We would like to give robots the ability to position and orient parts in the plane by pushing, particularly when the parts are too large or heavy to be grasped and lifted. Unfortunately, the motion of a pushed object is generally unpredictable due to unknown support friction forces. With multiple pushing contact points, however, it is possible to find pushing directions that cause the object to remain fixed to the manipulator. These are called stable pushing directions. In this article we consider the problem of planning pushing paths using stable pushes. Pushing imposes a set of nonholonomic velocity constraints on the motion of the object, and we study the issues of local and global controllability during pushing with point contact or stable line contact. We describe a planner for finding stable pushing paths among obstacles, and the planner is demon strated on several manipulation tasks.
Get full access to this article
View all access options for this article.
References
1.
Abell, T., and Erdmann, M.1995. Stably supported rotations of a planar polygon with two frictionless contacts. Proc. 1995 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 411-418.
2.
Aho, A.V., Hopcroft, J.E., and Ullman, J.D.1974. The Design and Analysis of Computer Algorithms. Reading, MA: Addison-Wesley.
3.
Aiyama, Y., Inaba, M., and Inoue, H.1993. Pivoting: A new method of graspless manipulation of object by robot fingers. Proc. 1993 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 136-143.
4.
Akella, S., and Mason, M.T.1992. Posing polygonal objects in the plane by pushing. In Proc. 1992 IEEE Int. Conf. Robotics and Automation, pp. 2255-2262.
5.
Alami, R., Simeon, T., and Laumond, J.-P.1989. A geometrical approach to planning manipulation tasks. The case of discrete placements and grasps. Fifth Int. Symp. Robotics Res . Cambridge, MA: MIT Press, pp. 453-459.
6.
Alexander, J.C., and Maddocks, J.H.1993. Bounds on the friction-dominated motion of a pushed object . Int. J. Robot. Res.12(3):231-248.
7.
Arai, H., and Khatib, O.1994. Experiments with dynamic skills. Proc. 1994 Japan-USA Symp. on Flexible Automation, pp. 81-84.
8.
Balorda, Z.1990. Reducing uncertainty of objects by robot pushing. Proc. 1990 IEEE Int. Conf. Robotics and Automation, pp. 1051-1056.
9.
Balorda, Z.1993. Automatic planning of robot pushing operations. Proc. 1993 IEEE Int. Conf. Robotics and Automation, Vol. 1, pp. 732-737.
10.
Barraquand, J., and Latombe, J.-C.1993. Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles. Algorithmica10:121-155.
11.
Brokowski, M., Peshkin, M., and Goldberg, K.1993. Curved fences for part alignment. Proc. 1993 IEEE Int. Conf. Robotics and Automation, Vol. 3, pp. 467-473.
12.
Brost, R.C.1988. Automatic grasp planning in the presence of uncertainty . Int. J. Robot. Res.7(1):3-17.
13.
Brost, R.C.1992. Dynamic analysis of planar manipulation tasks. Proc. 1992 IEEE Int. Conf. Robotics and Automation, pp. 2247-2254.
14.
Christiansen, A.D.1995. A machine learning perspective on modeling robot actions . In Goldberg, K., Halperin, D., Latombe, J-C., and Wilson, R. (eds.): Algorithmic Foundations of Robotics. Boston, MA: A. K. Peters, pp. 319-330.
15.
Dacre-Wright, B., Laumond, J.-P., and Alami, R.1992. Motion planning for a robot and a movable object amidst polygonal obstacles. Proc. 1992 IEEE Int. Conf. Robotics and Automation, pp. 2474-2480.
16.
Donald, B.R., Jennings, J., and Rus, D.1993. Information invariants for cooperating autonomous mobile robots. Sixth Int. Symp. Robotics Res. Cambridge, MA: MIT Press, pp. 29-48.
17.
Dubins, L.E.1957. On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents . Am. J. Math.79:497-516.
18.
Erdmann, M.A.1984. On motion planning with uncertainty. Master's thesis, Department of Computer Science and Electrical Engineering, Massachusetts Institute of Technology.
19.
Erdmann, M.A.1994. On a representation of friction in configuration space . Int. J. Robot. Res.13(3):240-271.
20.
Erdmann, M.A., and Mason, M.T.1988. An exploration of sensorless manipulation. IEEE Trans. Robot. Automation4(4):369-379.
21.
Gandolfo, F., Tistarelli, M., and Sandini, G.1991. Visual monitoring of robot actions. Proc. 1991 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 269-275.
22.
Goldberg, K.Y.1993. Orienting polygonal parts without sensors. Algorithmica10:201-225.
23.
Goldberg, K.Y.1995. Completeness in robot motion planning. In Goldberg, K., Halperin, D. , Latombe, J-C., and Wilson, R. (eds.): Algorithmic Foundations of Robotics. Boston, MA: A. K. Peters , pp. 419-429.
