Hostname: page-component-5c6d5d7d68-sv6ng Total loading time: 0 Render date: 2024-08-16T05:53:02.008Z Has data issue: false hasContentIssue false
  • English
  • Français

A discrete path/trajectory planner for robotic arms

Published online by Cambridge University Press:  17 February 2009

H. H. Tan  and
R. B. Potts
H. H. Tan
Affiliation:
Applied Mathematics Department, University of Adelaide, S.A.5000, Australia.
R. B. Potts
Affiliation:
Applied Mathematics Department, University of Adelaide, S.A.5000, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An interesting and challenging problem in robotics is the off-line determination of the minimum cost path along which an end effector should move from a given initial to a given final state. This paper presents a discrete minimum cost path/trajectory planner which provides a general solution and allows for a range of constraints such as bounds on joint coordinates, joint velocities, joint torques and joint jerks. To demonstrate the practicability and feasibility of the planner, simulation results are presented for the Stanford manipulator using three and then the full six of its degrees of freedom. Simulation runs with two-link planar arms are also presented to enable a comparison with previously published results.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 1 , July 1989 , pp. 1 - 28
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Ailon, A. and Langholz, G., “On the existence of time-optimal control of mechanical manipulators”, J. Opt. Theory Appls. 46 (1985) 1–21.CrossRefGoogle Scholar
[2]Bobrow, J. E., Dubowsky, S. and Gibson, J. S., “Time-optimal control of robotic manipulators along specified paths”, Int. J. Robotics Res. 4 (1985) 3–17.Google Scholar
[3]Brady, M. et al. (eds), Robot motion: planning and control (MIT Press, Cambridge MA, 1982).Google Scholar
[4]Brown, M. L., “Optimal robot planning via state space networks”, M. S. Thesis, Princeton University, 1984.Google Scholar
[5]Dubowsky, S., Norris, M. A. and Shiller, Z., “Time optimal trajectory planning for robotic manipulators with obstacle avoidance: a CAD approach”, Proc. IEEE Conf. Robotics Autom. (1986) 1906–1912.Google Scholar
[6]Flash, T. and Potts, R. B., “Discrete trajectory planning”, Int. J. Robotics Res. 7 (1988) 48–57.CrossRefGoogle Scholar
[7]Geering, H. P. et al. , “Time-optimal motions of robots in assembly tasks”, IEEE Trans. Autom. Contr. 31 (1986) 512–518.CrossRefGoogle Scholar
[8]Gilbert, E. G. and Johnson, D. W., “Distance functions and their applications to robot path planning in the presence of obstacles”, IEEE J. Robotics Autom. 1 (1985) 21–30.Google Scholar
[9]Gill, P. E. et al. , “User's Guide for NPSOL (Version 4.0)”, Stanford University, Department of Operations Research, Report SOL-86–2 (1986).Google Scholar
[10]Hearn, A. C., REDUCE User's Manual, Version 3 (Rand Corp, California, 1984).Google Scholar
[11]Hollerbach, J. M., “Dynamic scaling of manipulator trajectories”, ASME J. Dyn. Meas., Contr. 106 (1984) 102–106.CrossRefGoogle Scholar
[12]Kahn, M. E. and Roth, B., “The near-minimum-time control of open-loop articulated kine-matic chain”, J. Dyn. Sys., Meas., Contr. 93 (1971) 164–172.CrossRefGoogle Scholar
[13]Kim, B. K. and Shin, K. G., “Suboptimal control of industrial manipulators with a weighted time-fuel criterion”, IEEE Trans. Autom. Contr. 30 (1985) 1–10.Google Scholar
[14]Lynch, P. M., “Minimum-time, sequential axis operation of a cylindrical, two-axis manipulator”, Proc. Joint Autom. Contr. Conf. 1 (1981) paper WP-2A.Google Scholar
[15]Murtagh, B. A. and Saunders, M. A., “MINOS 5.1 User's Guide”, Stanford University, Department of Operations Research, Report SOL 83–20R (1987).Google Scholar
[16]Neuman, C. P. and Tourassis, V. D., “Discrete dynamic robot models”, IEEE Trans. Sys. Man Cyber. 15 (1985) 193–204.Google Scholar
[17]Niv, M. and Auslander, D. M., “Optimal control of a robot with obstacles”, Proc. Amer. Contr. Conf. (1984) 280–287.Google Scholar
[18]Paul, R. P., Robot manipulator—mathematics, programming and control (MIT Press, Cambridge, 1981).Google Scholar
[19]Potts, R. B., “Discrete Lagrange equations”, Bull. Austral. Math. Soc. 3 (1988) 227–233.Google Scholar
[20]Rajan, V. T., “Minimum time trajectory planning”, Proc. IEEE Conf. Robotics Autom. (1985) 759–764.Google Scholar
[21]Red, W. E. and Truong-Cao, H, “The configuration space approach to robot path planning”, Proc. Amer. Contr. Conf. (1984) 288–295.Google Scholar
[22]Sahar, G. and Hollerbach, J. M., “Planning of minimum-time trajectories for robot arms”, Int. J. Robotics Res. 5 (1986) 90–100.CrossRefGoogle Scholar
[23]Scheinman, V. and Roth, B., “On the optimal selection and placement of manipulators”, Proc. RoManSy. 5th CISM-IFToMM Symp. (1984) 39–46.Google Scholar
[24]Shin, K. G. and McKay, N. D., “Minimum-time control of robotic manipulators with geometric path constraints”, IEEE Trans. Autom. Contr. 30 (1985) 531–541.Google Scholar
[25]Shin, K. G. and McKay, N. D., “Selection of near-minimum time geometric paths for robotic manipulators”, Proc. Amer. Contr. Conf. (1985) 346–355.Google Scholar
[26]Snyder, W. E. and Gruver, W. A., “Microprocessor implementation of optimal control for a robotic manipulator system”, Proc. IEEE Conf. Dec. Contr. (1979) 839–841.Google Scholar
[27]Sontag, E. D. and Sussman, H. J., “Remarks on the time-optimal control of two link manipulators”, Proc. IEEE Conf. Dec. Contr. (1985) 1643–1652.Google Scholar
[28]Sontag, E. D. and Sussman, H. J., “Time-optimal control of manipulator”, Proc. IEEE Conf. Robotics Autom. (1986) 1692–1697.Google Scholar
[29]Tan, H. H. and Potts, R. B., “Minimum time trajectory planner for the discrete dynamic robot model with dynamic constraints”, IEEE J. Robotics Autom. 4 (1988) 174–185.CrossRefGoogle Scholar
[30]Tan, H. H. and Potts, R. B., “A discrete trajectory planner for robotic arms with six degrees of freedom”, University of Adelaide, Dept. of Applied Maths. Research Report UAAM-87–5 (1987).Google Scholar
[31]Tan, H. H. and Pots, R. B., “Minimum time robot motions”, University of Adelaide, Dept. of Applied Maths. Research Report UAAM-87–2 (1987).Google Scholar
[32]Tan, H. H. and Potts, R. B., “A discrete calculus of variations algorithm”, Bull. Austral. Math. Soc. 38 (1988) 365–371.Google Scholar
[33]Turner, T. L. and Gruver, W. A., “A viable suboptimal controller for robotic manipulators”, Proc. IEEE Conf. Dec. Contr. (1980) 83–87.Google Scholar
[34]Wen, J. and Desrochers, A., “Existence of the time optimal control for robotic manipulators”, Proc. Amer. Contr. Conf. (1986) 109–113.Google Scholar