摘要
行走是仿人机器人研究的重点，其运动稳定性及耗能问题对智能发展至关重要。目前机器人多采用主动行走方式，控制精度极高，但造价昂贵、质量较重。与主动行走相比，半驱动被动行走含有摆动与触地切换，在摆动过程中无需控制，步态自然、能耗更低。
adc什么意思但被动行走研究，目前主要针对系统复杂步态的分析以及理论控制算法，极少考虑到参数之间相互关联对系统的影响。Compass-like模型，是最能代表人类腿部结构的基础被动行走模型。本文在前人对Compass-like模型稳定周期步态的研究基础上，将理论分析和数值计算相结合，对其参数域及吸引域进行深入研究。主要工作如下：
1）对Compass-like模型系统进行了理论分析，包括简化及无量纲参数变量。对该模型的周期步态，运用庞加莱映射思想分析被动行走的稳定性，并研究单一参数变化对模型稳定性的影响。
重庆 培训2）介绍了如何寻找模型的稳定参数域，运用该方法寻找Compass-like模型的二维及三维参数域，提取域内参数代入系统方程中，通过分析系统相图，验证搜索算法可行性与可靠性。同时分析不同参数域内不同取值对吸引域的影响，对比求得更加稳定的参数组合。
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3）根据切换面附近轨线变化的雅克比矩阵，实现系统Lyapunov Exponent的切换补偿，判断Compass-like模型是否出现混沌，利用“降维-升维”的思想，借助Matlab工具箱，详细介绍了拓扑马蹄的寻找过程，在相空间中找到了一周期混沌步态的三维拓扑马蹄，判定了混沌步态的存在。
本文简化了Compass-like被动行走模型，分析了各个参数对模型稳定性的影响。提出了一种搜索全域稳定参数的方法，并对吸引域范围进行比较从而优化参数，为实际中搭建模型及其行走步态的控制提供理论基础。另外利用切换系统李雅普洛夫指数法和拓扑马蹄理论两种方法，为模型的混沌步态提供了实验证明。
关键词：被动行走，周期轨，混沌，参数域，拓扑马蹄
陪练专家
Abstract
The study of humanoid robot mainly focus on human-like walking, and the stability of the robot motion and energy dissipation problem are very important for its intelligent development. Currently, the way of active dynamic walking is often applied，which is of high control precision, but costs too much, and with heavy weight. The quasi-passive dynamic walking with swing and touch the ground switching process, without control among swing, is natural and in lower energy consumption.
However at prent, the passive dynamic walking is mainly ud for the analysis of the complex gait and the theoretical control algorithm, but with very little consideration of the influence of parameters on the system. The Compass-like model, propod by Goswami, is the most reprentative model of the human leg structure in the passive walking model. In this paper, the study are given on the parameter domain and the domain of attraction from the combination of theoretical analysis and numerical calculation bad on the previous studies on the Compass-like model.
1）The theoretical analysis of the Compass-like model system is made, including the dimensionless parameters and the system parameters. The authors analyze the stability of the passive walking motion by using the idea of Poincare map, and study the relationship between the stability of a single parameter and the stability of the model.
2）This paper describes the way of finding the stable parameter region of the model, and us the method to find the parameter region of 2D and 3D. Extraction of domain parameter generation into the system equation, and verifies the feasibility and reliability of the arch algorithm by analyzing the system pha diagram. This paper also analyzes the influence of different values in different parameters on the domain of attraction.
3）According to the changing trajectory near the switch surface of the Jacobian matrix, this paper achieves the compensation system of Lyapunov Exponent, judging whether the Compass-like model appears chaotic. Using "dimensionality reduction - rising dimension", and the Matlab toolbox, it introduces the topological arch in detail, and find a three-dimensional topological horshoe periodic chaotic gait in pha space, which determines the existence of chaotic gait.
In this paper, we simplified the Compass-like passive walking model and analyzed the influence of each parameter on the stability of the model. In this ca, we optimized the
attractor region and propod a method of rearching global stability parameters. And we ud the Lyapunov Exponent method and topological horshoe theory to demonstrate our rearch results.
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Keywords: passive dynamic walking, period-orbit, chaos, parameter region, topological horshoe
目录jme
第1章绪论 (1)
1.1 研究背景及意义 (1)
1.2 国内外研究现状 (2)
1.2.1 理论模型研究现状 (3)
1.2.2 实物样机研制 (4)
1.3 本文的研究内容和结构安排 (7)
第2章混沌动力学的理论基础 (9)
2.1 混沌的定义及特性 (9)
2.1.1 混沌的定义 (9)
2.1.2 混沌的特性 (10)
2.2 混沌动力学若干研究方法 (11)
2.2.1 混沌中的分岔现象 (11)
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2.2.2 Poincaré截面与映射 (12)
2.2.3 Lyapunov 指数判定法 (15)
2.2.4 拓扑马蹄理论 (18)
2.3 边界搜索算法 (19)
2.4 本章小结 (21)
第3章被动双足行走模型步态分析 (22)
3.1 动力学建模与数值仿真 (22)
3.1.1 模型介绍 (22)
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3.1.2 动力学方程 (23)
3.1.3 模型Poincaré映射的定义 (28)广州mba辅导
3.2 参数变化对Compass模型的步态影响 (29)
3.2.1 系统不动点的判定 (29)
3.2.2 模型内部参数对步态的影响 (30)
3.2.3 斜面倾角对步态的影响 (32)
3.3 本章小结 (35)
第4章被动双足行走模型参数域及吸引域 (36)
4.1 稳定周期步态 (36)
4.2 可靠参数域 (40)
4.2.1 二维参数域 (40)
4.2.2 三维参数域 (43)
4.3 不同参数对模型吸引域的影响 (44)
4.4 本章小结 (48)
第5章混沌步态的证明 (49)
5.1 Compass模型Lyapunov指数的混沌判定 (49)
5.2 混沌步态的拓扑马蹄证明 (51)
5.3 本章小结 (56)
第6章总结与展望 (57)
6.1 全文总结 (57)
6.2 未来工作展望 (57)
参考文献 (59)
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致谢 (64)
攻读硕士学位期间从事的科研工作及取得的成果 (65)
