Effective Viscous Damping Enables Morphological Computation in Legged Locomotion

Muscle models and animal observations suggest that physical damping is beneficial for stabilization. Still, only a few implementations of mechanical damping exist in compliant robotic legged locomotion. It remains unclear how physical damping can be exploited for locomotion tasks, while its advantages as sensor-free, adaptive force- and negative work-producing actuators are promising. In a simplified numerical leg model, we studied the energy dissipation from viscous and Coulomb damping during vertical drops with ground-level perturbations. A parallel spring-damper is engaged between touch-down and mid-stance, and its damper auto-disengages during mid-stance and takeoff. Our simulations indicate that an adjustable and viscous damper is desired. In hardware we explored effective viscous damping and adjustability and quantified the dissipated energy. We tested two mechanical, leg-mounted damping mechanisms; a commercial hydraulic damper, and a custom-made pneumatic damper. The pneumatic damper exploits a rolling diaphragm with an adjustable orifice, minimizing Coulomb damping effects while permitting adjustable resistance. Experimental results show that the leg-mounted, hydraulic damper exhibits the most effective viscous damping. Adjusting the orifice setting did not result in substantial changes of dissipated energy per drop, unlike adjusting damping parameters in the numerical model. Consequently, we also emphasize the importance of characterizing physical dampers during real legged impacts to evaluate their effectiveness for compliant legged locomotion

Evaluating Morphological Computation in Muscle and DC-motor Driven Models of Human Hopping

In the context of embodied artificial intelligence, morphological computation refers to processes which are conducted by the body (and environment) that otherwise would have to be performed by the brain. Exploiting environmental and morphological properties is an important feature of embodied systems. The main reason is that it allows to significantly reduce the controller complexity. An important aspect of morphological computation is that it cannot be assigned to an embodied system per se, but that it is, as we show, behavior- and state-dependent. In this work, we evaluate two different measures of morphological computation that can be applied in robotic systems and in computer simulations of biological movement. As an example, these measures were evaluated on muscle and DC-motor driven hopping models. We show that a state-dependent analysis of the hopping behaviors provides additional insights that cannot be gained from the averaged measures alone. This work includes algorithms and computer code for the measures.Comment: 10 pages, 4 figures, 1 table, 5 algorithm

External control strategies for self-propelled particles: optimizing navigational efficiency in the presence of limited resources

We experimentally and numerically study the dependence of different navigation strategies regarding the effectivity of an active particle to reach a predefined target area. As the only control parameter, we vary the particle's propulsion velocity depending on its position and orientation relative to the target site. By introducing different figures of merit, e.g. the time to target or the total consumed propulsion energy, we are able to quantify and compare the efficiency of different strategies. Our results suggest, that each strategy to navigate towards a target, has its strengths and weaknesses and none of them outperforms the other in all regards. Accordingly, the choice of an ideal navigation strategy will strongly depend on the specific conditions and the figure of merit which should be optimized

Muscle preflex response to perturbations in locomotion: In vitro experiments and simulations with realistic boundary conditions

Neuromuscular control loops feature substantial communication delays, but mammals run robustly even in the most adverse conditions. In vivo experiments and computer simulation results suggest that muscles’ preflex—an immediate mechanical response to a perturbation—could be the critical contributor. Muscle preflexes act within a few milliseconds, an order of magnitude faster than neural reflexes. Their short-lasting action makes mechanical preflexes hard to quantify in vivo. Muscle models, on the other hand, require further improvement of their prediction accuracy during the non-standard conditions of perturbed locomotion. Our study aims to quantify the mechanical work done by muscles during the preflex phase (preflex work) and test their mechanical force modulation. We performed in vitro experiments with biological muscle fibers under physiological boundary conditions, which we determined in computer simulations of perturbed hopping. Our findings show that muscles initially resist impacts with a stereotypical stiffness response—identified as short-range stiffness—regardless of the exact perturbation condition. We then observe a velocity adaptation to the force related to the amount of perturbation similar to a damping response. The main contributor to the preflex work modulation is not the change in force due to a change in fiber stretch velocity (fiber damping characteristics) but the change in magnitude of the stretch due to the leg dynamics in the perturbed conditions. Our results confirm previous findings that muscle stiffness is activity-dependent and show that also damping characteristics are activity-dependent. These results indicate that neural control could tune the preflex properties of muscles in expectation of ground conditions leading to previously inexplicable neuromuscular adaptation speeds

