Collision-Free Path Planning of Tensegrity Structures
Publication: Journal of Structural Engineering
Volume 140, Issue 4
Abstract
Path planning is a crucial step in shape control of tensegrity structures. A mathematical model for the path planning problem of tensegrities is proposed. Both external collision and internal collision are considered. A procedure combining trajectory tracking with collision checking is established and used as a local planner. An algorithm based on rapidly-exploring random trees (RRT), called RRT-Connect, is adopted as the global planner for the problem. The RRT-Connect algorithm integrated with the local planner is used to search collision-free paths for shape control of tensegrity structures. Typical examples are carried out. The proposed scheme is verified by the results of the examples.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51008271 and 51025828) and the Zhejiang Provincial Natural Science Foundation (Grant No. Y13E080003).
References
Aldrich, J. B., Skelton, R. E., and Kreutz-Delgado, K. (2003). “Control synthesis for a class of light and agile robotic tensegrity structures.” Proc., 2003 American Control Conf., IEEE, Piscataway, NJ, 5245–5251.
Barraquand, J., and Latombe, J. C. (1991). “Robot motion planning: A distributed representation approach.” Int. J. Rob. Res., 10(6), 628–649.
Bruce, J., and Veloso, M. (2002). “Real-time randomized path planning for robot navigation.” Proc., 2002 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, IEEE, Piscataway, NJ, 2383–2388.
Calladine, C. R. (1978). “Buckminster Fuller’s ‘tensegrity’ structures and Clerk Maxwell’s rules for the construction of stiff frames.” Int. J. Solids Struct., 14(2), 161–172.
Calladine, C. R. (1982). “Modal stiffness of a pretensioned cable net.” Int. J. Solids Struct., 18(10), 829–846.
Calladine, C. R., and Pellegrino, S. (1991). “First-order infinitesimal mechanisms.” Int. J. Solids Struct., 27(4), 505–515.
Cameron, S. A. (1985). “A study of the clash detection problem in robotics.” Proc., IEEE Int. Conf. on Robotics and Automation, Saint Louis, 1056–1063.
Cefalo, M., and Tur, J. M. M. (2010). “Real-time self-collision detection algorithms for tensegrity systems.” Int. J. Solids Struct., 47(13), 1711–1722.
Connelly, R. (1980). “The rigidity of certain cabled networks and the second order rigidity of arbitrarily triangulated convex surfaces.” Adv. Math., 37(3), 272–299.
Connelly, R. (1982). “Rigidity and energy.” Invent. Math., 66(1), 11–33.
Connelly, R., and Whiteley, W. (1996). “Second-order rigidity and prestress stability for tensegrity frameworks.” SIAM J. Discrete Math., 9(3), 453–491.
Culley, R. K., and Kempf, K. G. (1986). “A collision detection algorithm based on velocity and distance bounds.” Proc., IEEE Int. Conf. on Robotics and Automation, IEEE, Piscataway, NJ, 1064–1069.
Domer, B., and Smith, I. F. C. (2005). “An active structure that learns.” J. Comput. Civ. Eng., 16–24.
Fest, E., Shea, K., Domer, B., and Smith, I. F. C. (2003). “Adjustable tensegrity structures.” J. Struct. Eng., 515–526.
Fuller, R. B., and Applewhite, E. J. (1975). Synergetics: Explorations in the geometry of thinking, Macmillan, New York.
Furuya, H. (1992). “Concept of deployable tensegrity structures in space application.” Int. J. Space Struct., 7(2), 143–151.
Hanaor, A. (1993). “Double-layer tensegrity grids as deployable structures.” Int. J. Space Struct., 8(1–2), 135–145.
Hernández, S., and Tur, J. M. (2008). “Tensegrity frameworks: Static analysis review.” J. Mech. Mach. Theory, 43(7), 859–881.
Jiménez, P., Thomas, F., and Torras, C. (2001). “3D collision detection: A survey.” Comput. Graph., 25(2), 269–285.
