Foot Placement and Balance in 3D

Abstract

Humans use carefully chosen step locations to restore their balance during locomotion and in response to perturbations. Understanding the relationship between foot placement and balance restoration is key to developing useful dynamic human balance diagnostic tests and balance rehabilitation treatments. The link between foot placement and balance restoration is studied in this paper using a simplified monopedal model that has a circular foot, coined the Euler pendulum. The Euler pendulum provides a convenient method of studying the stability properties of three-dimensional (3D) bipedal systems without the burden of large system equations typical of multibody systems. The Euler pendulum has unstable regions of its state-space that can be made to transition to a statically stable region using an appropriate foot placement location prior to contacting the ground. The planar foot placement estimator (FPE) method developed by Wight et al. is extended in this work in order to find foot placement locations in 3D to balance the 3D Euler pendulum. Preliminary experimental data shows that the 3D foot placement estimator (3DFPE) location corresponds very well with human foot placement during walking, gait termination, and when landing from a jump. In addition, a sensitivity analysis revealed that the assumptions of the 3DFPE are reasonable for human movement. Metrics for bipedal instability and balance performance suggested in this work could be of practical significance for health care professionals.

Push recovery and online gait generation for 3D bipeds with the foot placement estimator

“…The FPE is computed using the conservation of angular momentum in the 2D plane, by finding the angle φ where the total energy of the biped after swing foot impact is equal to the peak potential energy. In both [13] and [14], extensions of the 2D FPE concept are made to take 3D dynamics into account. In both approaches, the 3D dynamics are projected into a vertical plane which passes through the COM, but the computation of the plane orientation about the vertical axis differs between the two methods.…”

“…A fixed plane is chosen, requiring separate out-of-plane control of balance, in [12]. In [13], the "3D FPE" is defined, based on an "Euler pendulum" monoped model with a disc foot, such that their model is a direct 3D extension of the planar compass biped in [10]. Finally, [14] defines the Generalized FPE (GFPE) using a rimless spoked wheel model, which includes interesting predictive aspects and can handle non-level ground, but is only used to recover from external disturbances while at rest with no discussion of its use while walking.…”

“…In this work, the methods in [13] to calculate the 3D FPE are used to determine the FPE point for a 14-DOF lower-body humanoid robot. This point is then used as a control reference to inform both a high-level state machine and its associated task-level trajectory generator.…”

“…However, the first deals only with planar bipeds with point feet, while the second uses a constant plane of motion, requires separate lateral stabilization, and has very limited discussion of external disturbances. This work uses a continuously updating plane, similar to [13] and [14], which allows it to respond in 3D to unknown external disturbances. It also includes dynamic gait generation, unlike [14], and is used directly as part of a unified control method, as opposed to a measurement method such as in [13].…”

“…This work uses a continuously updating plane, similar to [13] and [14], which allows it to respond in 3D to unknown external disturbances. It also includes dynamic gait generation, unlike [14], and is used directly as part of a unified control method, as opposed to a measurement method such as in [13]. This paper's main contribution is the use of the 3D FPE in combination with a continuously updated FPE plane to achieve disturbance compensation both while standing and while in motion.…”