Geodesic
Rolling bodies with regular surface: controllability theory and applications
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 1, pp. 101-132.

Voir la notice de l'article provenant de la source Math-Net.Ru

Pairs of bodies with regular rigid surfaces rolling onto each other in space form a nonholonomic system of a rather general type, posing several interesting control problems of which not much is known. The nonholonomy of such systems can be exploited in practical devices, which is very useful in robotic applications. In order to achieve all potential benefits, a deeper understanding of these types of systems and more practical algorithms for planning and controlling their motions are necessary. In this paper, we study the controllability aspect of this problem, giving a complete description of the reachable manifold for general pairs of bodies, and a constructive controllability algorithm for planning rolling motions for dexterous robot hands.
Keywords: nonholonomic systems, nonlinear controllability theory, robotic manipulation. 
@article{ND_2013_9_1_a8,
     author = {Alessia Marigo and Antonio Bicchi},
     title = {Rolling bodies with regular surface: controllability theory and applications},
     journal = {Russian journal of nonlinear dynamics},
     pages = {101--132},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2013_9_1_a8/}
}
TY  - JOUR
AU  - Alessia Marigo
AU  - Antonio Bicchi
TI  - Rolling bodies with regular surface: controllability theory and applications
JO  - Russian journal of nonlinear dynamics
PY  - 2013
SP  - 101
EP  - 132
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2013_9_1_a8/
LA  - ru
ID  - ND_2013_9_1_a8
ER  - 
%0 Journal Article
%A Alessia Marigo
%A Antonio Bicchi
%T Rolling bodies with regular surface: controllability theory and applications
%J Russian journal of nonlinear dynamics
%D 2013
%P 101-132
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2013_9_1_a8/
%G ru
%F ND_2013_9_1_a8
Alessia Marigo; Antonio Bicchi. Rolling bodies with regular surface: controllability theory and applications. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 1, pp. 101-132. http://geodesic.mathdoc.fr/item/ND_2013_9_1_a8/

[1] Baillieul J., “Open-loop control using oscillatory inputs”, The control systems handbook, 2nd ed., ed. W. S. Levine, CRC Press, Boca Raton, FL, 1996, 967–980

[2] Kolmanovsky I., McClamroch N. H., “Developments in nonholonomic control problems”, IEEE Contr. Syst. Mag., 15:6 (1995), 20–36 | DOI

[3] Brockett R. W., “On the rectification of vibratory motion”, Sensors and Actuators A, 20 (1989), 91–96 | DOI

[4] Nakamura Y., Mukherjee R., “Exploiting nonholonomic redundancy of free flying space robots”, IEEE Trans. Robot. Automat., 9:4 (1993), 499–506 | DOI

[5] Ostrowski J., Burdick J., “Geometric perspectives on the mechanics and control of robotic locomotion”, Robotics Research, Proc. of the 7th Internat. Symp., eds. G. Giralt, G. Hirzinger, Springer, New York, 1996, 536–547 | DOI

[6] Sørdalen O. J., Nakamura Y., “Design of a nonholonomic manipulator”, Proc. of the Internat. Conf. on Robotics and Automation (1994), 8–13

[7] Bicchi A., Sorrentino R., “Dexterous manipulation through rolling”, Proc. of the Internat. Conf. Robotics and Automation (1995), 452–457

[8] Cole A., Hauser J., Sastry S. S., “Kinematics and control of a multi-fingered robot hand with rolling contact”, IEEE Trans. Automat. Contr., 34:4 (1989), 398–404 | DOI | MR | Zbl

[9] Brockett R. W., “Asymptotic stability and feedback stabilization”, Differential geometric control theory, eds. R. W. Brockett, G. A. Millmann, H. Sussmann, Birkhäuser, Boston, 1982, 181–191 | MR

[10] Murray R. M., “Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems”, Math. Control Signals Systems, 7 (1994), 58–75 | DOI | MR | Zbl

[11] Tilbury D., Murray R. M., Sastry S. S., “Trajectory generation for the $n$-trailer problem using Goursat normal form”, IEEE Trans. Automat. Contr., 40:5 (1995), 802–819 | DOI | MR | Zbl