24.
Goyal, S., Ruina, A., and Papadopoulos, J.1991a. Planar sliding with dry friction. Part 1. Limit surface and moment function. Wear143:307-330.
25.
Goyal, S., Ruina, A., and Papadopoulos, J.1991b. Planar sliding with dry friction. Part 2. Dynamics of motion. Wear143:331-352.
Haynes, G.W., and Hermes, H.1970. Nonlinear controllability via Lie theory. SIAM J. Control8(4):450-460.
28.
Hermann, R., and Krener, A.J.1977. Nonlinear controllability and observability. IEEE Trans. Auto. ControlAC-22(5):728-740.
29.
Higuchi, T.1985. Application of electromagnetic impulsive force to precise positioning tools in robot systems. Second Int. Symp. Robotics Res. Cambridge, MA: MIT Press, pp. 281-285.
30.
Hong, J., Lafferiere, G., Mishra, B., and Tan, X.1990. Fine manipulation with multifinger hands. Proc. 1990 IEEE Int. Conf. Robotics and Automation, pp. 1568-1573.
31.
Huang, W., Krotkov, E.P., and Mason, M.T.1995. Impulsive manipulation. Proc. 1995 IEEE Int. Conf. Robotics and Automation, pp. 120-125.
32.
Inaba, M., and Inoue, H.1989. Vision-based robot programming. Fifth Int. Symp. Robotics Res. Cambridge, MA: MIT Press, pp. 129-136.
33.
Jacobs, P., and Canny, J.1989. Planning smooth paths for mobile robots. Proc. 1989 IEEE Int. Conf. Robotics and Automation, pp. 2-7.
34.
Jurdjevic, V.1972. Certain controllability properties of analytic control systems. SIAM J. Control10(2):354-360.
35.
Jurdjevic, V., and Sussmann, H.J.1972. Control systems on Lie groups. JournalDifferential Equations, 12:313-329.
36.
Koga, Y., and Latombe, J.-C.1994. On multi-arm manipulation planning. Proc. 1994 IEEE Int. Conf. Robotics and Automation, Vol. 2, pp. 945-952.
37.
Kurisu, M., and Yoshikawa, T.1994. Trajectory planning for an object in pushing operation . Proc. 1994 Japan-USA Symp. on Flexible Automation , pp. 1009-1016.
Laumond, J.-P.1986. Feasible trajectories for mobile robots with kinematic and environment constraints. Proc. 1986 Int. Conf. Intelligent Autonomous Systems, pp. 346-354.
40.
Laumond, J.-P., Jacobs, P.E., Taix, M., and Murray, R.M.1994. A motion planner for nonholonomic mobile robots. IEEE Trans. Robot. Automation, 10(5):577-593.
41.
Li, Z., and Canny, J.1990. Motion of two rigid bodies with rolling constraint. IEEE Trans. Robot. Automation, 6(1):62-72.
42.
Lynch, K.M.1992. The mechanics of fine manipulation by pushing. Proc. 1992 IEEE Int. Conf. Robotics and Automation, pp. 2269-2276.
43.
Lynch, K.M.1993. Estimating the friction parameters of pushed objects. Proc. 1993 IEEE/RSJ Int. Conf. Intelligent Robots and Systems , pp. 186-193.
44.
Lynch, K.M., Maekawa, H., and Tanie, K.1992. Manipulation and active sensing by pushing using tactile feedback. Proc. 1992 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 416-421.
45.
Lynch, K.M. and Mason, M.T.1996. Dynamic under-actuated nonprehensile manipulation. Proc. 1996 IEEE/RSJ Int. Conf. Intelligent Robots and Systems (Forthcoming).
46.
MacMillan, W.D.1936. Dynamics of Rigid Bodies. New York : Dover.
47.
Mani, M., and Wilson, W.1985. A programmable orienting system for flat parts. North American Manufacturing Research Institute Conference XIII .
48.
Markenscoff, X., Ni, L., and Papadimitriou, C.H.1990. The geometry of grasping . Int. J. Robot. Res.9(1):61-74.
49.
Mason, M.T.1986. Mechanics and planning of manipulator pushing operations . Int. J. Robot. Res.5(3):53-71.
50.
Mason, M.T.1989. Compliant sliding of a block along a wall. Proc. 1989 Int. Symp. Experimental Robotics, pp. 568-578.
51.
Mason, M.T., and Brost, R.C.1986. Automatic grasp planning: An operation space approach . Sixth Symp. on Theory and Practice of Robots and Manipulators. Alma Press, pp. 321-328.
52.
Mason, M.T., and Lynch, K.M.1993. Dynamic manipulation. Proc. 1993 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 152-159.
53.
