Solution of the Robot Forward Dynamics Problem by Using a Recursive Procedure Based on the General System Logical Theory

Abstract

The paper deals with the forward dynamics problem in robotics. The solution of the problem is found on the basis of a new theory, called “general system logical theory.” It uses operators and transformation of operators extensively to study objects and their relations in the real world. The basic notions and operator equations are given. The forward dynamics problem is presented as a diagram, called “elementary logical system.” The diagram unites a set of variables, a set of operators, and a set of relations between the operators. A generic form of a recursive process using the operators and the Lie product is described. The convergence of the process is discussed. Original operator procedures dedicated to the links of the robot are proposed. The wanted solution is found at the limit of the recursive process. An example is given, as well. The result obtained illustrates the ability of the theory to study robotics problems. The forward dynamics problem is solved in a new way and without inversion of the mass matrix of the robot.

Get full access to this article

View all access options for this article.

References

Brandle, H. R., Johanni, R., and Otter, M. 1986. A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass-matrix. In Proc. IFAC/IFIP Int. Symp. on Theory of Robots, pp. 95–100. Vienna: IFAC/IFIP .

Craig, J. J. 1989. Introduction to Robotics: Mechanics and Control. Reading, MA: Addison-Wesley .

Featherstone, R. 1983. The calculation of robot dynamics using articulated-body inertia . Intl. J. Robot. Res. 2(1): 13–30 .

Fijany, A., and Bejczy, A. K. 1989. A class of parallel algorithms for computation of the manipulator inertia matrix. In Proc. of IEEE Int. Conf. on Robotics and Automation, 1818–1826. Scottsdale, AZ: IEEE .

Gogoussis, A., and Donath, M. 1990. A method for the real time solution of the forward dynamics problem for robots incorporating friction . Trans. of ASME J. of Dyn. Syst. Meas. and Contr. 112(Dec): 630–639 .

Lee, C.S.G., and Chang, P. R. 1988. Efficient parallel algorithms for robot forward dynamics computation . IEEE Trans. on Systems, Man, and Cybernetics 18(2): 238–251 .

Otter, M., Elmqvist, H., and Cellier, F. E. 1993. Modeling of multibody systems with the object-oriented modeling language Dymola . Proc. of NATO/ASI: “Computer-Aided Analysis of Rigid and Flexible Mechanical Systems,” June 27-July 9, Troia, Portugal, 91–110 .

Petzold, L. R. 1993. Issues in the numerical solution of differential algebraic equations for mechanical systems simulation . Proc. of NATO/ASI: “Computer-Aided Analysis of Rigid and Flexible Mechanical Systems,” June 27-July 9, Troia, Portugal, 195–209 .

Resconi, G., and Jessel, M. 1986. A general system logical theory . Int. J. General Systems 12: 159–182 .

10.

Resconi, G., Tzvetkova Vassileva, G. 1991. Simulation of dynamic behaviour of robot manipulators by general system logical theory . Proc. of the 14th IASTED Int. Symp. “Manufacturing and Robotics,” June 25-27, Lugano, Switzerland, 103–106 .

11.

Rodrigues, G. 1987. Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics . IEEE J. of Rob. and Autom. RA-3(6): 624–639 .

12.

Toogood, R. W. 1989. Efficient robot inverse and direct dynamics algorithms using micro-computer based symbolic generation. IEEE Int. Conf. on Robotics and Automation, 1827–1832. Scottsdale, AZ: IEEE .

13.

Walker, M.W., and Orin, D.E. 1982. Efficientdynamiccomputer simulation of robotic mechanisms . Trans. ASME: Journal of Dynamic Systems, Measurement, and Control. 104(Sept): 205–211 .