Programming and control of robots by means of differential algebraic inequalities

IEEE Transactions on Robotics and Automation

Volumn 16, Issue 2, 2000, Pages 135-145

  Spiteri, Raymond J ^a   Pai, Dinesh K ^b   Ascher, Uri M ^b  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONSTRAINT THEORY; CONTROL SYSTEM SYNTHESIS; MOBILE ROBOTS; MOTION PLANNING; OPTIMAL CONTROL SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; SET THEORY;

CONSTRAINT PROGRAMMING; DIFFERENTIAL ALGEBRAIC INEQUALITIES; SUBOPTIMAL CONTROL;

ROBOT PROGRAMMING;

EID: 0033688083     PISSN: 1042296X     EISSN: None     Source Type: Journal    
DOI: 10.1109/70.843168     Document Type: Article

References (51)

1. R. Spiteri, U. Ascher, and D. Pai, "Numerical solution of differential systems with algebraic inequalities arising in robot programming," in Proc. IEEE Conf. Robot. Automat., Nagoya, Japan, 1995, pp. 2373-2380.
2. J. C. Latombe, Robot Motion Planning. Norwell, MA: Kluwer, 1991.
3. Z. Li and J. F. Canny, Nonholonomic Motion Planning. Norwell, MA: Kluwer, 1993.
4. J. Canny, A. Rege, and J. Reif, "An exact algorithm for kinodynamic planning in the plane," Discrete Comput. Geom., vol. 6, no. 5, pp. 461-484, 1991.
5. B. Donald, P. Xavier, J. Canny, and J. Reif, "Kinodynamic motion planning," J. Assoc. Comput. Mach., vol. 40, no. 5, pp. 1048-1066, 1993.
6. B. R. Donald and P. Xavier, "Provably good approximation algorithms for optimal kinodynamic planning: Robots with decoupled dynamics bounds," Algorithmica, vol. 14, no. 6, pp. 443-479, 1995.
7. _, "Provably good approximation algorithms for optimal kinodynamic planning for Cartesian robots and open-chain manipulators," Algorithmica, vol. 14, no. 6, pp. 480-530, 1995.
8. R. Brockett, Control Theory and Singular Riemannian Geometry, P. Hilton and G. Young, Eds. New York: Springer-Verlag, 1981, pp. 11-27.
9. A. M. Bloch and N. H. McClamroch, "Control of mechanical systems with classical nonholonomic constraints," in Proc. IEEE Conf. Decision and Control, Tampa, 1989, pp. 201-205.
10. G. Laffarriere and H. J. Sussmann, "Motion planning for completely controllable systems without drift," in Proc. IEEE Conf. Robotics and Automation, Sacramento, CA, 1991, pp. 1148-1153.
11. R. M. Murray and S. S. Sastry, "Steering nonholonomic systems using sinusoids," in Proc. IEEE Conf. Decision and Control, 1990.
12. P. Jacobs, J. P. Laumond, and M. Taix, "Efficient motion planners for nonholonomic mobile robots," in Proc. IEEE IROS, Osaka, Japan, Nov. 1991.
13. H. Tominaga and B. Bavarian, "Solving the moving obstacle path planning problem using embedded variational methods," in Proc. IEEE Int. Conf. Robot. Automat., Sacramento, CA, Apr. 1991, pp. 450-455.
14. O. Khatib, "Real time obstacle avoidance for manipulators and mobile robots," Int J. Robot. Res., vol. 5, no. 1, pp. 90-99, 1986.
15. N. Hogan, "Impedance control: An approach to manipulation," J Dyn. Syst., vol. 107, pp. 1-7, Mar. 1965.
16. W. S. Newman and N. Hogan, "High speed robot control and obstacle avoidance using dynamic potential functions," in Proc. IEEE Int. Conf. Robotics and Automation, Rayleigh, NC, 1987, pp. 14-24.
17. D. E. Koditschek, "Robot planning and control via potential functions," in The Robotics Review 1. Cambridge, MA: MIT Press, 1989.
18. C. I. Connolly and R. Grupen, "The applications of harmonic functions to robotics," J. Robotic Syst., vol. 10, no. 7, pp. 931-946, 1993.
19. _,"Harmonic control," in Proc. 1992 Int. Symp. Intelligent Control, Aug. 1992.
20. I. Mantegh, M. R. M. Jenkin, and A. A. Goldenburg, "Fast trajectory planning and obstacle avoidance for autonomous robots using nonholonomic modeling," in Proc. IEEE SMC Computational Eng. Syst. Applicat., 1998.
21. J. S. Zelek, "Complete real-time path planning during sensor-based discovery," in Proc. IEEE Conf. Intell. Robots Syst., 1998, pp. 1399-1404.
22. R. B. Tilove, "Local obstacle avoidance for mobile robots based on the method of artificial potentials," in Proc. IEEE Int. Conf. Robotics and Automation, Cincinnati, OH, May 1990, pp. 565-571.
