Inertial Properties in Robotic Manipulation: An Object-Level Framework

Abstract

Consideration of dynamics is critical in the analysis, design, and control of robot systems. This article presents an extensive study of the dynamic properties of several important classes of robotic structures and proposes a number of general dynamic strategies for their coordination and control. This work is a synthesis of both previous and new results developed within the task-oriented operational space formulation. Here we in troduce a unifying framework for the analysis and control of robotic systems, beginning with an analysis of inertial prop erties based on two models that independently describe the mass and inertial characteristics associated with linear and angular motions. To visualize these properties, we propose a new geometric representation, termed the belted ellipsoid, that displays the magnitudes of the mass/inertial properties directly rather than their square roots. Our study of serial macro/mini structures is based on two models of redundant mechanisms. The first is a description of the task-level dy namics that results from projecting the system dynamics into operational space. The second is a unique dynamically con sistent relationship between end-effector forces and joint torques. It divides control torques at the joint level into two dynamically decoupled vectors: torques that correspond to forces at the end effector, and torques that affect only internal motions. The analysis of inertial properties of macro-/mini- manipulator systems reveals another important characteristic: that of reduced effective inertia. We show that the effective mass/inertia of a macro-/mini-manipulator is bounded above by the mass/inertia of the mini-manipulator alone. Because mini structures have a limited range of motion, we also pro pose a dextrous dynamic coordination strategy to allow full use of the high mechanical bandwidth of the mini-structures in extended-motion operations. Finally, a study of the dy namics of parallel, multiarm structures reveals an important additive property. The effective mass and inertia of a multi arm system at some operational point are shown to be given by the sum of the effective masses and inertias associated with the object and each arm. Using this property, the mul tiarm system can be treated as a single augmented object and controlled by the total operational forces applied by the arms. Both the augmented object construct and the dynam ically consistent force/torque relationship are extended for the analysis and control of multiarm systems involving redun dancy.

Get full access to this article

View all access options for this article.

References

Alford, C.O. , and Belyeu, S.M. 1984. Coordinated control of two robot arms. Proc. IEEE Int. Conference on Robotics and Automation, Atlanta, GA, pp. 468-473.

Asada, H. , 1983. A geometrical representation of manipulator dynamics and its application to arm design. Trans. ASME J. Dynamic Sys. Measurement Control 105(3):131-135.

Cai, C.-H. , and Roth, B. 1987. Impact sensitivity to mass distribution of a planar manipulator . Proc. ICAR: 3rd Int. Conf. Advanced Robotics , Versailles, France, pp. 115-124.

Golub, G.H. , and Van Loan, C.F. 1983. Matrix Computations. Baltimore, MD : The Johns Hopkins University Press.

Hammer, R. , Hollis, L. , An, C.H. , and Hendricks, F. 1992. Design and control of an air-bearing supported three-degree-of-freedom fine positioner. Proc. IEEE Int. Conference on Robotics and Automation, Nice, France, pp. 677-684.

Hayati, S. 1986. Hybrid position/force control of multiarm cooperating robots. Proc. IEEE Int. Conference on Robotics and Automation, San Francisco, CA, pp. 1375-1380.

Hogan, N. 1984. Impedance control of industrial robots. Robotics Computer-Integrated Manufacturing 1(1):97-113.

Hollis, R. 1985. A planar XY robotics fine positioning device. Proc. IEEE Int. Conference on Robotics and Automation, St. Louis, MO, pp. 329-337.

Karidis, J.P. , McVicker, G. , Pawletko, J.P. , and Zai, L.C. 1992. The hummingbird minipositioner— providing three axis motion at 50 G's with low reactions. Proc. IEEE Int. Conference on Robotics and Automation, Nice, France, pp. 685-692.

10.

Khatib, O. 1980. Commande Dynamique dans l'Espace Opérationnel des Robots Manipulateurs en Présence d'Obstacles. Thése de Docteur-Ingénieur. École Nationale Supérieure de l'Aéronautique et de l'Espace, Toulouse, France.

11.

Khatib, O. 1986. Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1): 90-98.

12.

Khatib, O. 1987. A unified approach to motion and force control of robot manipulators: The operational space formulation. IEEE J. Robot. Automation 3(1):43-53.

13.

