Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-31T06:39:28.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Collision-free workspace of parallel mechanisms based on an interval analysis approach

Published online by Cambridge University Press:  22 August 2016

MohammadHadi FarzanehKaloorazi ,
Mehdi Tale Masouleh  and
Stéphane Caro
MohammadHadi FarzanehKaloorazi*
Affiliation:
CoRo, École de Technologie Supérieure, Montréal, Quebec, Canada
Mehdi Tale Masouleh
Affiliation:
Human-Robot Interaction Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran. E-mail: m.t.masouleh@ut.ac.ir
Stéphane Caro
Affiliation:
CNRS-IRCCyN, UMR 6597, 1 rue de la Noë, 44321 Nantes, France. E-mail: stephane.caro@irccyn.ec-nantes.fr
*
*Corresponding author. E-mail: hamidfarzane88@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

This paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

Keywords

Parallel mechanismCollision-free workspaceMechanical interferenceInterval analysis

Information

Type
Articles
Information
Robotica , Volume 35 , Issue 8 , August 2017 , pp. 1747 - 1760
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Merlet, J. P., Parallel Robots. (Springer, 2006).Google Scholar
2. Gosselin, C. M. and Jean, M., “Determination of the workspace of planar parallel manipulators with joint limits,” Robot. Auton. Syst. 17 (3), 129–138 (1996).Google Scholar
3. Bohigas, O., Henderson, M. E., Ros, L., Manubens, M. and Porta, J. M., “Planning singularity-free paths on closed-chain manipulators,” IEEE Trans. Robot. 29 (4), 888–898, (2013).CrossRefGoogle Scholar
4. Zi, B., Lin, J. and Qian, S., “Localization, obstacle avoidance planning and control of a cooperative cable parallel robot for multiple mobile cranes,” Robot. Comput.-Integr. Manuf. 34, 105–123, (2015).Google Scholar
5. Laliberte, T. and Gosselin, C. M., “Efficient Algorithms for the Trajectory Planning of Redundant Manipulators with Obstacle Avoidance,” 1994 IEEE International Conference on Robotics and Automation4, (1994), pp. 2044–2049.Google Scholar
6. Brock, O. and Khatib, O., “Elastic strips: A framework for motion generation in human environments,” Int. J. Robot. Res. 21 (12), 1031–1052 (2002).Google Scholar
7. Khatib, O., Yokoi, K., Brock, O., Chang, K. and Casal, A., “Robots in human environments: Basic autonomous capabilities,” Int. J. Robot. Res. 18 (7), 684–696 (1999).Google Scholar
8. Komainda, A. and Hiller, M., “Control of Heavy Load Manipulators in Varying Environments,” Proceedings of IAARC/IFAC/IEEE International Symposium on Automation and Robotics in Construction, Madrid, Spain (1999) pp. 22–24.Google Scholar
9. Jiménez, P., Thomas, F. and Torras, C., “3d collision detection: A survey,” Comput. Graph. 25 (2), 269–285 (2001).Google Scholar
10. Wenger, P. and Chedmail, P., “On the connectivity of manipulator free workspace,” J. Robot. Syst. 8 (6), 767–799 (1991).Google Scholar
11. Caro, S., Chablat, D., Goldsztejn, A., Ishii, D. and Jermann, C., “A branch and prune algorithm for the computation of generalized aspects of parallel robots,” Artif. Intell. 211, 34–50, (2014).CrossRefGoogle Scholar
12. FarzanehKaloorazi, M., Masouleh, M. T. and Caro, S., “Collision-Free Workspace of 3-rpr Planar Parallel Mechanism Via Interval Analysis,” In: Advances in Robot Kinematics. (Springer, 2014) pp. 327–334.Google Scholar
13. Bihari, B., Kumar, D., Jha, C., Rathore, V. S. and Dash, A. K., “A geometric approach for the workspace analysis of two symmetric planar parallel manipulators,” Robotica, 34 (4), 738–763, (2016).CrossRefGoogle Scholar
14. Moore, R. and Bierbaum, F., Methods and Applications of Interval Analysis. Vol. 2 (Society for Industrial Mathematics, 1979).Google Scholar
15. Jaulin, L., “Set-membership localization with probabilistic errors,” Robot. Auton. Syst. 59 (6), 489–495 (2011).Google Scholar
16. Kaloorazi, M. H. F., Masouleh, M. T., and Caro, S., “Determining the maximal singularity-free circle or sphere of parallel mechanisms using interval analysis,” Robotica 34 (1), 135–149, (2016).Google Scholar
17. Merlet, J., “Interval analysis and robotics,” Robot. Res., 147–156, (2010).Google Scholar
18. Merlet, J. P., “Solving the forward kinematics of a gough-type parallel manipulator with interval analysis,” Int. J. Robot. Res. 23 (3), 221–235, (2004).Google Scholar
