Sten Grimmer

Intelligence by mechanics.

Research on the biomechanics of animal and human locomotion provides insight into basic principles of locomotion and respective implications for construction and control. Nearly elastic operation of the leg is necessary to reproduce the basic dynamics in walking and running. Elastic leg operation can be modelled with a spring-mass model. This model can be used as a template with respect to both gaits in the construction and control of legged machines. With respect to the segmented leg, the humanoid arrangement saves energy and ensures structural stability. With the quasi-elastic operation the leg inherits the property of self-stability, i.e. the ability to stabilize a system in the presence of disturbances without sensing the disturbance or its direct effects. Self-stability can be conserved in the presence of musculature with its crucial damping property. To ensure secure foothold visco-elastic suspended muscles serve as shock absorbers. Experiments with technically implemented leg models, which explore some of these principles, are promising.

Running on uneven ground: leg adjustment to vertical steps and self-stability.

SUMMARY Human running is characterized by comparably simple whole-body dynamics. These dynamics can be modelled with a point mass bouncing on a spring leg. Theoretical studies using such spring–mass models predict that running can be self-stable. In simulations, this self-stability allows for running on uneven ground without paying attention to the ground irregularities. Whether humans actually use this property of the mechanical system in such an irregular environment is, however, unclear. One way to approach this question is to study how the leg stiffness in stance and the leg orientation in flight are changed in response to ground perturbations. Here, for 11 human subjects we studied two consecutive contacts during running on uneven ground with a force plate of adjustable height (step of +5, +10 and +15 cm). We found that runners adjust their leg stiffness to the height of a vertical step. The adjustment is characterized by a 9% increase in leg stiffness in preparation for the perturbation and by a systematic decrease in proportion to the step height. At the highest vertical step (+15 cm), leg stiffness was reduced by about 26%. We also observed that the angle of attack decreased from 68 deg. to 62 deg. with increasing ground height. These leg adjustments are in accordance with the predictions of a stable spring–mass system. Furthermore, we could describe the identified leg forces and leg compressions with a simple spring–mass simulation for a given body mass, leg stiffness, angle of attack and initial conditions. We compared the experimental findings with the self-stabilizing properties of the spring–mass model, and discuss how humans use a combination of strategies that include purely mechanical self-stabilization and active neuromuscular control. Finally, beyond self-stability, we suggest that control may apply to smooth centre of mass kinematics.

Running on uneven ground: Leg adjustments by muscle pre-activation control

In locomotion, humans have to deal with irregularities of the ground, i.e., pathways covered with stones, grass, or roots. When they encounter ground with changes in terrain height they seem to use spring-mass dynamics to help passively stabilize their locomotory trajectory. With increasing step heights humans reduce their leg stiffness, but it is as of yet unclear whether these leg adjustments are purely passively achieved or actively in a feed-forward manner. For this, we investigated the stiffness regulation in the ankle and knee joint and analyzed the correlation between EMG, kinematic, and dynamic parameters. Nine healthy participants were running along a 17m runway with a force plate of adjustable height (steps of 0, +5, +10, and +15cm). Whole body kinematics was monitored along with surface electromyography of three selected bilateral lower limb muscles. We found that the stiffness of the ankle joint is adjusted to the vertical height of a step, in a manner similar to global leg stiffness. Furthermore, the integrated 100ms pre-activation of the m. gastrocnemius medialis (GM) depends on the vertical height of a step and correlates highly significantly with the activation of the GM but also with kinematics and dynamics. Consequently, we identified the pre-activation control as a key for altering the leg posture in preparation for altered ground properties (e.g., the height of a step or an obstacle). During the stance phase the control of activation plays a minor role since geometry and the initial conditions (e.g., leg length, landing angle, and landing velocity) ensure an adequate adjustment of joint stiffness as well as leg stiffness.

