Current models of bending in soft arms are formulated in terms of experimentally determined, arm-specific parameters, which cannot evaluate fundamental differences in soft robot arm design. Existing models are successful at improving control of individual arms but do not give insight into how the structure of the arm affects the arm’s capabilities. For example, omnidirectional soft robot arms most frequently have three parallel actuators, but may have four or more, while common biological arms, including octopuses, have tens of distinct longitudinal muscle bundles. This article presents a quasi-static analytical model of soft arms bent with longitudinal actuators, based on equilibrium principles and assuming an unknown neutral axis location. The model is presented as a generalizable framework and specifically implemented for an arm with fluid-driven actuators, a subset of which are pressurized to induce a bend with a certain curvature and direction. The presented implementation is validated experimentally using planar (2D) and spatial (3D) bends. The planar model is used to initially estimate pressure for a closed-loop curvature control system and to bound the accessible configurations for a rapidly-exploring random trees (RRT) motion planner. A three-segment planar arm is demonstrated to navigate along a planned trajectory through a gap in a wall. Finally, the model is used to explore how the arm morphology affects maximum curvature and directional resolution. This research analytically connects soft arm structure and actuator behavior to unloaded arm performance, and the results may be used to methodically design soft robot arms.
AnsariYMantiMFaloticoECianchettiMLaschiC (2018) Multiobjective optimization for stiffness and position control in a soft robot arm module. IEEE Robotics and Automation Letters3(1): 108–115.
2.
AtakaAQiPLiuHAlthoeferK (2016) Real-time planner for multi-segment continuum manipulator in dynamic environments. In: 2016 IEEE International Conference on Robotics and Automation (ICRA). IEEE, pp. 4080–4085.
3.
BajoAGoldmanRESimaanN (2011) Configuration and joint feedback for enhanced performance of multi-segment continuum robots. In: 2011 IEEE International Conference on Robotics and Automation, pp. 2905–2912.
4.
BajoASimaanN (2015) Hybrid motion/force control of multi-backbone continuum robots. The International Journal of Robotics Research35(4): 422–434.
5.
BergelesCDupontPE (2013) Planning stable paths for concentric tube robots. In: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, pp. 3077–3082.
6.
BranyanCFlemingCRemaleyJ, et al. (2017) Soft snake robots: Mechanical design and geometric gait implementation. In: IEEE Conference on Robotics and Biomimetics (RoBio 2017).
7.
CalistiMGiorelliMLevyG, et al. (2011) An octopus-bioinspired solution to movement and manipulation for soft robots. Bioinspiration & Biomimetics6(3): 036002.
8.
CamarilloDBCarlsonCRSalisburyJK (2009) Configuration tracking for continuum manipulators with coupled tendon drive. IEEE Transactions on Robotics25(4): 798–808.
9.
CaseJBoothJShahDYuenMKramer-BottiglioR (2018) State and stiffness estimation using robotic fabrics. In: IEEE RoboSoft 2018.
10.
ChouCHannafordB (1996) Measurement and modeling of McKibben pneumatic artificial muscles. IEEE Transactions on Robotics and Automation12(1): 90–102.
11.
CianchettiMRanzaniTGerboniGFalcoIDLaschiCMenciassiA (2013) STIFF-FLOP surgical manipulator: mechanical design and experimental characterization of the single module. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2013).
12.
ConnollyFWalshCBertoldiK (2017) Automatic design of fiber-reinforced soft actuators for trajectory matching. Proceedings of the National Academy of Sciences of the United States of America114(1): 51–56.
13.
CroomJMRuckerDCRomanoJMWebsterRJ (2010) Visual sensing of continuum robot shape using self-organizing maps. In: 2010 IEEE International Conference on Robotics and Automation, pp. 4591–4596.
14.
DaerdenFLefeberD (2002) Pneumatic artificial muscles: Actuators for robotics and automation. European Journal of Mechanical and Environmental Engineering47(1): 11–21.
15.
DiMaioSPSalcudeanSE (2005) Needle steering and motion planning in soft tissues. IEEE Transactions on Biomedical Engineering52(6): 965–974.
16.
DoumitMFahimAMunroM (2009) Analytical modeling and experimental validation of the braided pneumatic muscle. IEEE Transactions on Robotics25(6): 1282–1291.
17.
FolladorMCianchettiMLaschiC (2012) Development of the functional unit of a completely soft octopus-like robotic arm. In: 4th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob 2012).
18.
GeraertsROvermarsMH (2007) Creating high-quality paths for motion planning. The International Journal of Robotics Research26(8): 845–863.
19.
GiannacciniMXiangCAtyabiATheodoridisTNefti-MezianiSDavisS (2018) Novel design of a soft lightweight pneumatic continuum robot arm with decoupled variable stiffness and positioning. Soft Robotics5(1): in press.
20.
GiorelliMRendaFCalistiMArientiAFerriGLaschiC (2015) Learning the inverse kinetics of an octopus-like manipulator in three-dimensional space. Bioinspiration & Biomimetics10(3): 035006.
21.
GodageIBransonDGuglielminoEMedrano-CerdaGCaldwellD (2011a) Shape function-based kinematics and dynamics for variable length continuum robotic arms. In: IEEE International Conference on Robotics and Automation, pp. 452–457.
22.
GodageIGuglielminoEBransonDMedrano-CerdaGCaldwellD (2011b) Novel model approach for kinematics of multisection continuum arms. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011).
23.
