A mathematical framework to study fast walking of human

The body of a walking human is an elaborated dynamic system that operates adaptively in various conditions such as fast walking. Due to dynamic redundancies, the individual motor control strategies for speeding up the walking can be different among normal subjects. However, in reality, we see that the pattern of motion is quite similar among people and it is only the profile of hip joint motion along its path which determines the speed. The objective of the current paper is to develop a mathematical framework to investigate time optimal motion of a human during walking. To this end, a nine-link planar biped model is used. The motion is considered to take place in sagittal plane and to follow a normal pattern of motion. The solution is obtained using a phase plane method to solve minimum time problem which is subjected to inequality constraints of variable maximum joint torques and stability conditions. The solution method can be used to find the maximum possible speed of a human with specific body characteristics and to obtain a hip joint trajectory which could produce that speed. The proposed method can be utilized to study quantitative effect of different parameters such as joint strength in fast walking.