灰色理論應用於六足機械之穩定步伐探討

Study on Hexapod’s Stable Gaits Based on Gray Theory

李柏威(Po-Wei Lee)

指導教授 ： 江昭皚

國立臺灣大學/生物資源暨農學院/生物產業機電工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.02064

摘要

本文提出一種以灰關聯、灰預測控制六足機械行走時的穩定度。其中灰預測用於六足機械步伐的預測、灰關聯用於判斷穩定度，取灰預測所預測出的狀態和吾人自定的穩定狀態做比較，可判斷出六足機械下一步是否穩定。文獻上控制六足機械穩定度之方法，多是由六足機械硬體，推導出複雜的數學模式，加以控制。本論文所提出的灰關聯、灰預測控制方法，是以簡單的灰理論數學模型，不須推導出艱難的數學模組，進行六足機械穩定度的控制。
本論文對於六足機械所採用的步行策略為波浪步伐。波浪步伐為六足機械步伐中最有效率的步行策略，但穩定度相對較差。但以本論文所提出的灰關聯、灰預測控制方法，可使執行波浪步伐的六足機械穩定的行走。
灰預測效能良窳與否決定整體六足機械步伐穩定度控制的準確性。本文模擬六足機械行走時的實際腳軌跡是依據其實際結構尺寸，採用Denavit-Hartenberg Representation of Forward Kinematic Equations所推導出的數據。採用一般的單數列灰預測模組於初始行走時，步伐位置預測誤差較大，而本論文所提之雙數列灰預測模組可大幅改善此現象。經模擬驗証，於六足機械行走10步時，雙數列灰預測步伐控制法，其平均誤即可下降至3.3%，而真正global座標誤差為0.14%。因此，使用本論文的提出的預測模組，對於採用波浪步伐的六足機械將可更準確的預測其腳座標位置，六足機械的穩定度控制。
最後，為了驗証所提出的理論，本研究亦架構一實驗平台。利用此一平台進行六足機械的實際操作，驗証本文所推導出的灰預測步伐控制理論。

關鍵字

灰預測 ； 灰關聯度 ； 六足機械 ； 波浪步伐

並列摘要

This thesis proposes a control scheme, which is based on gray relation and gray prediction, for controlling a hexapod when it treads. The hexapods’ gaits are predicted by gray prediction and the stability status of hexapod is estimated by gray relation. It can be determined if hexapods are stable on next step by the comparison between the two states. One is predicted by the gray prediction and another is the stability which this thesis proposes. There are methods to control the stability of hexapods in retrospection which is from complicated mathematical mode. In this thesis, a method of controlling hexapod’s stable is proposed by using a simple mathematical model of gray theory including gray prediction and gray relation instead of a difficult mathematical mode.
In this thesis, the strategy of hexapod’s gaits is wave gaits which are the most efficient but less stable. However, by simulating the proposed control method which is proposed in the thesis, the strategy of wave gaits can present good stability. According to Denavit-Hartenberg Representation of Forward Kinematic Equations, the simulating data is acquired. This thesis uses the practical operation on an experimental platform to proof the theory which the thesis proposes.

並列關鍵字

gray prediction ； gray relation ； wave gaits ； hexapods

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