指導教授：羅仁權臺灣大學：電機工程學研究所顧少騁Gu, Shao-ChengShao-ChengGu2014-11-282018-07-062014-11-282018-07-062014http://ntur.lib.ntu.edu.tw//handle/246246/262856雙足步行機器人比之於輪型機器人有很大的優勢，如行走在不平的地形，避開障礙物，避免碰撞，推動恢復，跨大步障礙，攀爬樓梯。為了保持平衡，兩足機器人的穩定性是至關重要的。零力矩點理論已經提出了判斷機器人是否穩定。如果零力矩點超過腳的多邊形的安全範圍，雙足機器人可能會摔倒。 基於零力矩點理論研究人員提出了一些簡化的模型。倒單擺模型，將所有的質量集中于一點。而為了減少直線倒立擺模型的模型誤差，便有了更精細的三質心模型和多質心模型的建立。除了這些，為了減少轉動慣量所造成的誤差，研究人員提出了一種由倒單擺模型改進的飛輪模型，將倒單擺模型的質心替換為一個有質量可旋轉的飛輪。為了進一步提高模型的準確性，我們提出了一個新的模型，結合了三個質心和角動量，命名為三質量與角動量模型。該模型不僅考慮軀幹的轉動考慮，也考慮兩條腿的轉動慣量對雙足行走的影響。 同時我們在文中給出了該模型的零力矩點的表達式以及運動方程式。 在雙足機器人爬樓梯過去的研究中，有國外的學者已經提出了使用倒單擺模型和虛擬斜面法去規劃行走軌跡。然而，使用倒單擺模型，機器人上半身是固定不動的。上半身的固定使得機器人不能通過扭動腰部來修正自己的走路姿態，分擔腿部馬達所出的力。此外，經過驗證，虛擬斜面法並不能證明其遇到比倒單擺模型更加複雜的其他模型時的正確性。所以這種方法不能直接運用在我們提出的新模型上。因此，本文提出了一種名為樓梯坡度轉換的新方法來解決這一問題。同時文章的實驗和模擬證明了本文的觀點。The approaches of biped walking robots have been proposed to overcome several situations, such as walking on uneven terrains, circumventing obstacles, collision avoidance, push recover, striding across obstacles, climbing stairway. In order to maintain balance, the stability of biped robots is crucial and fundamental. The zero moment point (ZMP) theory has been proposed for determining whether robots fall down or not. If ZMP exceed the scope of the polygon of the feet, the biped robots will fall down. Some simplified models have been proposed based on ZMP. Linear inverted pendulum model (LIPM), one-mass model, uses the limited dynamic parameters, concentrating total mass and angular momentum on one point. To reduce the model error of LIPM caused by mass, three-mass model and multiple masses inverted pendulum model (MMIPM) are developed. Apart from these, to reduce the error caused by moment of inertia, there is an improved model replace the point mass by a flywheel to explicitly represent embodiment of the centroid moment of inertia. To further improve the accuracy of model, we propose a new model that combine three-mass and angular momentum, named three-mass with angular momentum model. The proposed model not only take trunk''s rotation into account and also consider the effect of the rotational inertia of two legs. There are many research effects in the past for biped robot climbing stairs, virtual slope method for planning walking trajectory has been proposed based on one-mass model. However, using one-mass model does not considerate the rotation of the trunk. With the proposed model, it gains the freedom of using trunk rotation to reduce the moment of the support leg when climbing stairs. Moreover, due to the difficulty in verifying the correction of the virtual slope method with any models more complex than one-mass models. The virtual slope method cannot be directly used with proposed model. Therefore, this paper propose a new method named Stair-slope Transform Approach to solve this problem. The validation of this model and the method is confirmed from the simulations and experiments.誌謝 i 中文摘要 ii ABSTRACT iii CONTENTS v LIST OF FIGURES viii LIST OF TABLES xi Chapter 1 Introduction 1 1.1 Motivation 1 1.2 State-of-the-art Biped Robots 1 1.2.1 WABIAN 1 1.2.2 ASIMO 3 1.2.3 ATLAS 5 1.3 Literature Review 6 1.3.1 Zero Moment Point 6 1.3.2 Virtual Slope method 8 1.4 Organization 11 Chapter 2 System Structure 13 2.1 Hardware Structure 13 2.2 Software Structure 18 2.3 Robot Coordinate System 19 2.3.1 Forward kinematics analysis 20 2.3.2 Inverse kinematics Analysis 23 Chapter 3 Models for Biped Walking 27 3.1 Previous Models for Biped Robot 27 3.1.1 One-Mass Model 27 3.1.2 Three-Mass Model 28 3.1.3 Flywheel Model 29 3.2 Proposed Model 30 Chapter 4 Stair-slope Transform Method 32 4.1 Stair-slope Transformation of Kinematics 33 4.2 Stair-slope Transformation of Proposed Model 34 4.2.1 Original ZMP equations 34 4.2.2 Updated ZMP equations 39 4.3 Stair-slope Transformation of ZMP 41 Chapter 5 Walking Pattern Generation 44 5.1 Establishment of Stair-Slope Frame 44 5.2 ZMP and Foot Trajectories 45 5.3 Preview Control with Proposed Model 46 5.4 Compensation of ZMP Error 47 5.5 Whole Architecture 49 Chapter 6 Biped Experiment 51 6.1 Climbing Stairs 51 Chapter 7 Conclusions, Contributions, and Future works 59 7.1 Conclusions and Contributions 59 7.2 Future works 60 REFERENCE 61 VITA 654199783 bytesapplication/pdf論文公開時間：2014/08/08論文使用權限：同意有償授權(權利金給回饋學校)三質心角動量模型雙足機器人爬樓梯樓梯斜面轉換方法thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/262856/1/ntu-103-R01921084-1.pdf