Juan, S. H., and Tur, J. M. M. (2008). “A method to generate stable, collision free configurations for tensegrity based robots.” IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Nice, France, IEEE, Piscataway, NJ, 3769–3774.
Kalisiak, M., and Panne, M. (2006). “RRT-blossom: RRT with a local flood-fill behavior.” Proc., IEEE Int. Conf. on Robotics and Automation, IEEE, Piscataway, NJ, 1237–1242.
Kanchanasaratool, N., and Williamson, D. (2002). “Modelling and control of class NSP tensegrity structures.” Int. J. Control, 75(2), 123–139.
Karaman, S., Walter, M. R., Perez, A., Frazzoli, E., and Teller, S. (2011). “Anytime motion planning using the RRT.” 2011 IEEE Int. Conf. on Robotics and Automation, IEEE, Piscataway, NJ, 1478–1483.
Kuffner, J. J., and LaValle, S. M. (2000). “RRT-connect: An efficient approach to single-query path planning.” Proc., IEEE Int. Conf. on Robotics and Automation, IEEE, Piscataway, NJ, 995–100.
Kuwata, Y., Fiore, G. A., Teo, J., Frazzoli, E., and How, J. P. (2008). “Motion planning for urban driving using RRT.” 2008 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, IEEE, Piscataway, NJ, 1681–1686.
Kuznetsov, E. N. (1984). “Statics and geometry of underconstrained axisymmetric 3-nets.” J. Appl. Mech., 51(4), 827–830.
Kwan, A. S. K., and Pellegrino, S. (1993). “Design and performance of the octahedral deploayable space antenna (Odesa).” Int. J. Space Struct., 9(3), 163–173.
LaValle, S. M. (1998). “Rapidly-exploring random trees: A new tool for path planning.”, Computer Science Dept., Iowa State Univ.
Marks, R., and Fuller, R. B. (1973). The Dymaxion world of Buckminster Fuller, Garden City, New York.
MATLAB. (2007). “MATLAB R2007b.” MathWorks, Natick, MA.
Melchior, N. A., and Simmons, R. (2007). “Particle RRT for path planning with uncertainty.” IEEE Int. Conf. on Robotics and Automation, IEEE, Piscataway, NJ, 1617–1624.
Motro, R. (2003). Tensegrity: Structural systems for the future, Kogan Page Science, London.
Murakami, H. (2001a). “Static and dynamic analysis of tensegrity structures. Part I: Nonlinear equation for motion.” Int. J. Solids Struct., 38(20), 3599–3613.
Murakami, H. (2001b). “Static and dynamic analysis of tensegrity structures. Part II: Quasi-static analysis.” Int. J. Solids Struct., 38(20), 3615–3629.
Oppenheim, I. J., and Williams, W. O. (2001b). “Vibration of an elastic tensegrity structures.” Eur. J. Mech. A Solid, 20(6), 1023–1031.
Oppenheim, I. J., and Williams, W. O. (2001a). “Vibration and damping in three-bar tensegrity structure.” J. Aerosp. Eng., 85–91.
Paul, C., Lipson, H., and Valero-Cuevas, F. J. (2006). “Design and control of tensegrity robots for locomotion.” IEEE Trans. Rob., 22(5), 944–957.
Pellegrino, S., and Calladine, C. R. (1986). “Matrix analysis of statically and kinematically indeterminate frameworks.” Int. J. Solids Struct., 22(4), 409–428.
Pepy, R., and Lambert, A. (2006). “Safe path planning in an uncertain-configuration space using RRT.” Proc., 2006 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, IEEE, Piscataway, NJ, 5376–5381.
Pinaud, J. P., Solari, S., and Skelton, R. E. (2004). “Deployment of a class 2 tensegrity boom.” SPIE’s 11th Annual Int. Symp. on Smart Structures and Materials, SPIE, WA.
Pugh, A. (1976). An introduction to tensegrity, Univ. of California Press, Berkeley, CA.
Rhode-Barbarigos, L., Schulin, C., Ali, N. B. H., Motro, R., and Smith, I. F. C. (2012). “Mechanism based approach for the deployment of a tensegrity ring-module.” J. Struct. Eng., 539–548.
