
doi: 10.1007/BF02020331. |
| [16] |
B. Siciliano and O. Khatib, "Springer Handbook of Robotics," 2008. |
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