A Work-Loop Method for Characterizing Leg Function During Sagittal Plane Movements

An actuated dissipative spring-mass walking model: Predicting human-like ground reaction forces and the effects of model parameters

Simple models are widely used to understand the mechanics of human walking. The optimization-based minimal biped model and spring-loaded-inverted-pendulum (SLIP) model are two popular models that can achieve human-like walking patterns. However, ground reaction forces (GRF) from these two models still deviate from experimental data. In this paper, we proposed an actuated dissipative spring-mass model by integrating these two models to realize more human-like GRF patterns. We first explored the function of stiffness, damping, and weights of both energy cost and force cost in the objective function and found that these parameters have distinctly different influences on the optimized gait and GRF profiles. The stiffness and objective weight affect the number and size of peaks in the vertical GRF and stance time. The damping changes the relative size of the peaks but has little influence on stance time. Based on these observations, these parameters were manually tuned at three different speeds to approach experimentally measured vertical GRF and the highest correlation coefficient can reach 0.983. These results indicate that the stiffness, damping, and proper objective functions are all important factors in achieving human-like motion for this simple walking model. These findings can facilitate the understanding of human walking dynamics and may be applied in future biped models.

Human-like hopping in machines : Feedback- versus feed-forward-controlled motions

Template models of legged locomotion are powerful tools for gait analysis, but can also inspire robot design and control. In this paper, a spring-loaded inverted pendulum (SLIP) model is employed to control vertical hopping of a 2-segmented legged robot. Feed-forward and bio-inspired virtual model control using the SLIP model are compared. In the latter approach, the feedback control emulates a virtual spring between hip and foot. The results demonstrate similarity of human and robot hopping. Moreover, the feedback control proves to simplify and improve hopping control. It yields better perturbation recovery and locomotion adaptation and is even easier to tune. Thus, human-like hopping is achievable using a rather simple template-based controller, which ensures the required performance, robustness and versatility.

The rotary component of leg force during walking and running

The component of ground reaction force (GRF) acting perpendicular to the leg in the sagittal plane during human locomotion (acting in a rotary direction) has not been systematically investigated and is not well understood. In this paper, we investigate this rotary component of the GRF of 11 human subjects (mean age ± s.d.: 26.6 ± 2.9 years) while walking and speed walking on a treadmill, along with eight human subjects (mean age ± s.d.: 26.3 ± 3.1) running on a treadmill. The GRF on both legs was measured, along with estimates of the subject's mass centre and the centre of pressure of each foot to yield total leg lengths and leg angle. Across all steady walking and running speeds, we find that the rotary component of the GRF has significant magnitude (peak values from 5% to 38% of body weight, from slow walking to moderate running, respectively) and implies leg propulsion of the mass centre in the rotary direction. Furthermore, peak rotary force magnitude over stance increases with locomotion speed for both walking and running ( p < 0.05), and the time-averaged (mean) rotary force shows a slight increase with walking speed (though the mean force trend is uncertain for running). Also, an estimate of average power input from the rotary force of the leg acting at the mass centre shows moderate and strong positive correlation with locomotion speed for running and walking respectively ( p < 0.05). This study also shows that the rotary force acts differently in walking versus running: rotary force is predominantly positive during running, but during walking it exhibits both positive and negative phases with net positive force found over the whole stride.

Exploiting elasticity: Modeling the influence of neural control on mechanics and energetics of ankle muscle-tendons during human hopping

We present a simplified Hill-type model of the human triceps surae-Achilles tendon complex working on a gravitational-inertial load during cyclic contractions (i.e. vertical hopping). Our goal was to determine the role that neural control plays in governing muscle, or contractile element (CE), and tendon, or series elastic element (SEE), mechanics and energetics within a compliant muscle-tendon unit (MTU). We constructed a 2D parameter space consisting of many combinations of stimulation frequency and magnitude (i.e. neural control strategies). We compared the performance of each control strategy by evaluating peak force and average positive mechanical power output for the system (MTU) and its respective components (CE, SEE), force-length (F-L) and -velocity (F-V) operating point of the CE during active force production, average metabolic rate for the CE, and both MTU and CE apparent efficiency. Our results suggest that frequency of stimulation plays a primary role in governing whole-MTU mechanics. These include the phasing of both activation and peak force relative to minimum MTU length, average positive power, and apparent efficiency. Stimulation amplitude was primarily responsible for governing average metabolic rate and within MTU mechanics, including peak force generation and elastic energy storage and return in the SEE. Frequency and amplitude of stimulation both played integral roles in determining CE F-L operating point, with both higher frequency and amplitude generally corresponding to lower CE strains, reduced injury risk, and elimination of the need for passive force generation in the CE parallel elastic element (PEE).