Mayeda, H., and Wakatsuki, Y.1991. Strategies for pushing a 3D block along a wall. Proc. 1991 IEEE/RSJ Int. Conf. Intelligent Robots and Systems , pp. 461-466.
54.
Mishra, B., Schwartz, J.T., and Sharir, M.1987. On the existence and synthesis of multifinger positive grips. Algorithmica2(4):541-558.
55.
Miura, J.1989. Integration of problem solving and learning in intelligent robots. Fifth Int. Symp. Robotics Res. Cambridge, MA: MIT Press, pp. 13-20.
56.
Narasimhan, S.1995. Task-level strategies for robot tasks. Ph.D. thesis, Department of Computer Science and Electrical Engineering, Massachusetts Institute of Technology.
57.
Nijmeijer, H., and van der Schaft, A.J.1990. Nonlinear Dynamical Control Systems. New York: Springer-Verlag .
58.
Okawa, Y., and Yokoyama, K.1992. Control of a mobile robot for the push-a-box operation . Proc. 1992 IEEE Int. Conf. Robotics and Automation , pp. 761-766.
59.
Peshkin, M.A., and Sanderson, A.C.1988a. Planning robotic manipulation strategies for workpieces that slide. IEEE J. Robot. Automation4(5):524-531.
60.
Peshkin, M.A., and Sanderson, A.C.1988b. The motion of a pushed, sliding workpiece. IEEE J. Robot. Automation4(6):569-598.
61.
Peshkin, M.A., and Sanderson, A.C.1989. Minimization of energy in quasi-static manipulation. IEEE Trans. Robot. Automation5(1):53-60.
62.
Prescott, J.1923. Mechanics of Particles and Rigid Bodies. London: Longmans, Green, and Co.
63.
Reeds, J.A., and Shepp, L.A.1990. Optimal paths for a car that goes both forwards and backwards . Pacific J. Math.145(2):367-393.
64.
Rizzi, A.A., and Koditschek, D.E.1993. Further progress in robot juggling: The spatial two-juggle. Proc. 1993 IEEE Int. Conf. Robotics and Automation, Vol. 3, pp. 919-924.
65.
Salganicoff, M., Metta, G., Oddera, A., and Sandini, G.1993a. A direct approach to vision guided manipulation. Proc. 1993 Int. Conf. Advanced Robotics.
66.
Salganicoff, M., Metta, G., Oddera, A., and Sandini, G.1993b. A vision-based learning method for pushing manipulation. AAAI Fall Symp. on Machine Learning in ComputerVision.
67.
Salisbury, K., Eberman, B., Levin, M., and Townsend, W.1987. The design and control of an experimental whole-arm manipulator. Fourth Int. Symp. Robotics Res. Cambridge, MA: MIT Press, pp. 233-241.
68.
Sawasaki, N., Inaba, M., and Inoue, H.1989. Tumbling objects using a multi-fingered robot. 20th Int. Symp. Industrial Robots and Robot Exhibition, pp. 609-616.
69.
Schaal, S., and Atkeson, C.G.1993. Open loop stable control strategies for robot juggling . Proc. 1993 IEEE Int. Conf. Robotics and Automation , Vol. 3, pp. 913-918.
70.
Sussmann, H.J.1978. A sufficient condition for local controllability. SIAM J. Control Optimization16(5):790-802.
71.
Sussmann, H.J.1983. Lie brackets, real analyticity and geometric control. In Brockett, R. W., Millman, R. S., and Sussmann, H. J. (eds.): Differential Geometric Control Theory. Boston, MA: Birkhäuser, pp. 1-116.
72.
Sussmann, H.J.1987. A general theorem on local controllability. SIAM J. Control Optimization25(1):158-194.
73.
Sussmann, H.J., and Jurdjevic, V.1972. Controllability of nonlinear systems. J. Differential Equations12:95-116.
74.
Trinkle, J.C., Ram, R.C., Farahat, A.O., and Stiller, P.F.1993. Dexterous manipulation planning and execution of an enveloped slippery workpiece. Proc. 1993 IEEE Int. Conf. Robotics and Automation, Vol. 2, pp. 442-448.
75.
Wilfong, G.1988. Motion planning in the presence of movable obstacles. Proc. 4th ACM Symp. Computational Geometry, pp. 279-288.
76.
Yoshikawa, T., and Kurisu, M.1991. Identification of the center of friction from pushing an object by a mobile robot. Proc. 1991 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 449-454.
77.
Zrimec, T.1990. Towards autonomous learning of behavior by a robot. Ph.D. thesis, Department of Computer and Information Science , University of Ljubljana.
78.
Zumel, N.B., and Erdmann, M.A.1994. Balancing of a planar bouncing object. Proc. 1994 IEEE Int. Conf. Robotics and Automation, pp. 2949-2954.
