- 學位論文
建立具有雙腳著地階段之四個自由度的主動走路模型模擬不同體重的走路運動
Using a 4 degree of freedom walking model with double support phase to simulate walking with different weight
摘要
近年來，老人比例快速地增加，老人的受傷以及殘疾並會造成可觀的經濟消耗，其中，老者受傷有50%都是因為跌倒造成，同時跌倒也是最常造成老者死亡的原因，因此，了解老人走路的動態特性以及跌倒的原因是非常重要的，本篇論文希望建立能模擬具有雙腳著地階段之走路模型，這個模型能模擬不同走路模型之走路運動，我們期望這個模型能分析導致老人跌倒之主因，達成預防跌倒之目的，以減少因老人跌倒產生的社會成本。 首先，我們建立一個具有四個自由度的走路模型，此模型具有兩支腳，兩腳分別具有大腿、小腿以及膝蓋關節，此走路模型具有五個質點，分別位於兩腳之小腿、大腿以及臀部關節，我們並假設各質點位於該自由度之中央位置。接著，我們可利用尤拉拉格朗日法推導走路模型之動態方程式，並利用Matlab計算每一刻走路模型的參數變化。我們將步態區分為單腳著地以及雙腳著地兩個階段，定義走路模型之走路演算法。在單腳著地階段時，假設走路模型之走路運動類似倒單擺運動，因此我們可利用地面回饋力計算單腳著地階段的扭矩分布，當搖擺腳搖擺與地面產生撞擊產生角速度不連續，我們假設碰撞期間非常短，同時沒有受到外力影響，因此可利用角動量守恆推導換腳公式。在雙腳著地階段時，我們並於後腳加入臨時自由度的腳掌，並定義最佳化起始條件為抬腳離地時機。 為了使走路演算法具備更自然的走路步態，我們於演算法中加入補償扭矩參數以及效率參數，前者將走路模型的數據比較實際人類走路實驗數據，並於走路模型發生異常時施加彌補扭矩，後者利用走路模型的輸出能量與位能、動能互補之能量差，定義每個走路回圈的效率值，並最佳化扭矩輸出值。 我們藉由極限圈和Poincare圖探討走路模型是否具備穩定週期解，走路模型呈現兩種不同的極限圈，擷取每一步的周期後發現走路模型的走路運動產生了分岔現象，以兩步為單位產生週期解。接著，擷取步態的動能、位能和總能數據並進行能量流的分析，走路模型運動時的動能與位能僅於下降階段互相補足，其總能量主要隨著位能變化，並於搖擺腳撞擊產生能量損耗。 最後，我們定義無因次的參數簡化動態方程式，並改變質量參數的值模擬不同體態的走路模型，不同質量的走路模型之每兩步的週期大約相同，動能最大值、位能最大值與最小值與質量呈現線性關係，找出其線性關係後可畫出無因次化的能量流曲線。
並列摘要
The population of elderly has risen rapidly. There is considerable financial cost caused by injured and handicapped of elderly. Among all the cases, falling accounts for nearly half of injury cases, and is the leading cause of death. Thus, it is important to understand the locomotion of elderly and the reason why they fall. In this thesis, we want to develop a dynamic walking model with double support phase. This model is capable of simulating walking model withdifferent parameters. We hope this model can analyze the major determinations causing elder’s fall for future fall prevention, and thus reduce the financial cost for elderly fall. We built a 4 degreeoffreedom dynamic walking model which has two legs with calf and thigh separated by the knee joint. Our model has five mass points which are located on the middle of stance leg calf, stance leg thigh, hip, swing leg thigh and swing leg calf, respectively. We used Euler-Lagrange equation to find the dynamic equations of the walking model. We derived the control algorithm by single support phase and double support phase, respectively. In single support phase, we assumed locomotion of the walking model is similar to inverted pendulum dynamic. As a result, we can derive torque control of our walking model with ground reaction force. When heelstrike occurs, the angular velocities of all degree of freedom become discontinuous. We assumed the duration of heelstrike is infinitesimally small and no external force is applied to the walking model. Thus, we can derive the new state variables of all degree of freedom by the conservation of angular momentum of the whole system. In double support phase, we added a foot on back leg as an extra degree of freedom and defined theoptimal initial condition of next step as the end event of double support phase. In order to achieve available walking pattern, we defined phasic torque and efficiency in our control algorithm. The former compares the torques in walking model with clinical human walking data and applies phasic torques when there’re out of phase torques. The latter calculates the compensation rate of kinetic energy and potential energy for efficiency in every step. We then calculated the optimal torques applied on our walking model with less energy cost. We used limit cycle and Poincare’s map to analyze the gait periodicity. The walking model performs two kinds of limit cycle. We discovered the walking of our walking model bifurcates into two steps by period analysis. Besides, we derived kinetic energy, potential energy and total energy of the dynamic walking model in a walking cycle. During a walking cycle, the compensation of kinetic energy and potential energy occurs only at the terminal stance. The total energy changes with potential energy during walking and is dissipated when heelstrike occurs. In the end, we defined dimensionless parameters to simplify dynamic equations. We can simulate different cases of walking simply by changing dimensionless parameters. The period of walking models with different parameters is approximately same in every two step cycles. We then compared the maximum and minimum value of kinetic energy, potential energy and total energy. We derived the normalized curve for each case by the linear relationbetweenextreme values of energy flow andoverweight rate.