A simple CPG-based model to generate human hip moment pattern in walking by generating stiffness and equilibrium point trajectories

Abstract

Equilibrium point hypothesis (its developed version named as referent control theory)presents a theory about how the central nerves system (CNS) generates human movements. On the other hand, it has been shown that nerves circuits known as central pattern generators (CPG) likely produce motor commands to the muscles in rhythmic motions. In the present study, we designed a bio-inspired walking model, by coupling double pendulum to CPGs that produces equilibrium and stiffness trajectories as reciprocal and co-activation commands. As a basic model, it is has been shown that this model can regenerate pattern of a hip moment in the swing phase by high correlation ሺ ߩ ൌ 0 . 9 7 0 ሻ with experimental data. Moreover, it has been reported that a global electromyography (EMG) minima occurs in the mid-swing phase when the hip is more flexed in comparison with the other leg. Our model showed that equilibrium and actual hip angle trajectories match each other in mid-swing, similar to the mentioned posture, that is consistent with previous findings. Such a model can be used in active exoskeletons and prosthesis to make proper active stiffness and torque.controls the body?" [3, 4]. These theories explain how the CNS can release from complex calculations to control movements. According to EPH, at the muscle level, the CNS only determines a specific threshold (ߣ) for muscle [5, 6]. If actual muscle length goes beyond the defined threshold, EMG activity emerges as a result of the gap between actual and threshold muscle lengths. To control the joint, two commands are defined by the CNS: reciprocal (R) command and co-activation (C) command [7]. If joint is considered as rotational spring, R and C commands determine equilibrium point and stiffness of the joint, respectively. In accordance with the referent control theory, for multi-joint system (e.g. leg), it is assumed that initially, global R and C commands are set by CNS, then, by few-to-many mappings, r and c commands for various joints are defined. Finally, ߣ s for agonist and antagonist muscles emerged from these r and c by another mapping [8]. This hierarchical system is effective for making coordination between different joints and muscles [9]. One of the powerful experimental evidence for this hierarchical referent system is the global EMG minima [10]. When the referent (R) and actual configurations approach meet each other, a minimum EMG activity occurs for most of the muscles involved in the task [10]. This phenomena has been confirmed by many studies on various tasks such as walking and jumping [10], monkeys head movement [11], Jete in ballet dancers [12], and hammering [13]. It is shown that during stepping forward, a global EMG minima occurred during mid-swing when the hip flexion of the swing leg is slightly more than the other leg [14].On the other hand, the behavior of the joints as a rotational spring have commonly been used for investigating the relationship between torque(s) and angle(s). These studies are applicable to design anthropomorphic biped robots [15][16][...