[12] Sørdalen O. J., “Conversion of the kinematics of a car with $n$ trailers into a chained form”, Proc. of the Internat. Conf. on Robotics and Automation (1993), 382–387

[13] Brockett R., Dai L., “Nonholonomic kinematics and the role of elliptic functions in constructive controllability”, Nonholonomic motion planning, eds. Z. Li, J. F. Canny, Kluwer, Norwell, MA, 1993, 1–21 | DOI

[14] Murray R. M., Sastry S. S., “Nonholonomic motion planning: Steering using sinusoids”, IEEE Trans. Automat. Contr., 38 (1993), 700–716 | DOI | MR | Zbl

[15] Lafferriere G., Sussmann H., “Motion planning for controllable systems without drift”, Proc. of the Internat. Conf. on Robotics and Automation (1991), 1148–1153

[16] Monaco S., Normand-Cyrot D., “An introduction to motion planning under multirate digital control”, Proc. 31st IEEE Conf. on Decision and Control (1992), 1780–1785

[17] Jacobs G., “Motion planning by piecewise constant or polynomial inputs”, NOLCOS, Proc. IFAC Nonlinear Control Systems Symp. (1992), 628–633

[18] Rouchon P., Fliess M., Lèvine J., Martin P., “Flatness, motion planning and traile systems”, Proc. 32nd IEEE Conf. on Decision and Control (1993), 2700–2705

[19] Chelouah A., “Exensions of differentially flat fields and Liouvillian systems”, Proc. 36th IEEE Conf. on Decision and Control (1997), 4268–4273

[20] Montana D. J., “The kinematics of contact and grasp”, Int. J. Robot. Res., 7:3 (1988), 17–32 | DOI

[21] Li Z., Canny J., “Motion of two rigid bodies with rolling constraint”, IEEE Trans. Robot. Automat., 6:1 (1990), 62–72 | DOI

[22] Jurdjevic V., “The geometry of the plate-ball problem”, Arch. Ration. Mech. Anal., 124:4 (1993), 305–328 | DOI | MR | Zbl

[23] Levi M., “Geometric phases in the motion of rigid bodies”, Arch. Ration. Mech. Anal., 122:3 (1993), 213–229 | DOI | MR | Zbl

[24] Murray R., Li Z., Sastry S. S., A mathematical introduction to robotic manipulation, CRC Press, Boca Raton, FL, 1994, 456 pp. | MR | Zbl

[25] Sussmann H., “Orbits of families of vector fields and integrability of distributions”, Trans. Amer. Math. Soc., 180 (1973), 171–188 | DOI | MR | Zbl

[26] do Carmo M. P., Differential geometry of curves and surfaces, Prentice-Hall, Englewood Cliffs, NJ, 1976, 503 pp. | MR | Zbl

[27] Sontag E., “Control of systems without drift via generic loops”, IEEE Trans. Automat. Contr., 40:7 (1995), 1210–1219 | DOI | MR | Zbl

[28] Sussmann H., Chitour Y., “A continuation method for nonholonomic path-finding problems”, IMA Workshop on Robotics (1993)

[29] Bicchi A., Prattichizzo D., Sastry S. S., “Planning motions of rolling surfaces”, Proc. 34th IEEE Conf. on Decision and Control (1995), 2812–2817

[30] Agrachev A. A., Sachkov Y. L., An intrinsic approach to the control of rolling bodies. ISAS: Internat. School for Advanced Studies, Tech. Rep. SISSA 114/99/M, Sept. 1999

[31] Bicchi A., Marigo A., Prattichizzo D., “Dexterity through rolling: Manipulation of unknown objects”, Proc. of the Internat. Conf. on Robotics and Automation (1998), 1583–1568

[32] Ceccarelli M., Marigo A., Piccinocchi S., Bicchi A., “Planning motions of polyhedral parts by rolling”, Algorithmica, 26:3–4 (2000), 560–576 | MR | Zbl

[33] Arai H., Tachi S., “Dynamic control of a manipulator with passive joints in an operational coordinate space”, Proc. IEEE Internat. Conf. Robotics and Automation (1991), 1188–1195