本論文研究具有兩個致動關節以及平坦狀腳底板的單足機器人之穩定跳躍。機器人在起跳前經歷一特殊的欠致動狀態，亦即其腳底在地面上繞著未致動的腳趾旋轉。由於具備此欠致動的狀態，使得機器人跳躍的距離可以更遠，達到類似於人類穩定跳躍的動作。論文中藉由仔細地分析機器人整體的動態，包含腳底與地面間的碰撞情形和穩定跳躍的限制條件，提出一套系統化的最佳化演算法，進行各致動關節的軌跡規劃，並且此最佳化需建構在致動能量損耗最小的前提上。透過模擬結果以及硬體上的實驗實行，關於跳躍策略和最佳化軌跡設計的可行性可獲得驗證。實驗結果也進一步地印證，機器人除了能夠以不同的跳躍距離在水平面上連續且穩定地跳躍，並且亦可以成功地完成跳上、下階梯的動作。

In this paper, stable hopping of a one-legged, articulated robot with a flat foot is investigated. The robot has a special feature that before taking off, it goes through an underactuated phase in which the foot rotates about the unactuated toe on the ground. By having the under-actuated phase, the robot can perform stable human-like hops with longer hopping distances. To devise a systematic trajectory design methodology for the robot, its dynamics including the ground-foot impact and the hopping constraints are carefully studied. An optimization procedure is then proposed to compute the optimal trajectories for the actuated joints which can lead to minimum actuation energy. The feasibility of the hopping strategy and the optimal trajectories are verified by simulations and hardware implementation. Experiments indicate that the robot not only can stably perform hops with different hopping distances on the level ground but also can successfully hop up/down staircases.

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