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研究生： 何雅芳
Ho, Ya-Fang
論文名稱： 基於線性倒單擺模型之人形機器人步態規劃演算法之設計與實現
Design and Implementation of LIPM-based Gait Planning Algorithm for Humanoid Robots
指導教授： 李祖聖
Li, Tzuu-Hseng S.
學位類別： 博士
Doctor
系所名稱： 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 81
中文關鍵詞： 雙足步態規劃 、人形機器人 、線性倒單擺模型 、零力矩點
外文關鍵詞： Biped gait generation, humanoid robots, linear inverted pendulum model (LIPM), zero moment point (ZMP)
相關次數： 點閱：156  下載：8 
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    • 本論文主要探討基於線性倒單擺模型的人形機器人步態規劃演算法。線性倒單擺模型被廣泛地使用於簡化機器人模型以降低運算複雜度，其易於實現的特性亦適合應用於即時步態的產生。另一方面，零力矩點理論可說是人形機器人領域中最廣為人知的穩定性準則，當給予適當的零力矩點參考軌跡，即可透過線性倒單擺模型理論求得機器人之質心軌跡，並產生穩定之步態。因此，本論文定義出五種型態之零力矩點函數，並推導出各函數所對應之質心軌跡。此外，應用上述之零力矩點函數架構零力矩點參考軌跡並提出可參數化之步態規劃演算法，令使用者可調整每一步的步伐大小。然而，雖然線性倒單擺模型受益於其簡化之模型，但在特定情況下其模型誤差將會增加。在線性倒單擺模型理論中，為了忽略單擺擺線之質量，機器人之身體質量需遠大於足部之質量；而當此條件不成立時，其模型誤差將劇烈影響步態之穩定性。因此，本論文提出改良型之線性倒單擺模型，使用雙連桿模型以解決上述問題，亦將機器人之質量分佈納入於模型之中。最後，於機器人模擬器與實體機器人上驗證本論文所提出之相關演算法，模擬結果與實驗結果皆顯示出本論文之步態規劃演算法之可行性與實用性。

    This dissertation mainly focuses on the gait planning algorithms, which are based on Linear Inverted Pendulum Model (LIPM) theory, for humanoid robots. LIPM theory is widely used to simplify the robot model for reducing the computational complexity. It can be implemented easily and is suitable for real-time gait pattern generation. On the other hand, Zero Moment Point (ZMP) is the most well-known stability criterion in the field of humanoid robot. With proper ZMP references, the Center of Mass (CoM) trajectories can be acquired with LIPM theory, and a stable gait pattern can be generated. Thus, five types of ZMP functions are defined, and their corresponding CoM trajectories are derived with LIPM theory. Also, a natural ZMP reference is built with the proposed ZMP functions and a parameterized gait planning algorithm is presented. Hence, users can generate a stable gait pattern with a desired step size for each step. Although the linear inverted pendulum model benefits due to its simplified model, the modeling error increases in a curtain case. In LIPM theory, the mass of the body should be much greater than the mass of the leg so that the link of pendulum can be treated as massless. The modeling error increases and will strongly affect the walking stability when the mass of the body is not greater than the mass of the leg. Therefore, an enhanced linear inverted pendulum model is proposed. A Double-link Linear Inverted Pendulum Model (DLIPM) is utilized to eliminate the aforementioned problem, and the mass distribution of the robot can be considered into the model. Finally, the proposed methods are validated on a robot simulator and a real robot. Both of the simulation and experimental results can validate the feasibility and practicality of the proposed gait planning algorithms.

    Abstract I Acknowledgement III Contents IV List of Figures VII List of Tables IX Chapter 1. Introduction 1 1.1 Motivation and Literature Survey 1 1.1 Main Contributions 5 1.2 Dissertation Organization 5 Chapter 2. Implementation of David Junior 7 2.1 Introduction 7 2.2 Design Concept 7 2.3 System Architecture 12 2.4 Robot Model in Robot Simulator 13 2.5 Kinematics 14 2.5.1 Forward Kinematics 14 2.5.2 Inverse Kinematics 17 Chapter 3. Linear Inverted Pendulum Model 22 3.1 Introduction 22 3.2 Basic Concept of Zero Moment Point 23 3.3 Linear Inverted Pendulum Model 25 3.4 ZMP Functions 28 3.4.1 Step Function Type ZMP 28 3.4.2 Ramp Function Type ZMP 28 3.4.3 Parabolic Function Type ZMP 29 3.4.4 Cubic Function Type ZMP 30 3.4.5 Sine Function Type ZMP 31 3.5 CoM Trajectory Generation by Given ZMP References 32 3.5.1 Common ZMP Reference 32 3.5.2 Double Support Phase ZMP Reference 33 3.5.3 Moving ZMP Reference 34 Chapter 4. Double-link LIPM Gait Planning Algorithm 40 4.1 Introduction 40 4.2 Double-Link Linear Inverted Pendulum Model 41 4.2.1 Review of the Conventional LIPM 41 4.2.2 DLIPM 41 4.3 CoM Trajectories with Natural ZMP References 46 4.4 Parameterized Gait Planning Algorithm 50 Chapter 5. Experimental Results 56 5.1 Introduction 56 5.2 Experiments of Parameterized Gait Planning Algorithm 54 5.3 Simulations of DLIPM Algorithm 65 5.3.1 Comparisons for Normal Mass Distribution 66 5.3.2 Comparisons for Lower Body-to-leg Ratio 68 5.3.3 Comparisons for Higher Body-to-leg Ratio 68 5.4 Experiments of DLIPM Algorithm 71 Chapter 6. Conclusions and Future Works 74 6.1 Conclusions 74 6.2 Discussions and Future Works 75 References 77

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