ROBOT Vol.34, No.3 May, 2012 DOI /SP.J Vortex+OSG 52 Vortex TP242 A (2012) Structure

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1 ROBOT Vol.34, No.3 May, 2012 DOI /SP.J Vortex+OSG 52 Vortex TP242 A (2012) Structure Design and Kinematical Analysis of Lattice Distortion Actuating Self-reconfigurable Robots YIN BoXU WeiWANG ShigangLIANG ZhenningWANG Xianlong (School of Mechanical and Power Engineering, Shanghai Jiao Tong University, Shanghai , China) Abstract: For the difficulty of the large-scale lattice self-reconfigurable robot system moving as an ensemble, a novel method to achieve the whole motion through local lattice distortion is proposed. One of lattice distortion rules is given, a module structure is designed according to this rule, and the reconfiguration features of this module are analyzed with discrete substitution groups. Through a physical distortion experiment with 2 lattices consisted of 6 modules, it is validated that the lattice distortion can be achieved by the lattice composed of these modules. Through the high-fidelity virtual simulation platform based on Vortex+OSG, snake-like motion computer simulation of a lattice robot system consisted of 52 modules is conducted, and the results show that the proposed method can yield global motion through local lattice distortion. Keywords: self-reconfigurable robot; lattice distortion; structure design; Vortex; motion simulation 1 Introduction PolyBot [1] CONRO [2] Molecube [3] CKBot [4] Metamorphicsystem [5] Crystal [6] Catom [7] M-Cubes [8] Shen SuperBot [9] Sambot Sambot [10] Wolfe [11] 3 AMOEBA-I wangshigang@sjtu.edu.cn / /

2 [12] Funiak 1 [13] Vortex OSG 2 Introduction to lattice distortion actuating method [14] [15] Bravais Bravais 14 [15] P I F 1 2(b)(c) 2 Fig.2 Graph of lattice distortion rule 2(a) 2(b) θ ϕ θ = 2ϕ (1) 1 Fig.1 Structure of cube lattice (c)

316 2012 5 3 Structure design of the module 3.

60 30 60 30 3 Fig.3 Module structure 1 2 2 3 3.

3 Structure design of the module 3.1 2(c) 3 (1) 2 (2) 4 2 (3) Fig.3 Module structure Fig.5 Sketch map of connector face SMA 6 SMA A B B SMA Fig.6 6 Sketch map of connecting 4 Fig.4 Cube packaging a module

4 [14] 1 1 1 22 2 2 Wyckoff a,b,c, [15] 2 mm PVC

2 Technical specifications of a module 250 g 156

5 N m STC12C5410AD 7 V 10 V 8 9 4 8(a) (b) 18 8 9

1 The kinematics features of the module P432 22

4 Fig.7 Sketch map of locking mechanism 3.4 [14] Wyckoff a,b,c, [15] 2 mm PVC 2 2 Tab.2 Technical specifications of a module 250 g 156 mm 156 mm 156 mm CYS-S /s 1.5 N m STC12C5410AD 7 V 10 V (a) (b) (c) 8 4 (d) 1 Tab.1 The kinematics features of the module P Wyckoff d 2 Wyckoff f P2 1 Wyckoff 4 Lattice distortion experiment 6 2 mm 8 Fig.8 Graph of two-lattice distortion experiment 5 Snake-like motion simulation and analysis of lattice-type robot

318 2012 5 52 CMLabs Vortex OSG visual C++ 6.0 Vortex 5.

rad/s 1 4 s 2 52 12 6 n = 7 (1) 4 t i 4 5 0.19.8 m/s 2 2 9 12 9 12 Fig.

5 CMLabs Vortex OSG visual C Vortex 5.1 Serpenoid [16-18] t i θ i (t) = a sin b 2n sin(ωt + ib n + b 2n ) c (2) n a = π/3b = 14π/3c = 0ω = π/2 rad/s 1 4 s n = 7 (1) 4 t i m/s Fig.9 Snake-like gait simulation of 12-lattice robot system ϕ i (t) = π 3 12 sin(πt 2 + 2iπ 3 + π 3 ) (3) i = 1,2,,6 t04/38/34 i 3 3 Tab.3 The gait control table for snake-like motion (unit: ) step ID M1/2 M3/4 M5/6 M7/8 M9/10 M11/ Fig.10 The torque, angle, angular velocity and angular acceleration of motor No.1

