Physics-based simulation generate movement patterns based on a neuro-musculoskeletal model without relying on experimental movement data, offering a powerful approach to study how neuro-musculoskeletal properties shape locomotion. Yet, simulated gait patterns and metabolic powers do not always agree with experiments, pointing to modeling errors reflecting gaps in our understanding. Here, we systematically evaluated the predictive capability of simulations based on a 3D musculoskeletal model to predict gait mechanics, muscle activity, and metabolic power across gait conditions. We simulated the effect of adding mass to body segments, variations in walking speed, inclined walking, and crouched walking. We chose tasks that are relatively straightforward to model to limit the contribution of errors in modeling the task to prediction errors. The simulations predicted stride frequency and walking kinematics with reasonable accuracy but underestimated variation in metabolic power across conditions. In particular, simulations underestimated changes in metabolic power with respect to level walking in tasks requiring substantial positive mechanical work, such as incline walking (27% underestimation). We identified two possible errors in simulated metabolic power. First, the phenomenological metabolic power model produced high maximal mechanical efficiency (average 0.58) during concentric contractions, compared to the observed 0.2-0.3 in laboratory experiments. Second, when we multiplied the mechanical work with more realistic estimates of mechanical efficiency (i.e., 0.25), simulations overestimated the metabolic power by 84%. This suggests that positive work by muscle fibers was overestimated in the simulations. This overestimation may be caused by several assumptions and errors in (the parameters of) the musculoskeletal model including its interaction with the environment or in the cost function. This study highlights the need for more accurate models of musculoskeletal mechanics, energetics, passive elastic structures, and neural control (e.g., optimality criteria) to improve the realism of human movement simulations. Validating simulations across a broad range of conditions is important to pinpoint shortcomings in model-based simulations.

The unique structure of the human foot is seen as a crucial adaptation for bipedalism. The foot's arched shape enables stiffening the foot to withstand high loads when pushing off, without compromising foot flexibility. Experimental studies demonstrated that manipulating foot stiffness has considerable effects on gait. In clinical practice, altered foot structure is associated with pathological gait. Yet, experimentally manipulating individual foot properties (e.g. arch height or tendon and ligament stiffness) is hard and therefore our understanding of how foot structure influences gait mechanics is still limited. Predictive simulations are a powerful tool to explore causal relationships between musculoskeletal properties and whole-body gait. However, musculoskeletal models used in three-dimensional predictive simulations assume a rigid foot arch, limiting their use for studying how foot structure influences three-dimensional gait mechanics. Here, we developed a four-segment foot model with a longitudinal arch for use in predictive simulations. We identified three properties of the ankle-foot complex that are important to capture ankle and knee kinematics, soleus activation, and ankle power of healthy adults: (1) compliant Achilles tendon, (2) stiff heel pad, (3) the ability to stiffen the foot. The latter requires sufficient arch height and contributions of plantar fascia, and intrinsic and extrinsic foot muscles. A reduced ability to stiffen the foot results in walking patterns with reduced push-off power. Simulations based on our model also captured the effects of walking with anaesthetised intrinsic foot muscles or an insole limiting arch compression. The ability to reproduce these different experiments indicates that our foot model captures the main mechanical properties of the foot. The presented four-segment foot model is a potentially powerful tool to study the relationship between foot properties and gait mechanics and energetics in health and disease.

The metabolic energy rate of individual muscles is impossible to measure without invasive procedures. Prior studies have produced models to predict metabolic rates based on experimental observations of isolated muscle contraction from various species. Such models can provide reliable predictions of metabolic rates in humans if muscle properties and control are accurately modeled. This study aimed to examine how muscle-tendon model individualization and metabolic energy models influenced estimation of muscle-tendon states and time-series metabolic rates, to evaluate the agreement with empirical data, and to provide predictions of the metabolic rate of muscle groups and gait phases across walking speeds. Three-dimensional musculoskeletal simulations with prescribed kinematics and dynamics were performed. An optimal control formulation was used to compute muscle-tendon states with four levels of individualization, ranging from a scaled generic model and muscle controls based on minimal activations, inclusion of calibrated muscle passive forces, personalization of Achilles and quadriceps tendon stiffnesses, to finally informing muscle controls with electromyography. We computed metabolic rates based on existing models. Simulations with calibrated passive forces and personalized tendon stiffness most accurately estimate muscle excitations and fiber lengths. Interestingly, the inclusion of electromyography did not improve our estimates. The whole-body average metabolic cost was better estimated with a subset of metabolic energy models. We estimated metabolic rate peaks near early stance, pre-swing, and initial swing at all walking speeds. Plantarflexors accounted for the highest cost among muscle groups at the preferred speed and were similar to the cost of hip adductors and abductors combined. Also, the swing phase accounted for slightly more than one-quarter of the total cost in a gait cycle, and its relative cost decreased with walking speed. Our prediction might inform the design of assistive devices and rehabilitation treatment. The code and experimental data are available online.

