Walking Stability of a Variable Length Inverted Pendulum Controlled with Virtual Constraints

Abstract

Bipedal walking is a complex phenomenon that is not fully understood. Simplified models make it easier to highlight the important features. Here, the variable length inverted pendulum (VLIP) model is used, which has the particularity of taking into account the vertical oscillations of the center of mass (CoM). When the desired walking gait is defined as virtual constraints, i.e., as functions of a phasing variable and not on time, for the evolution of the swing foot and the vertical oscillation of the CoM, the walk will asymptotically converge to the periodic motion under disturbance with proper choice of the virtual constraints, thus a self-stabilization is obtained. It is shown that the vertical CoM oscillation, positions of the swing foot and the choice of the switching condition play crucial roles in stability. Moreover, a PI controller of the CoM velocity along the sagittal axis is also proposed such that the walking speed of the robot can converge to another periodic motion with a different walking speed. In this way, a natural walking gait is illustrated as well as the possibility of velocity adaptation as observed in human walking.

A self‐stabilised walking gait for humanoid robots based on the essential model with internal states

“…By considering the stability conditions discussed in the previous section, simulations will be performed for robots Romeo and TALOS in this section. The starting phase strategy used in [22] is applied here. Since the motion at the starting phase does not affect the stability of walking during the periodic motion, the starting phase strategy will not be discussed here.…”

“…As observed in human walking, the CoM of human beings is not constant during a step [29]. It has been proven in [22] that the vertical CoM velocity v m being negative at transition is crucial for obtaining stability for an inverted pendulum when no high‐level control is performed. How the vertical CoM motion affects walking stability of the robot Romeo is analysed here.…”

“…This model has been used to present the notion of self‐synchronization and self‐stabilisation [21]. The walking algorithm proposed in [21] has been extended in [22] by taking into account the vertical oscillation of the centre of mass (CoM). It has been proven in [22] that the vertical oscillation of the CoM contributes to obtaining self‐stabilisation during the walk.…”

“…The walking algorithm proposed in [21] has been extended in [22] by taking into account the vertical oscillation of the centre of mass (CoM). It has been proven in [22] that the vertical oscillation of the CoM contributes to obtaining self‐stabilisation during the walk. Given the results of simplified models, the extension of the walking algorithm considering the full dynamics of the robot is studied in this paper.…”

Comprehensive Review of Different Pendulum Structures in Engineering Applications

“…Figure8(b) shows a kinematic representation of a double pendulum with a variable length (DPVL), which provides a simplified and accurate model for planning static and dynamic human-like robots. Both the static and motion dynamics of human postures can be described with the variable parameters of the DPVL [37][38][39].…”