本研究計畫的目的是求出使人形機器人到達「臨界穩定狀態」之所有外力(包括慣 性力)的組合，「臨界穩定狀態」是指「不穩定」可能即將發生、但這時仍處在「動態 平衡」的狀態。本研究的特色為:1.目前已有的研究結果皆只針對機器人翻倒的情況， 而本研究不僅針對機器人翻倒，亦包括機器人滑動所造成之不穩定。2.目前已有的研究 結果皆未考慮機器人腳之彈性變形，而本研究將處理彈性變形的問題。3.研究結果將可 用來檢驗目前已有之穩定準則，訂出其適用範圍。 研究計畫將分兩年執行，第一年是假設機器人腳與地面先成為「點接觸」或「線接 觸」，然後才開始考慮彈性變形，這樣可直接利用赫氏接觸之結果。第二年則是從轉變 成「點接觸」或「線接觸」的過程就已經考慮彈性變形，如此就必須進行接觸力學分 析，求出每個階段接觸區域大小及接觸區域內正向應力的分布，直到接觸區域縮小至 點或線接觸為止。如此所得到之研究成果將提供目前最完整且正確之機器人穩定準則。 The purpose of this research is to determine all possible combinations of applied forces, including inertia forces, to bring a humanoid robot into a critical stable condition, that is, a condition the robot is still in dynamic equilibrium but is on the verge of losing stability. The characteristics of this research are as follows. 1. While all existing results only deal with tumbling or tipping over of a robot, in this research instability caused by both tumbling and slipping will be treated. 2. Elastic deformation of the robot foot has not yet been taken into consideration in existing results, and it will be included in this research. 3. Results of this research can be used to check the validity of existing stability criteria, establishing their applicable region. This research will be carried out in two years, in the first year elastic deformation is introduced only after the foot-to-ground contact is transformed into a point contact or a line contact, so that Hertz contact results can be used. In the second year elastic deformation is introduced at the outset of transforming the foot-to-ground contact into a point or a line contact, therefore, contact mechanics analysis will be performed at every stage to determine the size and the shape of the contact region and contact pressure in the region, until a condition is reached in which the contact region reduces to a point or a line. The results so obtained provide the most complete and accurate stability criterion.