19. Kaloorazi, M., Masouleh, M. T., and Caro, S., “Interval-Analysis-Based Determination of the Singularity-Free Workspace of Gough-Stewart Parallel Robots,” Electrical Engineering (ICEE), 2013 21st Iranian Conference on IEEE, (2013) pp. 1–6.Google Scholar
20. Kaloorazi, M. H. Farzaneh, Masouleh, M. Tale and Caro, S., “On the Maximal Singularity-free Workspace of Parallel Mechanisms via Interval Analysis,” Proceedings of the 2013 MultiBody Dynamics MBD2013, Zagreb, Croatia, (2013).Google Scholar
21. Merlet, J.-P., “Determination of 6d workspaces of gough-type parallel manipulator and comparison between different geometries,” Int. J. Robot. Res. 18 (9), 902–916 (1999).Google Scholar
22. Kaloorazi, M.-H. F., Masouleh, M. T. and Caro, S., “Determination of the maximal singularity-free workspace of 3-dof parallel mechanisms with a constructive geometric approach,” Mech. Mach. Theory 84, pp. 25–36 (2015).Google Scholar
23. Pott, A., Franitza, D. and Hiller, M., “Orientation Workspace Verification for Parallel Kinematic Machines with Constant Leg Length,” Proceedings of the Mechatronics and Robotics, Aachen, Germany (Sep. 2004) pp. 13–15.Google Scholar
24. Merlet, J.-P., “An Improved Design Algorithm Based on Interval Analysis for Spatial Parallel Manipulator with Specified Workspace,” IEEE International Conference on Robotics and Automation, 2001. Proceedings 2001 ICRA., vol. 2. IEEE, (2001), pp. 1289–1294.Google Scholar
25. Otis, M. J., Perreault, S., Nguyen-Dang, T.-L., Lambert, P., Gouttefarde, M., Laurendeau, D. and Gosselin, C., “Determination and management of cable interferences between two 6-dof foot platforms in a cable-driven locomotion interface,” IEEE Trans. Syst. Man Cybern. A 39 (3), 528–544 (2009).Google Scholar
26. Gouttefarde, M., Daney, D. and Merlet, J., “Interval-analysis-based determination of the wrench-feasible workspace of parallel cable-driven robots,” IEEE Trans. Robot. 27 (1), 1–13 (2011).Google Scholar
27. Dwyer, P., “Computation with approximate numbers,” pp. 11–34 (1951).Google Scholar
28. Sungana, T., “Theory of Interval Algebra and Application to Numerical Analysis,” pp. 29–46, (1958).Google Scholar
29. Warmus, M., “Calculus of approximations,” Bull. Acad. Pol. Sci. 4 (5), 253–257 (1956).Google Scholar
30. Wilkinson, J., “Turings work at the national physical laboratory and the construction of pilot ace, deuce, and ace,” Metropolis et al.[MHR80], pp. 101–114, (1980).Google Scholar
31. Moore, R. E., Interval Analysis. Series in Automatic Computation, (Prentice-Hall, Englewood Cliff, NJ, 1966).Google Scholar
32. Hansen, E. and Walster, G., Global Optimization Using Interval Analysis: Revised and Expanded (CRC, 2003, vol. 264).Google Scholar
33. Hao, F. and Merlet, J., “Multi-criteria optimal design of parallel manipulators based on interval analysis,” Mech. Mach. Theory 40 (2), 157–171 (2005).Google Scholar
34. Chablat, D., Wenger, P., Majou, F. and Merlet, J., “An interval analysis based study for the design and the comparison of three-degrees-of-freedom parallel kinematic machines,” Int. J. Robot. Res. 23 (6), 615–624 (2004).Google Scholar
35. Rao, R., Asaithambi, A. and Agrawal, S., “Inverse kinematic solution of robot manipulators using interval analysis,” J. Mech. Des. 120 (1), 147–150 (1998).Google Scholar
36. Fusiello, A., Benedetti, A., Farenzena, M. and Busti, A., “Globally convergent autocalibration using interval analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 26 (12), 1633–1638 (2004).Google Scholar
37. Wabinski, W. and Martens, H.-J. von, “Time Interval Analysis of Interferometer Signals for Measuring Amplitude and Phase of Vibrations,” Second International Conference on Vibration Measurements by Laser Techniques: Advances and Applications. International Society for Optics and Photonics, 1996, pp. 166–177.Google Scholar
38. Oetomo, D., Daney, D., Shirinzadeh, B., and Merlet, J., “Certified Workspace Analysis of 3RRR Planar Parallel Flexure Mechanism,” IEEE International Conference on Robotics and Automation (ICRA). IEEE, (2008) pp. 3838–3843.Google Scholar
39. Van Hentenryck, P., McAllester, D. and Kapur, D., “Solving polynomial systems using a branch and prune approach,” SIAM J. Numer. Anal. 34 (2), 797–827 (1997).Google Scholar