All leg joints contribute to quiet human stance: A mechanical analysis

According to the state of the art model (single inverted pendulum) the regulation of quiet human stance seems to be dominated by ankle joint actions. Recent findings substantiated both in-phase and anti-phase fluctuations of ankle and hip joint kinematics can be identified in quiet human stance. Thus, we explored in an experimental study to what extent all three leg joints actually contribute to the balancing problem of quiet human stance. We also aimed at distinguishing kinematic from torque contributions. Thereto, we directly measured ankle, knee, and hip joint kinematics with high spatial resolution and ground reaction forces. Then, we calculated the six respective joint torques and, additionally, the centre of mass kinematics. We searched for high cross-correlations between all these mechanical variables. Beyond confirming correlated anti-phase kinematics of ankle and hip, the main results are: (i) ankle and knee joint fluctuate tightly (torque) coupled and (ii) the bi-articular muscles of the leg are well suited to fulfil the requirements of fluctuations around static equilibrium. Additionally, we (iii) identified high-frequency oscillations of the shank between about 4 and 8 Hz and (iv) discriminated potentially passive and active joint torque contributions. These results demonstrate that all leg joints contribute actively and concertedly to quiet human stance, even in the undisturbed case. Moreover, they substantiate the single inverted pendulum paradigm to be an invalid model for quiet human stance.

The role of intrinsic muscle properties for stable hopping—stability is achieved by the force–velocity relation

A reductionist approach was presented to investigate which level of detail of the physiological muscle is required for stable locomotion. Periodic movements of a simplified one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements) were analyzed. Force-length and force-velocity relations of the muscle were varied in three levels of approximation (constant, linear and Hill-shaped nonlinear) resulting in nine different hopping models of different complexity. Stability of these models was evaluated by return map analysis and the performance by the maximum hopping height. The simplest model (constant force-length and constant force-velocity relations) outperformed all others in the maximum hopping height but was unstable. Stable hopping was achieved with linear and Hill-shaped nonlinear characteristic of the force-velocity relation. The characteristics of the force-length relation marginally influenced hopping stability. The results of this approach indicate that the intrinsic properties of the contractile element are responsible for stabilization of periodic movements. This connotes that (a) complex movements like legged locomotion could benefit from stabilizing effects of muscle properties, and (b) technical systems could benefit from the emerging stability when implementing biological characteristics into artificial muscles.

Integration of intrinsic muscle properties, feed-forward and feedback signals for generating and stabilizing hopping

It was hypothesized that a tight integration of feed-forward and feedback-driven muscle activation with the characteristic intrinsic muscle properties is a key feature of locomotion in challenging environments. In this simulation study it was investigated whether a combination of feed-forward and feedback signals improves hopping stability compared with those simulations with one individual type of activation. In a reduced one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements), the level of detail of the muscles force–length–velocity relation and the type of activation generation (feed-forward, feedback and combination of both) were varied to test their influence on periodic hopping. The stability of the hopping patterns was evaluated by return map analysis. It was found that the combination of feed-forward and proprioceptive feedback improved hopping stability. Furthermore, the nonlinear Hill-type representation of intrinsic muscle properties led to a faster reduction of perturbations than a linear approximation, independent of the type of activation. The results emphasize the ability of organisms to exploit the stabilizing properties of intrinsic muscle characteristics.

Energy management that generates terrain following versus apex-preserving hopping in man and machine

While hopping, 12 subjects experienced a sudden step down of 5 or 10 cm. Results revealed that the hopping style was “terrain following”. It means that the subjects pursued to keep the distance between maximum hopping height (apex) and ground profile constant. The spring-loaded inverse pendulum (SLIP) model, however, which is currently considered as template for stable legged locomotion would predict apex-preserving hopping, by which the absolute maximal hopping height is kept constant regardless of changes of the ground level. To get more insight into the physics of hopping, we outlined two concepts of energy management: “constant energy supply”, by which in each bounce—regardless of perturbations—the same amount of mechanical energy is injected, and “lost energy supply”, by which the mechanical energy that is going to be dissipated in the current cycle is assessed and replenished. When tested by simulations and on a robot testbed capable of hopping, constant energy supply generated stable and robust terrain following hopping, whereas lost energy supply led to something like apex-preserving hopping, which, however, lacks stability as well as robustness. Comparing simulated and machine hopping with human hopping suggests that constant energy supply has a good chance to be used by humans to generate hopping.

