在本研究中，我們提出了一種分散式強健隨機 H∞ 編隊追蹤控制設計方法，以解決對於多部雙足機器人的編隊追蹤控制問題。首先，基於和機器人足部運動相關的特定 body Jacobian，由雙足機器人任務空間與其軸空間所共同混合而成的正、逆向機器人動力學方程式可以被建構，並將雙足機器人系統化為廣義形式的隨機狀態空間模型。接著，利用 virtual leader 編隊結構以及分散式控制的概念，在編隊控制之下的多部雙足機器人可被視為是分別以隨機 H∞ 強健控制性能追蹤著各自所對應的目標行走路徑。因此，原先對於多部雙足機器人系統的強健隨機 H∞ 編隊追蹤控制設計問題便能轉化為數個相互獨立的 Hamilton-Jacobi inequality (HJI) 約束最佳化問題。為了克服在解算與強健隨機 H∞ 編隊追蹤控制設計相關的 HJI 時所遭遇的困難，我們采用了一種數值化框架來近似各部雙足機器人系統。結果，在 tensor-product (TP) 系統模型轉換技術的幫助之下，我們可以將與強健隨機 H∞ 編隊追蹤控制設計相關的 HJI 約束最佳化問題變換成等價的 linear matrix inequalities (LMIs) 約束最佳化問題，而後者則是能夠使用通常凸最佳化方法來有效的求解。最後，作為控制設計範例，我們給出六部雙足機器人同時沿著一條彎曲路徑進行固定編隊行走的部分模擬結果，以驗證本研究所提出的多部雙足機器人編隊控制設計方法之效用。

In this study, a decentralized robust stochastic H∞ team formation tracking control design is proposed to deal with the team formation tracking problem for a multi-biped robot system. Based on the specified body Jacobian associated with the leg motions, the hybrid task/joint-space dynamics and the inverse dynamics can be constructed to formulate multiple walking biped robots as generalized stochastic state-space systems. Under the concept of virtual leader-based team formation structure and the decentralized control approach, multiple biped robots walking in team formation are controlled to track their own corresponding paths with the robust stochastic H∞ tracking performances. Consequently, the original robust stochastic H∞ multi-biped robot team formation tracking control design problem can be transformed to several independent Hamilton-Jacobi inequality (HJI)-constrained optimization problems. To cope with the difficulties in solving the HJIs for the robust stochastic H∞ team formation tracking control design, a numerical framework is introduced to approximate the walking biped robot systems. As a result, based on the tensor-product (TP) model transformation technique, the HJI-constrained optimization problems for the robust stochastic H∞ team formation tracking control design are converted into the equivalent linear matrix inequalities (LMIs)-constrained optimization problems, which can be solved efficiently by the convex optimization methods. Finally, in the design example, several simulation results of six biped robots walking along a curved path in the desired rigid formation are given to validate the effectiveness of the proposed control scheme.

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