Six-strut tensegrity robot is a new mobile robot whose outer surface is an icosahedron containing 8 regular triangles and 12 isosceles triangles, and the robot performs rolling locomotion along the edges of the triangle. On the slope, it has lots of poses depending on the slope’s angles and positions of robot, which is difficult to control the rolling directions in the real world. This paper proposed a new method based on finite element method and a genetic algorithm to predict the rolling directions of the robot. The balanced forces equations of robot nodes are established using finite element method, which is a constrained optimization problem. The equations are transformed into an unconstrained optimization problem by the thinking of sequential unconstrained minimization technique. Finally, the unconstrained optimization problem is calculated by genetic algorithm, and the relations between the actuators and the rolling directions are obtained through the dot product of gravitational torque and the edge vector of bottom triangle. This method is verified by simulation and experiment results.
Fuller RB. Tensile integrity structures – a new method. Patent 3.063.521, USA, 1959.
3.
SadaoS. Fuller on tensegrity. Int J Space Struct1996; 11: 37–42.
4.
PughA. An introduction to tensegrity, Berkeley, CA: University of California Press, 1976.
5.
WanZSCaoZGSunY, et al.Pre-stressing method and structural behaviour of a Tensairity dome with multiple inflated cushions. Thin Wall Struct2018; 132: 585–595.
6.
AtigMEl OuniMHBen KahlaN. Dynamic stability analysis of tensegrity systems. Eur J Environ Civil Eng2019; 23: 675–692.
7.
Plescan C, Contiu M and Dosa A. A study of a tensegrity structure for a footbridge. In: 3rd China-Romania science and technology seminar (eds IV Abrudan, T Shi, S Lache, et al.), Brasov, Romania, 19 September 2018.
8.
BaumMBarosDJanataV. The new Comenius Bridge in Jaromer/Czech Republic. Stahlbau2018; 87: 1093–1100.
9.
Krishnan S and Li BY. Design of lightweight deployable antennas using the tensegrity principle. In: 16th Biennial International Conference on Engineering, Science, Construction, and Operations in Challenging Environments, Cleveland, Ohio, 9–12 April 2018. American Society of Civil Engineers. https://ascelibrary.org/doi/abs/10.1061/9780784481899.084.
10.
GangaPLMichelettiAPodio-GuidugliP, et al.Tensegrity rings for deployable space antennas: concept, design, analysis, and prototype testing. In: AFredianiBMohammadiOPironneau, et al.(eds). Variational analysis and aerospace engineering: mathematical challenges for the aerospace of the future, Berlin: Springer International Publishing, 2016, pp. 269–304.
11.
EkebergOPearsonK. Computer simulation of stepping in the hind legs of the cat: an examination of mechanisms regulating the stance-to-swing transition. J Neurophysiol2005; 94: 4256–4268.
12.
CaiJYangRWangX, et al.Effect of initial imperfections of struts on the mechanical behavior of tensegrity structures. Compos Struct2019; 207: 871–876.
13.
FraldiMPalumboSCarotenutoAR, et al.Buckling soft tensegrities: Fickle elasticity and configurational switching in living cells. J Mech Phys Solids2019; 124: 299–324.
14.
Paul C, Roberts JW, Lipson H, et al. Gait production in a tensegrity based robot. In: IEEE 12th International Conference on Advanced Robotics, Seattle, WA, USA, 18–20 July 2005, pp.216–222. IEEE. https://ieeexplore.ieee.org/document/1507415.
15.
PaulCValero-CuevasFJLipsonH. Design and control of tensegrity robots for locomotion. IEEE Transac Robot2006; 22: 944–957.
16.
Koizumi Y, Shibata M, Hirai S, et al. Rolling tensegrity driven by pneumatic soft actuators. In: IEEE international conference on robotics and automation, Saint Paul, MN, USA, 14–18 May 2012, pp.1988–1993. IEEE.
17.
IscenACaluwaertsKBruceJ, et al.Learning tensegrity locomotion using open-loop control signals and coevolutionary algorithms. Artif Life2015; 21: 119–140.
18.
