Anticipatory Control of Momentum for Bipedal Walking on Uneven Terrain

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.

Optimization of energy and time predicts dynamic speeds for human walking

Humans make a number of choices when they walk, such as how fast and for how long. The preferred steady walking speed seems chosen to minimize energy expenditure per distance traveled. But the speed of actual walking bouts is not only steady, but rather a time-varying trajectory, which can also be modulated by task urgency or an individual's movement vigor. Here we show that speed trajectories and durations of human walking bouts are explained better by an objective to minimize Energy and Time, meaning the total work or energy to reach destination, plus a cost proportional to bout duration. Applied to a computational model of walking dynamics, this objective predicts dynamic speed vs. time trajectories with inverted U shapes. Model and human experiment (N=10) show that shorter bouts are unsteady and dominated by the time and effort of accelerating, and longer ones are steadier and faster and dominated by steady-state time and effort. Individual-dependent vigor may be characterized by the energy one is willing to spend to save a unit of time, which explains why some may walk faster than others, but everyone may have similar-shaped trajectories due to similar walking dynamics. Tradeoffs between energy and time costs can predict transient, steady, and vigor-related aspects of walking.

Uneven terrain treadmill walking in younger and older adults

We developed a method for altering terrain unevenness on a treadmill to study gait kinematics. Terrain consisted of rigid polyurethane disks (12.7 cm diameter, 1.3-3.8 cm tall) which attached to the treadmill belt using hook-and-loop fasteners. Here, we tested four terrain unevenness conditions: Flat, Low, Medium, and High. The main objective was to test the hypothesis that increasing the unevenness of the terrain would result in greater gait kinematic variability. Seventeen younger adults (age 20-40 years), 25 higher-functioning older adults (age 65+ years), and 29 lower-functioning older adults (age 65+ years, Short Physical Performance Battery score < 10) participated. We customized the treadmill speed to each participant's walking ability, keeping the speed constant across all four terrain conditions. Participants completed two 3-minute walking trials per condition. Using an inertial measurement unit placed over the sacrum and pressure sensors in the shoes, we calculated the stride-to-stride variability in step duration and sacral excursion (coefficient of variation; standard deviation expressed as percentage of the mean). Participants also self-reported their perceived stability for each condition. Terrain was a significant predictor of step duration variability, which roughly doubled from Flat to High terrain for all participant groups: younger adults (Flat 4.0%, High 8.2%), higher-functioning older adults (Flat 5.0%, High 8.9%), lower-functioning older adults (Flat 7.0%, High 14.1%). Similarly, all groups exhibited significant increases in sacral excursion variability for the Medium and High uneven terrain conditions, compared to Flat. Participants were also significantly more likely to report feeling less stable walking over all three uneven terrain conditions compared to Flat. These findings support the hypothesis that altering terrain unevenness on a treadmill will increase gait kinematic variability and reduce perceived stability in younger and older adults.

Legged locomotion over irregular terrains: state of the art of human and robot performance

Legged robotic technologies have moved out of the lab to operate in real environments, characterized by a wide variety of unpredictable irregularities and disturbances, all this in close proximity with humans. Demonstrating the ability of current robots to move robustly and reliably in these conditions is becoming essential to prove their safe operation. Here, we report an in-depth literature review aimed at verifying the existence of common or agreed protocols and metrics to test the performance of legged system in realistic environments. We primarily focused on three types of robotic technologies, i.e., hexapods, quadrupeds and bipeds. We also included a comprehensive overview on human locomotion studies, being it often considered the gold standard for performance, and one of the most important sources of bioinspiration for legged machines. We discovered that very few papers have rigorously studied robotic locomotion under irregular terrain conditions. On the contrary, numerous studies have addressed this problem on human gait, being nonetheless of highly heterogeneous nature in terms of experimental design. This lack of agreed methodology makes it challenging for the community to properly assess, compare and predict the performance of existing legged systems in real environments. On the one hand, this work provides a library of methods, metrics and experimental protocols, with a critical analysis on the limitations of the current approaches and future promising directions. On the other hand, it demonstrates the existence of an important lack of benchmarks in the literature, and the possibility of bridging different disciplines, e.g., the human and robotic, towards the definition of standardized procedures that will boost not only the scientific development of better bioinspired solutions, but also their market uptake.

Evaluating anticipatory control strategies for their capability to cope with step-down perturbations in computer simulations of human walking

Previous simulation studies investigated the role of reflexes and central pattern generators to explain the kinematic and dynamic adaptations in reaction to step-down perturbations. However, experiments also show preparatory adaptations in humans based on visual anticipation of a perturbation. In this study, we propose a high-level anticipatory strategy augmenting a low-level muscle-reflex control. This strategy directly changes the gain of the reflex control exclusively during the last contact prior to a drop in ground level. Our simulations show that especially the anticipatory reduction of soleus activity and the increase of hamstrings activity result in higher robustness. The best results were obtained when the change in stimulation of the soleus muscle occurred 300 ms after the heel strike of the contralateral leg. This enabled the model to descend perturbation heights up to - 0.21 m and the resulting kinematic and dynamic adaptations are similar to the experimental observations. This proves that the anticipatory strategy observed in experiments has the purpose of increasing robustness. Furthermore, this strategy outperforms other reactive strategies, e.g., pure feedback control or combined feedback and feed-forward control, with maximum perturbation heights of - 0.03 and - 0.07 m, respectively.

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.