Effect of Heel to Toe Walking on Time Optimal Walking of a Biped During Single Support Phase

Abstract

Dynamic modeling of a biped has gained lots of attention during past few decades. While stability and energy consumption were among the first issues which were considered by researchers, nowadays achieving maximum speed and improving pattern of motion to reach that speed are the important targets in this field. Walking model of bipeds usually includes two phases, single support phase (SSP), in which only the stance foot is in contact with the ground while the opposite leg is swinging; and double support phase (DSP) in which the swing leg is in contact with the ground in addition to the rear foot. It is common in the simplified model of walking to assume the stance leg foot, flat during the entire SSP; but one may know that for human walking, there is also a sub-phase during SSP in which the heel of stance foot leaves the ground while the whole body is supported by toe link. Actually in this sub phase the stance leg foot rotates around the toe joint. This paper is trying to study the effect of toe-link and heel to toe walking model on dynamic and specially speed of walking compare to flat foot model.

A model based study of a quantitative relation between joint strengthening and the highest achievable speed of human walking

“…In the following paragraphs, the basic theory of the employed mathematical frameworks is described to demonstrate the overall view of the solution process for human walking and the mathematical details are ignored for the sake of brevity. The application of the proposed time optimal solution for a biped robot is explained in details in [28,31] and interested readers are referred to these references for complete solution procedures and mathematical formulations.…”

“…To circumvent this problem one should note that the ZMP criterion in Eq. (6), is satisfied if and only if the resultant of normal reaction forces in both edges of the supporting polygon in sagittal plane are positive [27,28,31]. Therefore, the inequality constraints of ZMP can be restated in a new form as a function of F in Eq.…”

“…2) [31]. In other word, to map the problem to phase plane, it was essential to define 'n-1' constraint equations in terms of q and a parameter s in the form of g i (q,s) = 0.…”

“…Dimensions of above matrices were different for various phases/sub-phases of motion, which implies that three different sets of equations of motion were needed to study a single step [28,31].…”

“…2). To simulate the heel to toe walking pattern of normal subject, which is determinant in modeling the high speed walking of human [31], it was assumed that one step included two main phases, Double Support Phase (DSP) and Single Support Phase (SSP); which SSP itself consisted of two sub-phases, one sub-phase right after Table 1. Table 1 -Anthropometric properties of human body, including trunk, thigh, shin, foot links [32].…”