Using a 4 degree of freedom walking model with double support phase to simulate walking with different weight
Date Issued
2014
Date
2014
Author(s)
Chang, Yi-Lung
Abstract
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.
Subjects
走路模型
倒單擺
走路演算法
無因次化
分岔現象
Type
thesis
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