柔性腿无缘轮被动动态行走器建模与分析

Modeling and analysis of the passive dynamic walker of flexible legged rimless wheel

摘要

研究柔性腿无缘轮被动动态行走器建模，并分析阻尼系数对系统动力学的影响。根据行走器的几何特征，选择独立广义坐标描述系统的位置，使用第二类拉格朗日方程建立柔性腿无缘轮被动动态行走器的动力学模型。对柔性腿的结构和物理性质进行分析，得到腿与地面的冲击阶段伸缩腿的切向发生冲击，而径向不传递冲击力的结论，并提出部分冲击假设条件下的状态跳变模型。采用不同的阻尼参数进行柔性腿无缘轮被动动态行走的数值仿真，结果验证了所提方法的有效性。选择较大的阻尼系数，周期行走的双支撑阶段占整个行走周期的77.6%，单支撑阶段占整个行走周期的22.4%，斜坡角度在0.1～0.7 rad范围内可以实现周期行走。柔性腿无缘轮可被动动态行走的斜坡角度，随着阻尼系数的减小而减小。

Abstract

The modeling of the passive dynamic walker of flexible legged rimless wheel is studied，and the influence of damping coefficient on system dynamics is analyzed.According to the geometric characteristics of the walker，the independent generalized coordinates are selected to describe the position of the system，and the second kind of Lagrange equation is used to establish the dynamic model of the passive dynamic walker of flexible legged rimless wheel.By analyzing the structure and physical properties of the flexible leg，it is concluded that the impact occurs in the tangential direction of the telescopic leg and the impact force is not transmitted between the leg and the ground in the radial direction during the impact stage，and a state jump model under the assumption of partial impact is proposed.The numerical simulation of passive dynamic walking of flexible legged rimless wheels using different damping parameters verifies the effectiveness of the proposed method.When a larger damping coefficient is selected，the double-limb support period of periodic walking accounts for 77.6% of the whole walking cycle，while the single-limb support period accounts for 22.4% of the whole walking cycle.The periodic walking can be achieved when the slope angle is in the range of 0.1-0.7 rad.The slope angle of the flexible legged rimless wheel that can passively and dynamically walk on decreases as the damping coefficient decreases.

关键词

被动动态行走 / 冲击模型 / 极限环 / 柔性腿无缘轮

Key words

passive dynamic walking / impact model / limit cycle / flexible legged rimless wheel

参考文献

[1] MCGEER T. Passive dynamic walking[J]. International journal of robotics research， 1990， 9（2）： 62-82.

[2] COLLINS S， RUINA A， TEDRAKE R， et al. Efficient bipedal robots based on passive-dynamic walkers[J]. Science， 2005， 307（5712）： 1082-1085.

[3] QI F， BI L Y， WANG T S， et al. The experimental study on the contact process of passive walking[J]. Acta mechanica Sinica， 2012， 28（4）： 1163-1168.

[4] LIU N， LI J F， WANG T S. Passive walker that can walk down steps：simulations and experiments[J]. Acta mechanica Sinica， 2008， 24（5）： 569-573.

[5] COLLINS S H， WISSE M， RUINA A. A three-dimensional passive-dynamic walking robot with two legs and knees[J]. The international journal of robotics research， 2001， 20（7）： 607-615.

[6] HSU C S. A discrete method of optimal control based upon the cell state space concept[J]. Journal of optimization theory and applications， 1985， 46（4）： 547-569.

[7] 徐皆苏， 徐建学. 高阶非线性动力系统全局分析——胞胞映射法应用[J]. 应用数学和力学， 1985， 6（11）： 953-962.

[8] XU Jiesu， XU Jianxue. The global analysis of higher order non-linear dynamical systems and the application of cell-to-cell mapping method[J]. Applied mathematics and mechanics， 1985， 6（11）： 953-962（in Chinese）.

[9] 谢勇， 徐健学， 江俊. 胞映射搜索最优控制路径的新策略[J]. 应用力学学报， 2003， 20（4）： 19-23.

