Minimally Actuated Walking: Identifying Core Challenges to Economical Legged Locomotion Reveals Novel Solutions

Estimating Gaits of an Ancient Crocodile-Line Archosaur Through Trajectory Optimization, With Comparison to Fossil Trackways

Fossil trackways provide a glimpse into the behavior of extinct animals. However, while providing information of the trackmaker size, stride, and even speed, the actual gait of the organism can be ambiguous. This is especially true of quadrupedal animals, where disparate gaits can have similar trackway patterns. Here, predictive simulation using trajectory optimization can help distinguish gaits used by trackmakers. First, we demonstrated that a planar, five-link quadrupedal biomechanical model can generate the qualitative trackway patterns made by domestic dogs, although a systematic error emerges in the track phase (relative distance between ipsilateral pes and manus prints). Next, we used trackway dimensions as inputs to a model of Batrachotomus kupferzellensis, a long-limbed, crocodile-line archosaur (clade Pseudosuchia) from the Middle Triassic of Germany. We found energetically optimal gaits and compared their predicted track phases to those of fossil trackways of Isochirotherium and Brachychirotherium. The optimal results agree with trackways at slow speeds but differ at faster speeds. However, all simulations point to a gait transition around a non-dimensional speed of 0.4 and another at 1.0. The trackways likewise exhibit stark differences in the track phase at these speeds. In all cases, including when simulations are constrained to the fossil track phase, the optimal simulations after the first gait transition do not correspond to a trot, as often used by living crocodiles. Instead, they are a diagonal sequence gait similar to the slow tölt of Icelandic horses. This is the first evidence that extinct pseudosuchians may have exhibited different gaits than their modern relatives and of a gait transition in an extinct pseudosuchian. The results of this analysis highlight areas where the models can be improved to generate more reliable predictions for fossil data while also showcasing how simple models can generate insights about the behavior of extinct animals.

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic "Spring-mass" computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.

Evaluating the energetics of entrainment in a human-machine coupled oscillator system

During locomotion, humans sometimes entrain (i.e. synchronize) their steps to external oscillations: e.g. swaying bridges, tandem walking, bouncy harnesses, vibrating treadmills, exoskeletons. Previous studies have discussed the role of nonlinear oscillators (e.g. central pattern generators) in facilitating entrainment. However, the energetics of such interactions are unknown. Given substantial evidence that humans prioritize economy during locomotion, we tested whether reduced metabolic expenditure is associated with human entrainment to vertical force oscillations, where frequency and amplitude were prescribed via a custom mechatronics system during walking. Although metabolic cost was not significantly reduced during entrainment, individuals expended less energy when the oscillation forces did net positive work on the body and roughly selected phase relationships that maximize positive work. It is possible that individuals use mechanical cues to infer energy cost and inform effective gait strategies. If so, an accurate prediction may rely on the relative stability of interactions with the environment. Our results suggest that entrainment occurs over a wide range of oscillation parameters, though not as a direct priority for minimizing metabolic cost. Instead, entrainment may act to stabilize interactions with the environment, thus increasing predictability for the effective implementation of internal models that guide energy minimization.

Why highly compliant poles are not energetically beneficial during running: Evidence from an optimization-based biped model

Springy poles are a unique load-carrying tool and inspire novel designs of other load-carrying systems. Previous experiments have shown that highly compliant poles with a natural frequency lower than step frequency are more economical than rigid poles during load carriage in walking and this was successfully explained in later modeling studies. However, an energetic benefit was not observed during running with highly compliant poles. We speculate that gait type (running versus walking) may be a factor accounting for the different observations. An optimization-based biped model is adopted to predict the energy cost of load carriage with poles during running, with the parameters from previous experimental studies. The predicted load motion and load-body interaction force agree well with experimental measurements. Compared to running with rigid poles, the highly compliant pole results in reduced peak ground reaction force, longer stance phase duration, and higher energy cost. The changes in running energetics are further found to depend on the natural frequency of the load-pole system relative to the step frequency, but with an opposite trend compared to the changes in walking energetics during pole carriage. Highly compliant poles cost more energy than rigid poles during running, while stiffer poles with a higher natural frequency may offer energetic benefits. This study indicates that the fundamental difference in gait type has a profound influence on the energetic performance of load-carrying devices and this should be taken into consideration in future device designs.

