Energy-optimal relative timing of stance-leg push-off and swing-leg retraction in walking

Abstract

SUMMARYSwing-leg retraction in walking is the slowing or reversal of the forward rotation of the swing leg at the end of the swing phase prior to ground contact. For retraction, a hip torque is often applied to the swing leg at about the same time as stance-leg push-off. Due to mechanical coupling, the push-off force affects leg swing, and hip torque affects the stance-leg extension. This coupling makes the energetic costs of retraction and push-off depend on their relative timing. Here, we find the energy-optimal relative timing of these actions. We first use a simplified walking model with non-regenerative actuators, a work-based energetic-cost, and impulsive actuations. Depending on whether the late-swing hip torque is retracting or extending (pushing the leg forward), we find that the optimum is obtained by applying the impulsive hip torque either following or prior to the impulsive push-off force, respectively. These trends extend to other bipedal models and to aperiodic gaits, and are independent of step lengths and walking speeds. In one simulation, the cost of a walking step is increased by 17.6% if retraction torque comes before push-off. To consider non-impulsive actuation and the cost of force production, we add a force-squared (F2) term to the work cost. We show that this cost promotes simultaneous push-off force and retracting torque, but does not change the result that any extending torque should come prior to push-off. A high-fidelity optimization of the Cornell Ranger robot is consistent with the swing-retraction trends from the models above.

The converse effects of speed and gravity on the energetics of walking and running

“…If exchange between energy forms is not a critical determinant of the selected coordination pattern in gait, what does influence the choice of movement strategy in any given circumstance? One alternative suggests that gait solutions are optimized compromises between competing physical penalties (Kuo, 2001, Hasaneini et al, 2015, McGeer, 1990a. Some insight into the factors influencing the CNS strategy can be inferred by using predictive models as quantitative hypotheses, where model predictions of gait coordination in specific circumstances can be tested against the movement patterns selected by human subjects negotiating the same physical conditions.…”

Form in the context of function: Fundamentals of an energy effective striding walk, the role of the plantigrade foot and its expected size

“…An animate biped is able to replace lost energy but can also actively adjust the geometric relationship of the glancing collision by using muscular action during the transition between support limbs (when both limbs are on or near ground contact). A highly effective strategy in this regard is to apply a pre‐emptive push‐off by the previous stance limb just prior to the heel strike that initiates contact by the next support limb (Bertram & Hasaneini, 2013; Hasaneini, Bertram, & Macnab, 2015; Kuo, 2002; Ruina et al, 2005; Srinivasan, 2011). This alters the geometry of the glancing collision as the new support limb makes contact in a way that substantially reduces energy loss (Figure 1b).…”

Robust Control of Semi-passive Biped Dynamic Locomotion based on a Discrete Control Lyapunov Function

“…31 Then the swing leg trajectory can be planned by using a simple cubic interpolation. With the planned swing leg trajectory, the control torque used to realized robust walking can be derived according to the dynamic model in formula (4).…”

“…Both the task-space and joint-space control methods have been studied. [1][2][3][4][5] The biped robot can realize the pre-defined walking pattern with active torque control methods, 6,7 while the passive walker can present a human-like walking pattern on a declined slope depending only on its gravity changing and physical structure. 8,9 To make best use of these two methods' advantages and bypass their disadvantages, the idea to combine the active control and passive walking is proposed, called passive-based control.…”