GodageIMedrano-CerdaGBransonDGuglielminoECaldwellD (2016) Dynamics for variable length multisection continuum arms. The International Journal of Robotics Research35(6): 695–722.
24.
GodageISBransonDTGuglielminoECaldwellDG (2012) Path planning for multisection continuum arms. In: 2012 International Conference on Mechatronics and Automation (ICMA). IEEE, pp. 1208–1213.
25.
HaoLXiangCGiannacciniM, et al. (2018) Design and control of a novel variable stiffness soft arm. Advanced Robotics32(11): 605–622.
26.
JonesBWalkerI (2005) A new approach to jacobian formulation for a class of multi-section continuum robots. In: IEEE International Conference on Robotics and Automation (ICRA 2005).
27.
JonesBWalkerI (2006a) Kinematics for multisection continuum robots. IEEE Transactions on Robotics22(1): 43–55.
28.
JonesBAWalkerID (2006b) Practical kinematics for real-time implementation of continuum robots. IEEE Transactions on Robotics22(6): 1087–1099.
29.
KatzschmannRKMarcheseADRusD (2015) Autonomous object manipulation using a soft planar grasping manipulator. Soft Robotics2(4): 155–164.
30.
KierWSmithK (1985) Tongues, tentacles and trunks: The biomechanics of movement in muscular-hydrostats. Zoological Journal of the Linnean Society83(4): 307–324.
31.
LaValleSM (1998) Rapidly-exploring random trees: A new tool for path planning. Technical Report 98-11, Computer Science Department, Iowa State University.
32.
LeibrandtKBergelesCYangGZ (2017) Concentric tube robots: Rapid, stable path-planning and guidance for surgical use. IEEE Robotics & Automation Magazine24(2): 42–53.
33.
MarcheseATendrakeRRusD (2016) Dynamics and trajectory optimization for a soft spatial fluidic elastomer manipulator. The International Journal of Robotics Research35(8): 1000–1019.
34.
MarcheseADKatzschmannRKRusD (2014) Whole arm planning for a soft and highly compliant 2D robotic manipulator. In: IEEE International Conference on Intelligent Robots and Systems (IROS).
35.
MishraAMondiniADel DottoreESadeghiATramacereFMazzolaiB (2018) Modular continuum manipulator: Analysis and characterization of its basic module. Biomimetics3(1): 3.
36.
PenningRSJungJBorgstadtJAFerrierNJZinnMR (2011) Towards closed loop control of a continuum robotic manipulator for medical applications. In: 2011 IEEE International Conference on Robotics and Automation, pp. 4822–4827.
37.
RendaFBoyerFDiasJSeneviratneL (2018) Discrete Cosserat approach for multisection soft manipulator dynamics. IEEE Transactions on Robotics34: 1518–1533.
38.
RendaFCacuccioloVDiasJSeneviratneL (2016) Discrete Cosserat approach for soft robot dynamics: A new piece-wise constant strain model with torsion and shears. IEEE International Conference on Intelligent Robots and Systems (IROS).
39.
ShapiroYGaborKWolfA (2015) Modeling a hyperflexible planar bending actuator as an inextensible Euler–Bernoulli beam for use in flexible robots. Soft Robotics2(2): 71–79.
40.
SinghGXiaoCKrishnanGHsiao-WeckslerE (2016) Design and analysis of soft pneumatic sleeve for arm orthosis. In: ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference.
41.
SunYSongSLiangXRenH (2016) A miniature soft robotic manipulator based on novel fabrication methods. IEEE Robotics and Automation Letters1(2): 617–623.
42.
SuzumoriKIikuraSTanakaH (1991) Development of flexible microactuator and its applications to robotic mechanisms. In: IEEE International Conference on Robotics and Automation (ICRA 1991).
43.
UmedachiTVikasVTrimmerB (2016) Softworms: The design and control of non-pneumatic, 3D-printed, deformable robots. Bioinspiration & Biomimetics11(2): 025001.
44.
WalkerIDawsonDFlashT, et al. (2005) Continuum robot arms inspired by cephalopods. In: Proceedings SPIE Conference on Unmanned Ground Vehicle Technology VII, pp. 303–314.
45.
WebsterRJonesB (2010) Design and kinematic modeling of constant curvature continuum robots: A review. The International Journal of Robotics Research29(13): 1661–1683.
46.
WegheMVFergusonDSrinivasaSS (2007) Randomized path planning for redundant manipulators without inverse kinematics. In: IEEE-RAS International Conference on Humanoid Robots. IEEE, pp. 477–482.
47.
WuKWuLRenH (2015) Motion planning of continuum tubular robots based on centerlines extracted from statistical atlas. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5512–5517.
48.
XuJDuindamVAlterovitzRGoldbergK (2008) Motion planning for steerable needles in 3D environments with obstacles using rapidly-exploring random trees and backchaining. In: 2008 IEEE International Conference on Automation Science and Engineering (CASE), pp. 41–46.
49.
XuKSimaanN (2010) Analytic formulation for kinematics, statics, and shape restoration of multibackbone continuum robots via elliptic integrals. Journal of Mechanisms and Robotics2(1): 011006.
50.
ZhangWPolygerinosP (2018) Distributed planning of multi-segment soft robotic arms. In: 2018 Annual American Control Conference (ACC). IEEE, pp. 2096–2101.
51.
ZhaoHO’BrienKLiSShepherdR (2016) Optoelectronically innervated soft prosthetic hand via stretchable optical waveguides. Science Robotics1(1): eaai7529.