Balance impairments are common in cerebral palsy. When balance is perturbed by backward support surface translations, children with cerebral palsy have increased co-activation of the plantar flexors and tibialis anterior muscle as compared to typically developing children. However, it is unclear whether increased muscle co-activation is a compensation strategy to improve balance control or is a consequence of reduced reciprocal inhibition. During translational perturbations, increased joint stiffness due to co-activation might aid balance control by resisting movement of the body with respect to the feet. In contrast, during rotational perturbations, increased joint stiffness will hinder balance control as it couples body to platform rotation. Therefore, we expect increased muscle co-activation in response to rotational perturbations if co-activation is caused by reduced reciprocal inhibition but not if it is merely a compensation strategy. We perturbed standing balance by combined backward translational and toe-up rotational perturbations in 20 children with cerebral palsy and 20 typically developing children. Perturbations induced forward followed by backward movement of the center of mass. We evaluated reactive muscle activity and the relation between center of mass movement and reactive muscle activity using a linear feedback model based on center of mass kinematics. In typically developing children, perturbations induced plantar flexor balance correcting muscle activity followed by tibialis anterior balance correcting muscle activity, which was driven by center of mass movement. In children with cerebral palsy, the switch from plantar flexor to tibialis anterior activity was less pronounced than in typically developing children due to increased muscle co-activation of the plantar flexors and tibialis anterior throughout the response. Our results thus suggest that a reduction in reciprocal inhibition causes muscle co-activation in reactive standing balance in children with cerebral palsy.

Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while neglecting physiological noise, and stochastic simulations account for noise while simplifying the dynamics. We took advantage of recent approaches where stochastic optimal control problems are approximated using deterministic optimal control problems, which can be solved efficiently using direct collocation. We were thus able to extend predictions of stochastic optimal control as a theory of motor coordination to include muscle coordination and movement patterns emerging from non-linear musculoskeletal dynamics. In stochastic optimal control simulations of human standing balance, we demonstrated that the inclusion of muscle dynamics can predict muscle co-contraction as minimal effort strategy that complements sensorimotor feedback control in the presence of sensory noise. In simulations of reaching, we demonstrated that nonlinear multi-segment musculoskeletal dynamics enables complex perturbed and unperturbed reach trajectories under a variety of task conditions to be predicted. In both behaviors, we demonstrated how interactions between task constraint, sensory noise, and the intrinsic properties of muscle influence optimal muscle coordination patterns, including muscle co-contraction, and the resulting movement trajectories. Our approach enables a true minimum effort solution to be identified as task constraints, such as movement accuracy, can be explicitly imposed, rather than being approximated using penalty terms in the cost function. Our approximate stochastic optimal control framework predicts complex features, not captured by previous simulation approaches, providing a generalizable and valuable tool to study how musculoskeletal dynamics and physiological noise may alter neural control of movement in both healthy and pathological movements.

Standing and walking balance control in humans relies on the transformation of sensory information to motor commands that drive muscles. Here, we evaluated whether sensorimotor transformations underlying walking balance control can be described by task-level center of mass kinematics feedback similar to standing balance control. We found that delayed linear feedback of center of mass position and velocity, but not delayed linear feedback from ankle angles and angular velocities, can explain reactive ankle muscle activity and joint moments in response to perturbations of walking across protocols (discrete and continuous platform translations and discrete pelvis pushes). Feedback gains were modulated during the gait cycle and decreased with walking speed. Our results thus suggest that similar task-level variables, i.e. center of mass position and velocity, are controlled across standing and walking but that feedback gains are modulated during gait to accommodate changes in body configuration during the gait cycle and in stability with walking speed. These findings have important implications for modelling the neuromechanics of human balance control and for biomimetic control of wearable robotic devices. The feedback mechanisms we identified can be used to extend the current neuromechanical models that lack balance control mechanisms for the ankle joint. When using these models in the control of wearable robotic devices, we believe that this will facilitate shared control of balance between the user and the robotic device.