Rodriguez, S., Tang, X., Lien, J. M., and Amato, N. M. (2006). “An obstacle-based rapidly-exploring random tree.” Proc., IEEE Int. Conf. on Robotics and Automation, IEEE, Piscataway, NJ, 895–900.
Roth, B., and Whiteley, W. (1981). “Tensegrity frameworks.” Trans. Am. Math. Soc., 265(2), 419–446.
Rovira, A. G., and Tur, J. M. M. (2009). “Control and simulation of a tensegrity-based mobile robot.” Rob. Autom. Syst., 57(5), 526–535.
Shea, K., Fest, E., and Smith, I. F. C. (2002). “Developing intelligent tensegrity structures with stochastic search.” Adv. Eng. Inf., 16(1), 21–40.
Skelton, R. E., Pinaud, J. P., and Mingori, D. L. (2001). “Dynamics of the shell class of tensegrity structures.” J. Franklin Inst., 338(2–3), 255–320.
Smith, I. F. C. (2003). “From active to intelligent stuctures.” Seventh Int. Conf. on the Application of Artificial Intelligence to Civil and Structural Engineering, Civil-Comp, Stirling, Scotland.
Snelson, K. (1973). Tensegrity masts, Shelter, Bolinas, CA.
Sultan, C. (2009). “Tensegrity: Sixty years of art, science and engineering.” Adv. Appl. Mech., 43, 70–145.
Sultan, C., Corless, M., and Skelton, R. E. (2002a). “Linear dynamics of tensegrity structures.” Eng. Struct., 24(6), 671–685.
Sultan, C., Corless, M., and Skelton, R. E. (2002b). “Symmetrical reconfiguration of tensegrity structures.” Int. J. Solids Struct., 39(8), 2215–2234.
Sultan, C., and Skelton, R. E. (2003). “Deployment of tensegrity structures.” Int. J. Solids Struct., 40(18), 4637–4657.
Tibert, A. G. (2002). “Deployment tensegrity structure for space applications.” Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden.
Tibert, A. G., and Pellegrino, S. (2003). “Review of form-finding methods for tensegrity structures.” Int. J. Space Struct., 18(4), 209–223.
Tur, J. M. M., and Hernández, S. (2009). “Tensegrity frameworks: Dyanmic analysis review and open problems.” Mech. Mach. Theory, 44(1), 1–18.
Whiteley, W. (1984). “Infinitesimal motions of a bipartite framework.” Pac. J. Math., 110(1), 233–255.
Xu, J., Duindam, V., Alterovitz, R., and Goldberg, K. (2008). “Motion planning for steerable needles in 3D environments with obstacles using rapidly-exploring random trees and backchaining.” IEEE Int. Conf. on Automation Science and Engineering, IEEE, Piscataway, NJ41–46.
Xu, X., and Luo, Y. (2008). “Multiobjective shape control of prestressed structures with genetic algorithms.” Proc. Inst. Mech. Eng. G J. Aerosp., 222(8), 1139–1147.
Xu, X., and Luo, Y. (2009). “Nonlinear displacement control of prestressed cable structures.” Proc. Inst. Mech. Eng. G J. Aerosp., 223(8), 1001–1007.
Xu, X., and Luo, Y. (2010). “Form-finding of nonregular tensegrities using a genetic algorithm.” Mech. Res. Commun., 37(1), 85–91.
Xu, X., and Luo, Y. (2011). “Multistable tensegrity structures.” J. Struct. Eng., 117–123.
Xu, X., and Luo, Y. (2013). “Collision free shape control of a plane tensegrity structure using an incremental dynamic relaxation method and a trial-and-error process.” Proc. Inst. Mech. Eng. G J. Aerosp., 227(2), 263–269.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 140 • Issue 4 • April 2014
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jun 1, 2012
Accepted: Jun 19, 2013
Published online: Jun 21, 2013
Published in print: Apr 1, 2014
Discussion open until: Apr 26, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.