Humans plan for the near future to walk economically on uneven terrain.

Humans experience small fluctuations in their gait when walking on uneven terrain. The fluctuations deviate from the steady, energy-minimizing pattern for level walking and have no obvious organization. But humans often look ahead when they walk, and could potentially plan anticipatory fluctuations for the terrain. Such planning is only sensible if it serves some an objective purpose, such as maintaining constant speed or reducing energy expenditure, that is also attainable within finite planning capacity. Here, we show that humans do plan and perform optimal control strategies on uneven terrain. Rather than maintaining constant speed, they make purposeful, anticipatory speed adjustments that are consistent with minimizing energy expenditure. A simple optimal control model predicts economical speed fluctuations that agree well with experiments with humans (N = 12) walking on seven different terrain profiles (correlated with model [Formula: see text] , [Formula: see text] all terrains). Participants made repeatable speed fluctuations starting about six to eight steps ahead of each terrain feature (up to ±7.5 cm height difference each step, up to 16 consecutive features). Nearer features matter more, because energy is dissipated with each succeeding step's collision with ground, preventing momentum from persisting indefinitely. A finite horizon of continuous look-ahead and motor working space thus suffice to practically optimize for any length of terrain. Humans reason about walking in the near future to plan complex optimal control sequences.

Visual feedback-dependent modulation of arousal, postural control, and muscle stretch reflexes assessed in real and virtual environments.

Introduction: The mechanisms regulating neuromuscular control of standing balance can be influenced by visual sensory feedback and arousal. Virtual reality (VR) is a cutting-edge tool for probing the neural control of balance and its dependence on visual feedback, but whether VR induces neuromodulation akin to that seen in real environments (eyes open vs. closed or ground level vs. height platform) remains unclear. Methods: Here we monitored 20 healthy young adults (mean age 23.3 ± 3.2 years; 10 females) during four conditions of quiet standing. Two real world conditions (eyes open and eyes closed; REO and REC) preceded two eyes-open virtual 'low' (ground level; VRL) and 'high' (14 m height platform; VRH) conditions. We measured arousal via electrodermal activity and psychosocial questionnaires rating perceived fear and anxiety. We recorded surface electromyography over the right soleus, medial gastrocnemius, and tibialis anterior, and performed force plate posturography. As a proxy for modulations in neural control, we assessed lower limb reflexive muscle responses evoked by tendon vibration and electrical stimulation. Results: Physiological and perceptual indicators of fear and anxiety increased in the VRH condition. Background soleus muscle activation was not different across conditions; however, significant increases in muscle activity were observed for medial gastrocnemius and tibialis anterior in VRH relative to REO. The mean power frequency of postural sway also increased in the VRH condition relative to REO. Finally, with a fixed stimulus level across conditions, mechanically evoked reflexes remained constant, while H-reflex amplitudes decreased in strength within virtual reality. Discussion: Notably, H-reflexes were lower in the VRL condition than REO, suggesting that these ostensibly similar visual environments produce different states of reflexive balance control. In summary, we provide novel evidence that VR can be used to modulate upright postural control, but caution that standing balance in analogous real and virtual environments may involve different neural control states.

Humans optimally anticipate and compensate for an uneven step during walking.

The simple task of walking up a sidewalk curb is actually a dynamic prediction task. The curb is a disturbance that could cause a loss of momentum if not anticipated and compensated for. It might be possible to adjust momentum sufficiently to ensure undisturbed time of arrival, but there are infinite possible ways to do so. Much of steady, level gait is determined by energy economy, which should be at least as important with terrain disturbances. It is, however, unknown whether economy also governs walking up a curb, and whether anticipation helps. Here, we show that humans compensate with an anticipatory pattern of forward speed adjustments, predicted by a criterion of minimizing mechanical energy input. The strategy is mechanistically predicted by optimal control for a simple model of bipedal walking dynamics, with each leg's push-off work as input. Optimization predicts a triphasic trajectory of speed (and thus momentum) adjustments, including an anticipatory phase. In experiment, human subjects ascend an artificial curb with the predicted triphasic trajectory, which approximately conserves overall walking speed relative to undisturbed flat ground. The trajectory involves speeding up in a few steps before the curb, losing considerable momentum from ascending it, and then regaining speed in a few steps thereafter. Descending the curb entails a nearly opposite, but still anticipatory, speed fluctuation trajectory, in agreement with model predictions that speed fluctuation amplitudes should scale linearly with curb height. The fluctuation amplitudes also decrease slightly with faster average speeds, also as predicted by model. Humans can reason about the dynamics of walking to plan anticipatory and economical control, even with a sidewalk curb in the way.

Anticipatory Control of Momentum for Bipedal Walking on Uneven Terrain.

Humans and other walking bipeds often encounter and compensate for uneven terrain. They might, for example, regulate the body's momentum when stepping on stones to cross a stream. We examined what to do and how far to look, as a simple optimal control problem, where forward momentum is controlled to compensate for a step change in terrain height, and steady gait regained with no loss of time relative to nominal walking. We modeled planar, human-like walking with pendulum-like legs, and found the most economical control to be quite stereotypical. It starts by gaining momentum several footfalls ahead of an upward step, in anticipation of the momentum lost atop that step, and then ends with another speed-up to regain momentum thereafter. A similar pattern can be scaled to a variety of conditions, including both upward or downward steps, yet allow for considerably reduced overall energy and peak power demands, compared to compensation without anticipation. We define a "persistence time" metric from the transient decay response after a disturbance, to describe how momentum is retained between steps, and how far ahead a disturbance should be planned for. Anticipatory control of momentum can help to economically negotiate uneven terrain.

Optimal regulation of bipedal walking speed despite an unexpected bump in the road.

Bipedal locomotion may occur over imperfect surfaces with bumps or other features that disrupt steady gait. An unexpected bump in the road is generally expected to slow down most types of locomotion. On wheels, speed may be regained quite readily with "cruise control" performed in continuous time. But legged locomotion is less straightforward, because the stance leg may be under-actuated, and the continuous-time dynamics are periodically disrupted by discrete ground contact events. Those events may also afford good control opportunities, albeit subject to the delay between discrete opportunities. The regulation of walking speed should ideally use these opportunities to compensate for lost time, and with good economy if possible. However, the appropriate control strategy is unknown. Here we present how to restore speed and make up for time lost going over a bump in the road, through discrete, once-per-step control. We use a simple dynamic walking model to determine the optimal sequence of control actions-pushing off from the leg at the end of each stance phase-for fast response or best economy. A two-step, deadbeat sequence is the fastest possible response, and reasonably economical. Slower responses over more steps are more economical overall, but a bigger difference is that they demand considerably less peak power. A simple, reactive control strategy can thus compensate for an unexpected bump, with explicit trade-offs in time and work. Control of legged locomotion is not as straightforward as with wheels, but discrete control actions also allow for effective and economical reactions to imperfect terrain.