The arrangement and physiology of muscle fibres can strongly influence musculoskeletal function and whole-organismal performance. However, experimental investigation of muscle function during in vivo activity is typically limited to relatively few muscles in a given system. Computational models and simulations of the musculoskeletal system can partly overcome these limitations, by exploring the dynamics of muscles, tendons and other tissues in a robust and quantitative fashion. Here, a high-fidelity, 26-degree-of-freedom musculoskeletal model was developed of the hindlimb of a small ground bird, the elegant-crested tinamou (Eudromia elegans, ~550 g), including all the major muscles of the limb (36 actuators per leg). The model was integrated with biplanar fluoroscopy (XROMM) and forceplate data for walking and running, where dynamic optimization was used to estimate muscle excitations and fibre length changes throughout both gaits. Following this, a series of static simulations over the total range of physiological limb postures were performed, to circumscribe the bounds of possible variation in fibre length. During gait, fibre lengths for all muscles remained between 0.5 to 1.21 times optimal fibre length, but operated mostly on the ascending limb and plateau of the active force-length curve, a result that parallels previous experimental findings for birds, humans and other species. However, the ranges of fibre length varied considerably among individual muscles, especially when considered across the total possible range of joint excursion. Net length change of muscle-tendon units was mostly less than optimal fibre length, sometimes markedly so, suggesting that approaches that use muscle-tendon length change to estimate optimal fibre length in extinct species are likely underestimating this important parameter for many muscles. The results of this study clarify and broaden understanding of muscle function in extant animals, and can help refine approaches used to study extinct species.

Using joint actuators to drive the skeletal movements is a common practice in character animation, but the resultant torque patterns are often unnatural or infeasible for real humans to achieve. On the other hand, physiologically-based models explicitly simulate muscles and tendons and thus produce more human-like movements and torque patterns. This paper introduces a technique to transform an optimal control problem formulated in the muscle-actuation space to an equivalent problem in the joint-actuation space, such that the solutions to both problems have the same optimal value. By solving the equivalent problem in the joint-actuation space, we can generate human-like motions comparable to those generated by musculotendon models, while retaining the benefit of simple modeling and fast computation offered by joint-actuation models. Our method transforms constant bounds on muscle activations to nonlinear, state-dependent torque limits in the joint-actuation space. In addition, the metabolic energy function on muscle activations is transformed to a nonlinear function of joint torques, joint configuration and joint velocity. Our technique can also benefit policy optimization using deep reinforcement learning approach, by providing a more anatomically realistic action space for the agent to explore during the learning process. We take the advantage of the physiologically-based simulator, OpenSim, to provide training data for learning the torque limits and the metabolic energy function. Once trained, the same torque limits and the energy function can be applied to drastically different motor tasks formulated as either trajectory optimization or policy learning.

An increasing number of robotic systems are using compliant actuators in which springs are placed in series with the actuator. The need for identification procedures tailored to these systems is consequently rising. When measurements of both the link side and the motor side of the spring are available the dynamic parameters can be identified independent of the spring model. The excitation of the identification procedure is optimized for the identification of the dynamical parameters to provide a rich data set by maximizing a reduced information matrix. Adopting this reduced matrix leads to a near-optimal excitation. A Fourier series is chosen as parametrization of the excitation, resulting in a periodic movement of the system under identification. This periodicity is exploited to develop an alternative weighting of the parameter estimation. This proposed weighting uses the motor torque variance at each time step of the trajectory, instead of one global torque variance. This identification procedure is demonstrated and validated on one leg of a lower limb exoskeleton. Only the dynamic model in the sagital plane (2D) is identified.

This paper presents a unified task specification formalism and a unified control scheme for the lowest control level of sensor-based robot tasks. The formalism is based on: (i) the integration of any sensor that provides (direct or indirect) distance (and time derivatives) and force information; (ii) the possibility to use multiple "Tool Centre Points", e.g. defined relative to the robot end effector, other links or the environment; (iii) the integration of optimization functions for underconstrained as well as overconstrained specifications with linear constraints; (iv) the integration of on-line estimators; and (v) compatibility with all major low level control approaches. The unified formalism applies to the whole range from industrial manipulators over cooperating robots to humanoid robots, and from pure position control tasks over industrial processes to interaction between a humanoid robot and its environment.