Kinematics Analysis and Dynamics Modeling of Bionic Water Snake Robot Based on D-H Parameters and Lagrange Equations

doi:10.3901/JME.2024.15.134

Abstract

Abstract: With the increasing demand for underwater environment operations, higher requirements have been put forward for robots in extreme environmental operations, multitasking requirements, and other aspects. In order to meet the high-performance requirements of environmental adaptability and maneuverability for underwater robots, it is urgent to design a highly flexible underwater snake like robot, and conduct in-depth research on its structural optimization and mathematical modeling. Therefore, based on the analysis of the biomimetic mechanism of biological snakes, a modular and reconfigurable multi segment biomimetic water snake robot structural model is designed. Based on the D-H parameter method, analyze the motion trajectories and forward speeds of each joint on the spatial motion waveform, and establish a motion mapping relationship; The hydrodynamic model is established considering the water resistance and reaction forces generated by underwater motion, and combined with the Lagrange equation, The equivalent kinematics and dynamics models of the water snake robot are established. Based on the established joint model, a detailed analysis is conducted on the key parameters that affect the joint angular motion, forward speed, and other performance of the water snake robot. Using a sinuous gait as the input reference signal, a joint simulation verification is conducted using Matlab and Adams. The results showed that when the gait amplitude is taken as 0.8 rad, the angular frequency is taken as 2 rad/s, and the phase difference between adjacent joints is taken as π/3 rad, the robot presented an ideal sinuous gait; At the same time, Adams is used to analyze the driving torque and power of each joint of the robot. The results show that the driving torque and power from the two end joints to the middle joint of the robot increased from about 0.6 N/m to 14.3 N/m, and from 1.1 N•m/s to 14.8 N•m/s, respectively; Finally, a robot prototype experiment is built to verify the driving function and torque of the snake robot's winding motion. The experimental results show that the driving torque and power required by the middle joint of the snake robot were greater than those of the two end joints, and the driving torque of the middle joint was 3.2 times that of the two end joints. This is consistent with the simulation conclusion and provides a theoretical basis for the underwater motion of the snake robot.

Key words: water snake robot, biomimetic mechanism, meandering movement, kinematic model, dynamic modeling

CLC Number:

TG156

WANG Min, SUN Jingjian, DING Jiheng, SUN Yi, PENG Yan, PU Huayan, LUO Jun, XIE Shaorong. Kinematics Analysis and Dynamics Modeling of Bionic Water Snake Robot Based on D-H Parameters and Lagrange Equations[J]. Journal of Mechanical Engineering, 2024, 60(15): 134-148.