The Benefit of Combining Neuronal Feedback and Feed-Forward Control for Robustness in Step Down Perturbations of Simulated Human Walking Depends on the Muscle Function

It is often assumed that the spinal control of human locomotion combines feed-forward central pattern generation with sensory feedback via muscle reflexes. However, the actual contribution of each component to the generation and stabilization of gait is not well understood, as direct experimental evidence for either is difficult to obtain. We here investigate the relative contribution of the two components to gait stability in a simulation model of human walking. Specifically, we hypothesize that a simple linear combination of feedback and feed-forward control at the level of the spinal cord improves the reaction to unexpected step down perturbations. In previous work, we found preliminary evidence supporting this hypothesis when studying a very reduced model of rebounding behaviors. In the present work, we investigate if the evidence extends to a more realistic model of human walking. We revisit a model that has previously been published and relies on spinal feedback control to generate walking. We extend the control of this model with a feed-forward muscle activation pattern. The feed-forward pattern is recorded from the unperturbed feedback control output. We find that the improvement in the robustness of the walking model with respect to step down perturbations depends on the ratio between the two strategies and on the muscle to which they are applied. The results suggest that combining feed-forward and feedback control is not guaranteed to improve locomotion, as the beneficial effects are dependent on the muscle and its function during walking

Weekly Time Course of Neuro-Muscular Adaptation to Intensive Strength Training

Detailed description of the time course of muscular adaptation is rarely found in literature. Thus, models of muscular adaptation are difficult to validate since no detailed data of adaptation are available. In this article, as an initial step toward a detailed description and analysis of muscular adaptation, we provide a case report of 8 weeks of intense strength training with two active, male participants. Muscular adaptations were analyzed on a morphological level with MRI scans of the right quadriceps muscle and the calculation of muscle volume, on a voluntary strength level by isometric voluntary contractions with doublet stimulation (interpolated twitch technique) and on a non-voluntary level by resting twitch torques. Further, training volume and isokinetic power were closely monitored during the training phase. Data were analyzed weekly for 1 week prior to training, pre-training, 8 weeks of training and 2 weeks of detraining (no strength training). Results show a very individual adaptation to the intense strength training protocol. While training volume and isokinetic power increased linearly during the training phase, resting twitch parameters decreased for both participants after the first week of training and stayed below baseline until de-training. Voluntary activation level showed an increase in the first 4 weeks of training, while maximum voluntary contraction showed only little increase compared to baseline. Muscle volume increased for both subjects. Especially training status seemed to influence the acute reaction to intense strength training. Fatigue had a major influence on performance and could only be overcome by one participant. The results give a first detailed insight into muscular adaptation to intense strength training on various levels, providing a basis of data for a validation of muscle fatigue and adaptation models

Spreading out Muscle Mass within a Hill-Type Model: A Computer Simulation Study

It is state of the art that muscle contraction dynamics is adequately described by a hyperbolic relation between muscle force and contraction velocity (Hill relation), thereby neglecting muscle internal mass inertia (first-order dynamics). Accordingly, the vast majority of modelling approaches also neglect muscle internal inertia. Assuming that such first-order contraction dynamics yet interacts with muscle internal mass distribution, this study investigates two questions: (i) what is the time scale on which the muscle responds to a force step? (ii) How does this response scale with muscle design parameters? Thereto, we simulated accelerated contractions of alternating sequences of Hill-type contractile elements and point masses. We found that in a typical small muscle the force levels off after about 0.2 ms, contraction velocity after about 0.5 ms. In an upscaled version representing bigger mammals' muscles, the force levels off after about 20 ms, and the theoretically expected maximum contraction velocity is not reached. We conclude (i) that it may be indispensable to introduce second-order contributions into muscle models to understand high-frequency muscle responses, particularly in bigger muscles. Additionally, (ii) constructing more elaborate measuring devices seems to be worthwhile to distinguish viscoelastic and inertia properties in rapid contractile responses of muscles

A geometry- and muscle-based control architecture for synthesising biological movement