Load carrying with flexible bamboo poles: optimization of a coupled oscillator system

In Asia, flexible bamboo poles are routinely used to carry substantial loads on the shoulder. Various advantages have been attributed to this load-carrying strategy (e.g. reduced energy consumption), but experimental evidence remains inconsistent – possibly because carriers in previous studies were inexperienced. Theoretical models typically neglect the individual's capacity to optimize interactions with the oscillating load, leaving the complete dynamics underexplored. This study used a trajectory optimization model to predict gait adaptations that minimize work-based costs associated with carrying compliant loads and compared the outcomes with naturally selected gait adaptations of experienced pole carriers. Gait parameters and load interactions (e.g. relative amplitude and frequency, phase) were measured in rural farmworkers in Vietnam. Participants carried a range of loads with compliant and rigid poles and the energetic consequences of step frequency adjustments were evaluated using the model. When carrying large loads, the empirical step frequency changes associated with pole type (compliant versus rigid) were largely consistent with model predictions, in terms of direction (increase or decrease) and magnitude (by how much). Work-minimizing strategies explain changes in leg compliance, harmonic frequency oscillations and fluctuations in energetic cost associated with carrying loads on a compliant bamboo pole.

The Landscape of Movement Control in Locomotion: Cost, Strategy, and Solution

Features of gait are determined at multiple levels, from the selection of the gait itself (e.g., walk or run) through the specific parameters utilized (stride length, frequency, etc.) to the pattern of muscular excitation. The ultimate choices are determined neurally, but what is involved with deciding on the appropriate strategy? Human locomotion appears stereotyped not so much because the pattern is predetermined, but because these movement patterns are good solutions for providing movement utilizing the machinery available to the individual (the legs and their requisite components). Under different circumstances the appropriate solution may differ broadly (different gait) or subtly (different parameters). Interpretation of the neural decision making process would benefit from understanding the influences that are utilized in the selection of the appropriate solution in any set of circumstances, including normal conditions. In this review we survey an array of studies that point to energetic cost as a key input to the gait coordination system, and not just an outcome of the gait pattern implemented. We then use that information to rigorously define the construct proposed by Sparrow and Newell (1998) where the effects of environment, organism, and task act as constraints determining the solution set available, and the coordination pattern is then implemented under pressure for energetic economy. The fit between the environment and the organism define affordances that can be actualized. We rely on a novel conceptualization of task that recognizes that the task goal needs to be separated from the mechanisms that achieve it so that the selection of a particular implementation strategy can be exposed and understood. This reformulation of the Sparrow and Newell construct is then linked to the proposed pressure for economy by considering it as an optimization problem, where the most readily selected gait strategy will be the one that achieves the task goal at (or near) the energetic minimum.

Determinants of optimal leg use strategy: horizontal to vertical transition in the parkour wall climb

This study examined the mechanics of the horizontal to vertical transition used by parkour athletes in wall climbing. We used this task as an alternative to normal running - where the functional options differ substantially - exposing the movement control priorities required to successfully complete the task. Ground reaction forces were measured in several expert parkour athletes and centre of mass trajectory was calculated from force plates embedded in the ground and the wall. Empirical measures were compared with movements predicted by a work-based control optimization model. The model captured the fundamental dynamics of the transition and therefore allowed an exploration of parameter sensitivity for success at the manoeuvre (run-up speed, foot placement, etc.). The optimal transition of both the model and the parkour athletes used a common intermediate run-up speed and appears determined largely by a trade-off between positive and negative leg work that accomplishes the task with minimum overall work.