[10] XIE Yong， XU Jianxue， JIANG Jun. New approach for searching optimal control path by cell mapping[J]. Chinese journal of applied mechanics， 2003， 20（4）： 19-23（in Chinese）.

[11] 李自刚， 严旺， 康佳琪， 等. 数据驱动印度洋海域全局动力学研究[J]. 力学学报， 2021， 53（9）： 2595-2602.

[12] LI Zigang， YAN Wang， KANG Jiaqi， et al. Data-driven global dynamics of the Indian Ocean[J]. Chinese journal of theoretical and applied mechanics， 2021， 53（9）： 2595-2602（in Chinese）.

[13] 柳宁， 李俊峰， 王天舒. 双足模型步行中的倍周期步态和混沌步态现象[J]. 物理学报， 2009， 58（6）： 3772-3779.

[14] LIU Ning， LI Junfeng， WANG Tianshu. Period-doubling gait and chaotic gait of biped walking model[J]. Acta physica Sinica， 2009， 58（6）： 3772-3779（in Chinese）.

[15] GRITLI H， BELGHITH S. Bifurcations and chaos in the semi-passive bipedal dynamic walking model under a modified OGY-based control approach[J]. Nonlinear dynamics， 2016， 83（4）： 1955-1973.

[16] 郑鹏， 王琪， 吕敬， 等. 摩擦与滚阻对被动行走器步态影响的研究[J]. 力学学报， 2020， 52（1）： 162-170.

[17] ZHENG Peng， WANG Qi， LÜ Jing， et al. Study on the influence of friction and rolling resistance on the gait of passive dynamic walker[J]. Chinese journal of theoretical and applied mechanics， 2020， 52（1）： 162-170（in Chinese）.

[18] ASANO F. Stealth walking with reduced double-limb support phase and its extension to careful legged locomotion[J]. Multibody system dynamics， 2018， 44（4）： 421-447.

[19] ASANO F， TOKUDA I. Indirectly controlled limit cycle walking of combined rimless wheel based on entrainment to active wobbling motion[J]. Multibody system dynamics， 2015， 34（2）： 191-210.

[20] LI L C， TOKUDA I， ASANO F. Energy-efficient locomotion generation and theoretical analysis of a quasi-passive dynamic walker[J]. IEEE robotics and automation letters， 2020， 5（3）： 4305-4312.

[21] XIAO X， ASANO F. Generating 1-DOF limit cycle walking at target walking speed by feed-forward and feedback limit cycle control[J]. Multibody system dynamics， 2017， 40（2）： 155-175.

[22] ASANO F， ZHENG Y Q. High-speed and energy-efficient collision-less walking of underactuated rimless wheel[J]. Artificial life and robotics， 2018， 23（4）： 523-531.

[23] HARADA T， TANAKA H A， HANKINS M J， et al. Optimal waveform for the entrainment of a weakly forced oscillator[J]. Physical review letters， 2010， 105（8）： 088301.

[24] LI L C， TOKUDA I， ASANO F. Nonlinear analysis of an indirectly controlled limit cycle walker[J]. Artificial life and robotics， 2018， 23（4）： 508-514.

[25] ASANO F， KAWAMOTO J. Modeling and analysis of passive viscoelastic-legged rimless wheel that generates measurable period of double-limb support[J]. Multibody system dynamics， 2014， 31（2）： 111-126.

[26] BUTTERFIELD J K， SIMHA S N， DONELAN J M， et al. The split-belt rimless wheel[J]. The international journal of robotics research， 2022， 41（11/12）： 1043-1076.

[27] 宋嘉琦， 张奇志， 周亚丽. 变长度弹性伸缩腿双足机器人动力学与控制[J]. 力学季刊， 2019， 40（2）： 235-242.

[28] SONG Jiaqi， ZHANG Qizhi， ZHOU Yali. Dynamics and control of bipedal robot with variable length telescopic legs[J]. Chinese quarterly of mechanics， 2019， 40（2）： 235-242（in Chinese）.

基金资助

国家自然科学基金资助项目(12172059)