References

[1] WANG C，PURANAM V R，MISRA S.A snake-inspired multi-segmented magnetic soft robot towards medical applications[J].IEEE Robotics and Automation Letters，2022，7(2):5795-5802.
[2] 王国彪，陈殿生，陈科位，等.仿生机器人研究现状与发展趋势[J].机械工程学报，2015，51(13):27-44.WANG Guobiao，CHEN Diansheng，CHEN Kewei，et al.Research status and development trend of bionic robot[J].Journal of Mechanical Engineering，2015，51(13):27-44.
[3] RICHTER F，GAVRILOV P V，LAM H M.ARCSnake:Reconfigurable snakelike robot with archimedean screw propulsion for multidomain mobility[J].IEEE Transactions on Robotics，2022，38(2):797-809.
[4] GONG C，TRAVERS M J，ASTLEY H C，et al.Kinematic gait synthesis for snake robots[J].The International Journal of Robotics Research，2016，35(1-3):100-113.
[5] BRANYAN C，HATTON R L，MENGUC Y.Snake-inspired kirigami skin for lateral undulation of a soft snake robot[J].IEEE Robotics and Automation Letters，2020，5(2):1728-1733.
[6] HIROSE S，MORI M.Biologically inspired snake-like robots[C]//IEEE International Conference on Robotics and Biomimetics，Shenyang，China:IEEE，2004:1-7.
[7] HU D L，NIRODY J，SCOTT T，et al.The mechanics of slithering locomotion[J].Proceedings of the National Academy of Sciences，2009，106(25):10081-10085.
[8] CHANG A H，VELA P A.Evaluation of bio-inspired scales on locomotion performance of snake-like robots[J].Robotica，2019，37(8):1302-1319.
[9] LI B，MA S，YE C，et al.Development of an amphibious snake-like robot[C]//World Congress on Intelligent Control and Automation，Jinan，China:IEEE.2010:613-618.
[10] KAKOGAWA A，KOMURASAKI Y，MA S，et al.Shadow-based operation assistant for a pipeline- inspection robot using a variance value of the image histogram[J].Journal of Robotics and Mechatronics，2019，31(6):772-780.
[11] GART S W，MITCHEL T W，LI C.Snakes partition their body to traverse large steps stably[J].Journal of Experimental Biology，2019，222(8):jeb185-991.
[12] FU Q，LI C.Robotic modelling of snake traversing large，smooth obstacles reveals stability benefits of body compliance[J].Royal Society Open Science，2020，7(2):191192.
[13] TRAVERS M，WHITMAN J，CHOSET H.Shape-based coordination in locomotion control[J].The International Journal of Robotics Research，2018，37(10):1253-1268.
[14] KELASIDI E，PETTERSEN K Y，KOHL A M，et al.An experimental investigation of path following for an underwater snake robot with a caudal fin[J].IFAC-PapersOnLine，2017，50(1):11182-11190.
[15] GUO X，MA S，LI B，et al.A novel serpentine gait generation method for snakelike robots based on geometry mechanics[J].IEEE/ASME Transactions on Mechatronics，2018，23(3):1249-1258.
[16] 时月天.面向月球陨石坑探测的蛇形机器人运动特性研究[D].哈尔滨:哈尔滨工业大学，2019.SHI Yuetian.Hour month day research on the motion characteristics of serpentine robot for lunar crater exploration[D].Harbin:Harbin University of Technology，2019.
[17] 郑文凯.绳驱蛇形机器人轨迹规划与控制[D].哈尔滨:哈尔滨工业大学，2020.ZHENG Wenkai.Trajectory planning and control of rope driven snake like robot[D].Harbin:Harbin University of Technology，2020.
[18] ALBEN S.Efficient bending and lifting patterns in snake locomotion[J].Proceedings of the Royal Society A:Mthematical，Physical and Engineering Sciences，2022，478(2266):20220312.
[19] MA S.Analysis of snake movement forms for realization of snake-like robots[C]//Proceedings 1999 IEEE International Conference on Robotics and Automation.Detroit，MI，USA: IEEE，1999:3007-3013.
[20] 邓蕊，王亚慧，邢利辉，等.一种管道探测蛇形机器人的建模仿真与实验研究[J].小型微型计算机系统，2021，42(12):2496-2500.DENG Rui，WANG Yahui，XING Lihui，et al.Modeling，simulation and experimental research on a pipeline detection snake robot[J].Small Microcomputer System，2021，42(12):2496-2500.
[21] 魏武，李艳杰，廖志鹏，等.基于旋量理论的蛇形机器人运动学建模[J].华南理工大学学报，2019，47(2):1-8.WEI Wu，LI Yanjie，LIAO Zhipeng，et al.Kinematic modeling of snake like robot based on screw theory[J].Journal of South China University of Technology，2019，47(2):1-8.
[22] 郭宪，马书根，李斌，等.基于微分几何的蛇形机器人动力学与控制统一模型[J].中国科学:信息科学，2015，45(8):1080-1094.GUO Xian，MA Shugen，LI Bin，et al.A unified model of dynamics and control for snake robots based on differential geometry[J].Chinese Science:Information Science，2015，45(8):1080-1094
[23] DATE H，TAKITA Y.Control of 3D snake-like locomotive mechanism based on continuum modeling[C]//International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.Long Beach，CA:ASME，2005，47438:1351-1359.
[24] TALAEIZADEH A，FOROOTAN M，ZZBIHI M，et al.Comparison of Kane’s and Lagrange’s methods in analysis of constrained dynamical systems[J].Robotica，2020，38(12):2138-2150.
[25] GARBEROGLIO F F，APESTEGUIA S，SIMOES T R，et al.New skulls and skeletons of the Cretaceous legged snake Najash，and the evolution of the modern snake body plan[J].Science Advances，2019，5(11):eaax5833.
[26] CAPANO J G.Reaction forces and rib function during locomotion in snakes[J].Integrative and Comparative Biology，2020，60(1):215-231.
[27] ASTLEY H C.The biomechanics of multi-articular muscle–tendon systems in snakes[J].Integrative and Comparative Biology，2020，60(1):140-155.
[28] ARIIZUMI R，MATSUNO F.Dynamic analysis of three snake robot gaits[J].IEEE Transactions on Robotics，2017，33(5):1075-1087.
[29] WIENS A J，NAHON M.Optimally efficient swimming in hyper-redundant mechanisms:Control，design，and energy recovery[J].Bioinspiration & Biomimetics，2012，7(4):046016.
[30] FAN S S，WOOLSEY C A.Underwater vehicle control and estimation in nonuniform currents[C]//2013 American Control Conference.Washington，DC:IEEE，2013:1400-1405.
[31] ZHANG J，CHEN Y，LIU Y，et al.Dynamic modeling of underwater snake robot by hybrid rigid-soft actuation[J].Journal of Marine Science and Engineering，2022，10(12):1914
[32] 安晓松，李智卿，马书根，等.水下蛇形机器人关节旋转机构建模与运动分析[J].传感器与微系统，2023，42(4):35-38 AN Xiaosong，LI Zhiqing，MA Shugen，et al.Modeling and motion analysis of the joint rotation mechanism of underwater snake like robots[J].Transducer and Microsystem Technologies，2023，42(4):35-38.
[33] 张军豪，陈英龙，杨双喜，等.蛇形机器人:仿生机理、结构驱动和建模控制[J].机械工程学报，2022，58(7):75-92.ZHANG Junhao，CHEN Yinglong，YANG Shuangxi，et al.Snake shaped robots:Biomimetic mechanisms，structural driving，and modeling control[J].Journal of Mechanical Engineering，2022，58(7):75-92.