A key problem for biological motor control is to establish a link between an idea of a movement and the generation of a set of muscle-stimulating signals that lead to the movement execution. The number of signals to generate is thereby larger than the body's mechanical degrees of freedom in which the idea of the movement may be easily expressed, as the movement is actually executed in this space. A mathematical formulation that provides a solving link is presented in this paper in the form of a layered, hierarchical control architecture. It is meant to synthesise a wide range of complex three-dimensional muscle-driven movements. The control architecture consists of a 'conceptional layer', where the movement is planned, a 'structural layer', where the muscles are stimulated, and between both an additional 'transformational layer', where the muscle-joint redundancy is resolved. We demonstrate the operativeness by simulating human stance and squatting in a three-dimensional digital human model (DHM). The DHM considers 20 angular DoFs and 36 Hill-type muscle-tendon units (MTUs) and is exposed to gravity, while its feet contact the ground via reversible stick-slip interactions. The control architecture continuously stimulates all MTUs ('structural layer') based on a high-level, torque-based task formulation within its 'conceptional layer'. Desired states of joint angles (postural plan) are fed to two mid-level joint controllers in the 'transformational layer'. The 'transformational layer' communicates with the biophysical structures in the 'structural layer' by providing direct MTU stimulation contributions and further input signals for low-level MTU controllers. Thereby, the redundancy of the MTU stimulations with respect to the joint angles is resolved, i.e. a link between plan and execution is established, by exploiting some properties of the biophysical structures modelled. The resulting joint torques generated by the MTUs via their moment arms are fed back to the conceptional layer, closing the high-level control loop. Within our mathematical formulations of the Jacobian matrix-based layer transformations, we identify the crucial information for the redundancy solution to be the muscle moment arms, the stiffness relations of muscle and tendon tissue within the muscle model, and the length-stimulation relation of the muscle activation dynamics. The present control architecture allows the straightforward feeding of conceptional movement task formulations to MTUs. With this approach, the problem of movement planning is eased, as solely the mechanical system has to be considered in the conceptional plan

Bioinspired preactivation reflex increases robustness of walking on rough terrain

Abstract Walking on unknown and rough terrain is challenging for (bipedal) robots, while humans naturally cope with perturbations. Therefore, human strategies serve as an excellent inspiration to improve the robustness of robotic systems. Neuromusculoskeletal (NMS) models provide the necessary interface for the validation and transfer of human control strategies. Reflexes play a crucial part during normal locomotion and especially in the face of perturbations, and provide a simple, transferable, and bio-inspired control scheme. Current reflex-based NMS models are not robust to unexpected perturbations. Therefore, in this work, we propose a bio-inspired improvement of a widely used NMS walking model. In humans, different muscles show an increase in activation in anticipation of the landing at the end of the swing phase. This preactivation is not integrated in the used reflex-based walking model. We integrate this activation by adding an additional feedback loop and show that the landing is adapted and the robustness to unexpected step-down perturbations is markedly improved (from 3 to 10 cm). Scrutinizing the effect, we find that the stabilizing effect is caused by changed knee kinematics. Preactivation, therefore, acts as an accommodation strategy to cope with unexpected step-down perturbations, not requiring any detection of the perturbation. Our results indicate that such preactivation can potentially enable a bipedal system to react adequately to upcoming unexpected perturbations and is hence an effective adaptation of reflexes to cope with rough terrain. Preactivation can be ported to robots by leveraging the reflex-control scheme and improves the robustness to step-down perturbation without the need to detect the perturbation. Alternatively, the stabilizing mechanism can also be added in an anticipatory fashion by applying an additional knee torque to the contralateral knee

Evaluating Morphological Computation in Muscle and DC-Motor Driven Models of Hopping Movements

In the context of embodied artificial intelligence, morphological computation refers to processes, which are conducted by the body (and environment) that otherwise would have to be performed by the brain. Exploiting environmental and morphological properties are an important feature of embodied systems. The main reason is that it allows to significantly reduce the controller complexity. An important aspect of morphological computation is that it cannot be assigned to an embodied system per se, but that it is, as we show, behavior and state dependent. In this work, we evaluate two different measures of morphological computation that can be applied in robotic systems and in computer simulations of biological movement. As an example, these measures were evaluated on muscle and DC-motor driven hopping models. We show that a state-dependent analysis of the hopping behaviors provides additional insights that cannot be gained from the averaged measures alone. This work includes algorithms and computer code for the measures