Khatib, O. 1988. Object manipulation in a multi-effector robot system. In Bolles, R. , and Roth, B. (eds.): Robotics Research 4. Cambridge, MA: MIT Press, pp. 137-144.

14.

Khatib, O. 1990. Reduced effective inertia in macro/mini-manipulator systems . In Miura, H. , and Arimoto, S. (eds.): Robotics Research 5. Cambridge, MA: MIT Press, pp. 279-284.

15.

Khatib, O. , and Agrawal, S. 1989. Isotropic and uniform inertial and acceleration characteristics: Issues in the design of manipulators. In Schweitzer, G. , and Man-sour, M. (eds.): Dynamics of Controlled Mechanical Systems. New York: Springer-Verlag, pp. 259-270.

16.

Khatib, O. , and Burdick, J. 1985. Dynamic optimization in manipulator design: The operational space formulation. In Donath, M., and Leu, M. (eds.): Robotics and Manufacturing Automation. Proc. ASME Winter Annual Meeting, Miami, Vol. 15, pp. 169-174.

17.

Kumar, V. , and Waldron, K.J. 1988. Force distribution in closed kinematic chains. Proc. IEEE Int. Conference on Robotics and Automation, Philadelphia, PA, pp. 114-119.

18.

Kumar, V. , Yun, X. , Paljug, E. , and Sarkar, N. 1991. Control of contact conditions for manipulation with multiple robotic systems. Proc. IEEE Int. Conference on Robotics and Automation, Sacramento, CA, pp. 170-175.

19.

Luh, J.Y.S. , Walker, M.W. , and Paul, P. 1980. Resolved acceleration control of mechanical manipulators . IEEE Trans. Auto. Control 25(3):468-474.

20.

Merlet, J.P. 1988. Force-feedback control of parallel manipulators. Proc. IEEE Int. Conference on Robotics and Automation, Philadelphia, PA, pp. 1484-1489.

21.

Nakamura, Y. 1988. Minimizing object strain energy for coordination of multiple robotic mechanisms. Proc. American Control Conference , pp. 499-504.

22.

Reboulet, C. , and Robert, A. 1986. Hybrid control of a manipulator equipped with an active compliant wrist. In Faugeras, O. , and Giralt, G. (eds.): Robotics Research: 3rd International Symposium. Cambridge, MA: MIT Press, pp. 237-241.

23.

Russakow, J. , and Khatib, O. 1992. A new control structure for free-flying space robots. International Symposium on Artificial Intelligence, Robotics and Automation in Space, Toulouse, France, pp. 395-403.

24.

Sharon, A. , Hogan, N. , and Hardt, D. 1988. High bandwidth force regulation and inertia reduction using a macro-/micro manipulator system. Proc. IEEE Int. Conference on Robotics and Automation, Philadelphia, PA, pp. 126-132.

25.

Takase, K. 1977. Task-oriented variable control of manipulator and its software servoing system. Proc. IFAC Int. Symp , pp. 139-145.

26.

Tarn, T.J. , Bejczy, A.K. , and Yun, X. 1987. Design of dynamic control of two cooperating robot arms: Closed chain formulation. Proc. IEEE Int. Conference on Robotics and Automation, Raleigh, NC, pp. 7-13.

27.

Tilley, S.W. , Cannon, R.H. , and Kraft, R. 1986. Endpoint force control of a very flexible manipulator with a fast end-effector. Proc. ASME Winter Annual Meeting, Anaheim, CA, Vol. 3, pp. 1-9.

28.

Uchiyama, M. , and Dauchez, P. 1988. A symmetric hybrid position/force control scheme for the coordination of two robots. Proc. IEEE Int. Conference on Robotics and Automation, Philadelphia, PA, pp. 350-356.

29.

Williams, D. , and Khatib, O. 1993. The virtual linkage: A model for internal forces in multi-grasp manipulation. Proc. IEEE Int. Conference on Robotics and Automation, Atlanta, GA, pp. 1025-1030.

30.

Williams, D. , and Khatib, O. 1993. Experiments in multiarm manipulation. Preprints of the Third International Symposium on Experimental Robotics (ISER 3), Kyoto, Japan, pp. 321-330.

31.

Zheng, Y.F. , and Luh, J.Y.S. 1986. Joint torques for control of two coordinated moving robots . Proc. IEEE Int. Conference on Robotics and Automation , San Francisco, CA, pp. 1375-1380.