6 Fig.11 The torque, angle, angular velocity and angular acceleration of motor No.12 No N m 3 : 1 6 Conclusion Bravais Wyckoff d Funiak References Fig.12 The torque, angle, angular velocity and angular acceleration of motor No.24 1/24 No.1No.12 [1] Yim M, Duff D G, Roufas K D. PolyBot: A modular reconfigurable robot[c]//ieee International Conference on Robotics and Automation. Piscataway, NJ, USA: IEEE, 2000: [2] Shen W M, Salemi B, Will P. Hormone-inspired adaptive communication and distributed control for CONRO selfreconfigurable robots[j]. IEEE Transactions on Robotics and Automation, 2002, 18(5): [3] Zykov V, Mytilinaios E, Adams B, et al. Self-reproducing machines[j]. Nature, 2005, 435(7039): [4] Sastra J, Chitta S, Yim M. Dynamic rolling for a modular loop robot[j]. International Journal of Robotics Research, 2009, 28(6): [5] Chirikjian G, Pamecha A, Ebert-Uphoff I. Evaluating efficiency of self-reconfiguration in a class of modular robots[j]. Journal of Robotic Systems, 1996, 13(5):

7 [6] Rus D, Vona M. Crystalline robots: Self-reconfiguration with compressible unit modules[j]. Autonomous Robots, 2001, 10(1): [7] Goldstein S C, Campbell J D, Mowry T C. Invisible computing: Programmable matter[j]. Computer, 2005, 38(6): [8] M-Cubes [J]200718(12) Xia P, Fei Y Q, Zhu X J, et al. Distortion analysis of the M- Cubes self-reconfigurable robot during docking process[j]. Chinese Mechanical Engineering, 2007, 18(12): [9] Shen W M, Krivokon M, Chiu H, et al. Multimode locomotion via SuperBot reconfigurable robots[j]. Autonomous Robots, 2006, 20(2): [10] Wei H X, Chen Y D, Tan J D, et al. Sambot: A self-assembly modular robot system[j]. IEEE/ASME Transactions on Mechatronics, 2011, 16(4): [11] Wolfe K C, Kutzer M D M, Armand M, et al. Trajectory generation and steering optimization for self-assembly of a modular robotic system[c]//ieee International Conference on Robotics and Automation. Piscataway, NJ, USA: IEEE, 2010: [12] Liu J G, Ma S G, Wang Y C, et al. Configuration representation of a link-type self-reconfigurable mobile robot[c]//ieee Asia- Pacific Conference on Circuits and Systems. Piscataway, NJ, USA: IEEE, 2008: [13] Funiak S, Pillai P, Ashley-Rollman M P, et al. Distributed localization of modular robot ensembles[j]. International Journal of Robotics Research, 2009, 28(8): [14] Brener N, Ben Amar F, Bidaud P. Designing modular lattice systems with chiral space groups[j]. International Journal of Robotics Research, 2008, 27(3/4): [15] [M] Wang P, Li G C. Crystallography tutorial[m]. Beijing: National Defense Industry Press, [16] Hirose S. Biologically inspired robots Snake-like locomotors and manipulators[m]. USA: Oxford University Press, [17] [J]200440(12) Chen L, Wang Y C, Ma S G, et al. Analysis of traveling wave locomotion of snake robot[j]. Chinese Journal of Mechanical Engineering, 2004, 40(12): [18] [J]200527(6) Ye C L, Ma S G, Li B, et al. Dynamics analysis on serpentine locomotion of a new snake-like robot[j]. Robot, 2005, 27(6): [16] Duda R O, Hart P E. Use of the Hough transformation to detect lines and curves in pictures[j]. Communications of the ACM, 1972, 15(1): [17] Marchant J A, Brivot R. Real-time tracking of plant rows using a Hough transform[j]. Real-Time Imaging, 1995, 1(5): [18] Xu L, Oja E. Randomized Hough transform (RHT): Basic mechanisms, algorithms and computational complexities[j]. Computer Vision Graphics and Image Processing Image Understanding, 1993, 57(2): [19] Zhang H, Hou D B, Zhou Z K. A novel lane detection algorithm based on support vector machine[j]. PIERS Online, 2005, 1(4): [20] Saxena A, Chung S H, Ng A Y. 3-D depth reconstruction from a single still image[j]. International Journal of Computer Vision, 2008, 76(1):

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