Combining forces and kinematics for calculating consistent centre of mass trajectories

SUMMARY The motion of centre of mass (CoM) is a fundamental object of investigation in biomechanical analysis. In principle, the CoM motion can either be calculated from force data (dynamic method) or motion capture data (kinematic method). In both approaches, the accuracy of the calculated trajectories depends on the quality of the original signals. Interestingly, the inaccuracies in each method are related to different parts of the Fourier spectrum. Here, we present a new approach to compute CoM motion based on the reliable frequency range of force and kinematic measurements. As a result we obtain physically consistent CoM and force signals, i.e. the second derivative of the CoM trajectory equals the force. The algorithm is verified on simulation data and applied to selected experimental data. We show that the new algorithm can eliminate typical inaccuracies inherent in kinematic and force signals. Also, we discuss the biological and technical origins of these findings.

Phase synchronisation of the three leg joints in quiet human stance.

Quiet human stance is a dynamic multi-segment phenomenon. In literature, coupled ankle and hip actions are in the focus and examinations are usually restricted to frequency contributions below 4 Hz. Very few studies point to the knee playing an active role, and just one study gives evidence of higher frequency contributions. In order to investigate the dynamic coupling of all three leg joints in more depth, we revisited an experimental data set on quiet human stance. Since phase synchronisation is a strong indicator of non-linear coupling behind, we used the phase synchronisation index (PSI) to quantify the degree of leg joint coupling as a function of frequency. One main result is that we did not find any synchronisation between ankle and hip across the whole frequency range examined up to 8 Hz. In contrast, there is significant synchronisation between ankle and knee at a couple of frequencies between 1.25 Hz and 8 Hz when looking at the kinematics. Their joint torques rather synchronise below 2 Hz. There is also synchronisation between knee and hip kinematics above 6 Hz, however, only significant at one frequency bin in our data set. From this, we would infer that the multiple mechanical degrees of freedom contributing to quiet human stance should be chosen according to, thus map, physiology. Thereby, the knee is indispensable and bi-articular muscles play a central role in organising quiet human stance. Examining the non-stationarity of phase synchronisations will probably advance the understanding of self-organisation of quiet human stance.Quiet human stance is a dynamic multi-segment phenomenon. In literature, coupled ankle and hip actions are in the focus and examinations are usually restricted to frequency contributions below 4 Hz. Very few studies point to the knee playing an active role, and just one study gives evidence of higher frequency contributions. In order to investigate the dynamic coupling of all three leg joints in more depth, we revisited an experimental data set on quiet human stance. Since phase synchronisation is a strong indicator of non-linear coupling behind, we used the phase synchronisation index (PSI) to quantify the degree of leg joint coupling as a function of frequency. One main result is that we did not find any synchronisation between ankle and hip across the whole frequency range examined up to 8 Hz. In contrast, there is significant synchronisation between ankle and knee at a couple of frequencies between 1.25 Hz and 8 Hz when looking at the kinematics. Their joint torques rather synchronise below 2 Hz. There is also synchronisation between knee and hip kinematics above 6 Hz, however, only significant at one frequency bin in our data set. From this, we would infer that the multiple mechanical degrees of freedom contributing to quiet human stance should be chosen according to, thus map, physiology. Thereby, the knee is indispensable and bi-articular muscles play a central role in organising quiet human stance. Examining the non-stationarity of phase synchronisations will probably advance the understanding of self-organisation of quiet human stance. 2010 Elsevier B.V. All rights reserved.

Foot Function in Spring Mass Running

The leg function in human running can be characterized by spring-like behaviour. The human leg itself has several segments, which influence the leg function. In this paper a simple model based on spring-mass-running but with with a compliant ankle joint is introduced to investigate the influence of a rigid foot segment. The predicted force-length-curve explains changes in leg stiffness as well as changes in leg length during stance phase similar to what is observed in human running.