23. J. Borenstein and Y. Koren, "Real-time obstacle avoidance for fast mobile robots," IEEE Trans. Syst., Man, Cybern., vol. 19, pp. 1179-1187, Sept./Oct. 1989.
24. Y. Zhang and A. Mackworth, "Constraint programming in constraint nets," in Proc. 1st Workshop Principles and Practice of Constraint Programming, 1993, pp. 303-312.
25. D. K. Pai, "Programming anthropoid walking: Control and simulation," Cornell Univ., Tech. Rep. TR90-1178, 1990.
26. _, "Least constraint: A framework for the control of complex mechanical systems," in Proc. American Control Conf., 1991, pp. 615-621.
27. J. Funda, R. Taylor, K. Gruben, and D. LaRose, "Optimal motion control for teleoperated surgical robots," in Proc. SPIE Symp. Optical Tools for Manufacturing and Advanced Automation, Boston, MA, Sept. 1993.
28. W. Wannasuphoprasit, R. B. Gillespie, J. E. Colgate, and M. Peshkin, "Cobot control," in Proc. IEEE Int. Conf. Robotics and Automation, 1997, pp. 3571-3576.
29. K. Brenan, S. Campbell, and L. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. New York: North-Holland, 1989.
30. E. Hairer and G. Warmer, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. New York: Springer-Verlag, 1991.
31. R. J. Spiteri, "Solution methods for differential systems subject to algebraic inequality constraints," Ph.D. dissertation, Univ. British Columbia, Inst. Appl. Mathematics and Dept. Mathematics, Sept. 1997.
32. J. P. Aubin, Viability Theory. Berlin, Germany: Birkhauser, 1991.
33. J. P. Aubin and A. Cellina, Differential Inclusions. New York: Springer-Verlag, 1984.
34. F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and P. R. Wolenski, "Qualitative properties of trajectories of control systems: A survey," J. Dynamical Contr. Syst., vol. 1, no. 1, pp. 1-48, 1995.
35. A. Subbotin, Generalized Solutions of First-Order PDES. Boston, MA: Birkhauser, 1995.
36. R. Isaacs, Differential Games A Mathematical Theory With Applications to Warfare and Pursuit, Control and Optimization. New York: Wiley, 1965.
37. R. Fletcher, Practical Methods of Optimization. New York: Wiley, 1980, vol. I.
38. R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC Press, 1994.
39. J. F. Canny and M. C. Lin, "An opportunistic global path planner," Algorithmica, vol. 10, no. 2-4, pp. 102-120, 1993.
40. U. M. Ascher, S. J. Ruuth, and R. J. Spiteri, "Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations," Appl. Numerical Math., vol. 25, no. 2-3, pp. 151-167, 1997.
41. R. Fletcher, Practical Methods of Optimization. New York: Wiley, 1981, vol. II.
42. _, "An ideal penalty function for constrained optimization," J. Inst. Math. Applicat., vol. 15, pp. 319-342, 1975.
43. M. R. Hestenes, "Multiplier and gradient methods," J. Opt. Theory. Applicat., vol. 4, pp. 303-320, 1969.
44. J. Lewin, Differential Games Theory and Methods for Solving Game Problems with Singular Surfaces. New York: Springer-Verlag, 1994.
45. H. P. Huang and N. H. McClamroch, "Time-optimal control for a robotic contour following problem," IEEE Trans. Robot. Automat., vol. 4, pp. 140-149, Apr. 1988.
46. A. W. Divelbiss and J. Wen, Nonholonomic Path Planning with Inequality Constraints. Piscataway, NJ: IEEE, 1994, pp. 52-57.
47. R. Barman, S. Kingdon, J. J. Little, A. K. Mackworth, D. K. Pai, M. Sahota, H. Wilkinson, and Y. Zhang, "Dynamo: Real-time experiments with multiple mobile robots," in Proc. IEEE Intelligent Vehicles Conf., Tokyo, Japan, July 1993, pp. 261-266.
48. M. K. Sahota, "Real-time intelligent behavior in dynamic environments: Soccer-playing robots," Master's thesis, Dept. Comput. Sci., Univ. British Columbia, Vancouver, BC, Canada, 1991.
49. V. Schulz, "Reduced SQP methods for large-scale optimal control problems in DAE with application to path planning problems for satellite mounted robots," Ph.D. dissertation, Interdisziplindres Zentrum für Wissenschaftliches Rechnen, Univ. Heidelberg, 1996.
50. L. Ingber, "Simulated annealing: Practice versus theory," Math. Comput. Modeling, vol. 18, no. 11, pp. 29-57, 1993.
51. C. I. Connolly, J. B. Burns, and R. Weiss," Path planning using Laplace's equation," in Proc. 1990 IEEE Int. Conf. Robautics and Automation, May 1990, pp. 2102-2106.