Sabelhaus AP, Bruce J, Caluwaerts K, et al. System design and locomotion of SUPERball, an untethered tensegrity robot. In: IEEE international conference on robotics and automation, Seattle, WA, USA, 26–30 May 2015, pp.2867–2873. IEEE.
19.
Vespignani M, Friesen JM, SunSpiral V, et al. Design of SUPERball v2, a compliant tensegrity robot for absorbing large impacts. In: IEEE/RSJ international conference on intelligent robots and systems (eds AA Maciejewski, A Okamura, A Bicchi, et al.), Madrid, Spain, 1–5 October 2018, pp.2865–2871. IEEE.
20.
Skelton RE and Sultan C. Controllable tensegrity, a new class of smart structures. In: Proceedings SPIE 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, San Diego, CA, United States,13 June 1997, pp.166–177.
21.
SkeltonRESkeltonRE. Dynamics and control of tensegrity systems. Solid Mech Appl2005; 130: 309–318.
22.
Oliveira MC and Skelton RE. Tensegrity Systems. New York: Springer-Verlag US, 2009, pp.179–198.
23.
Schorr P, Bohm V, Zentner L, et al. An approach to the estimation of the actuation parameters for mobile tensegrity robots with tilting movement sequences. In: 2018 International Conference on Reconfigurable Mechanisms and Robots (ReMAR), 2018, pp.1–8. Delft, Netherlands: IEEE.
24.
DuWMaSLiB, et al.Force analytic method for rolling gaits of tensegrity robots. IEEE/ASME Transac Mechatron2016; 21: 2249–2259.
25.
Vespignani M, Ercolani C, Friesen JM, et al. Steerable locomotion controller for six-strut icosahedral tensegrity robots. In: IEEE/RSJ international conference on intelligent robots and systems (eds AA Maciejewski, A Okamura, A Bicchi, et al.), Madrid, Spain, 1–5 October 2018, pp. 2886–2892. IEEE.
26.
Chen L-H, Cera B, Zhu EL, et al. Inclined surface locomotion strategies for spherical tensegrity robots. In: IEEE/RSJ international conference on intelligent robots and systems (eds A Bicchi and A Okamura), Vancouver, BC, Canada, 24–28 September 2017, pp. 4976–4981. IEEE.
27.
ChenL-HKimKTangE, et al.Soft spherical tensegrity robot design using rod-centered actuation and control. J Mech Robot2017; 9: 1–9–1–9.
28.
WangZLiKHeQ, et al.A light-powered ultralight tensegrity robot with high deformability and load capacity. Adv Mater2019; 31: e1806849–e1806849.
Zhu S, Surovik D, Bekris K, et al. Efficient model identification for tensegrity locomotion. In: IEEE/RSJ international conference on intelligent robots and systems (eds AA Maciejewski, A Okamura, A Bicchi, et al.), Madrid, Spain, 1–5 October 2018, pp.2985–2990. IEEE.
31.
Cera B and Agogino AM. Multi-cable rolling locomotion with spherical tensegrities using model predictive control and deep learning. In: IEEE/RSJ international conference on intelligent robots and systems (eds AA Maciejewski, A Okamura, A Bicchi, et al.), Madrid, Spain, 1–5 October 2018, pp.6595–6600. IEEE.
32.
Luo J, Edmunds R, Rice F, et al. Tensegrity robot locomotion under limited sensory inputs via deep reinforcement learning. In: IEEE international conference on robotics and automation, Brisbane, QLD, Australia, 21–25 May 2018, pp. 6260–6267. IEEE.
33.
Li B, Du W, Wang C, et al. Mechanism design and motion control system realization for 6-strut tensegrity robots. In: Proceedings of the 15th IASTED international conference intelligent systems and control (ISC 2016), Campinas, Brazil, 16–18 August 2016, pp.349–353. ACTA Press.
34.
DebK. An introduction to genetic algorithms. Sadhana1999; 24: 293–315.
35.
RahliMPirotteP. Optimal load flow using sequential unconstrained minimization technique (SUMT) method under power transmission losses minimization. Electr Power Syst Res1999; 52: 61–64.
36.
Smith R. Open Dynamics Engine. Online Referencing, www.ode.org/ (2007, accessed 12 October 2018).
