Optimal Gait Research Articles

Influence of Gait Retraining on Running Economy: A Review and Potential Applications

ABSTRACT Running gait retraining has been reported to reduce lower-extremity loads and the risk for some running-related injuries. This has provided evidence that distance running gait can safely be modified in runners. Optimal running gait at a given speed is the product of anthropometric, neuromuscular, fatigue, and external factors. Because running biomechanics are integrally linked with economy, a major determinant of endurance running performance, it is conceivable that gait retraining could improve performance. The evidence investigating the influence of gait retraining on running economy will be evaluated and potential applications discussed.

Dynamical Modeling and Gait Optimization of a 2-D Modular Snake Robot in a Confined Space

Abstract A model-based optimal gait is obtained for the 2-D locomotion of a modular snake robot in a duct. Optimality is considered in the sense of traveling as fast as possible or traveling with minimal energy consumption. The novelty of the work lies in the development of a framework to cast the full dynamic behavior, including contact constraints with simple objects, into an optimization problem which allows for gait parameter, control parameter and/or physical parameter optimization. Optimal gait and control parameters are found via a surrogate optimization procedure which reveals optimal locomotion strategies depending on the duct width and optimization criteria. The framework is tested and illustrated with a number of optimizations of 2-D locomotion of a snake robot where either traveling time or energy consumption is minimized.

Robustness and efficiency insights from a mechanical coupling metric for ankle-actuated biped robots

This paper presents results pertaining to the coupling between the actuated and unactuated degrees of freedom for biped robots. It is focused on revealing the qualitative relationship between a mechanical coupling metric and gait characteristics for an ankle-actuated biped robot. By considering robot models with varying masses, leg lengths and positions of the center of mass of the legs, it validates the universality of prior results based on a single robot model. The development of a method for designing ankle-actuated biped gaits is given in detail, and numerical computation is utilized to find the initial conditions needed to generate the ankle-actuated candidate gait regions. The correlation between the coupling metric and the maximum magnitude of disturbance that can be rejected is significant, regardless of the robot parameters. It indicates that robust gaits tend to have small coupling under zero disturbance so that the “reserve” coupling may be utilized to reject the disturbance. Furthermore, for the same walking speed, gaits with smaller cost of transport under zero disturbances have smaller coupling and therefore should be more robust, which highlights the value of gait optimization for biped walking. The coupling metric for hip actuation is also briefly discussed as a contrast.

Gait Optimization for Quadruped Rovers

SUMMARYThis paper studies the gait characteristics of a quadruped rover that mimics domestic cats, and attempts to optimize these characteristics. The kinematics and dynamics formulation of the rover’s three-dimensional model is developed, and its gait, pose and corresponding control parameters are computed to minimize torque or maximize speed, using a genetic algorithm. The optimization model consists of a set of equality and inequality constraints that ensure the feasibility and stability of the gaits, while considering the entire gait spectrum that feline species exhibit. The optimal gaits for minimizing the torque closely resemble lateral sequence gaiting, with a trotting behaviour as speed increases. A running gait is obtained at the maximum speed. The optimization results appear to conform to the biological observations of feline species, suggesting the tendency of conserving energy in biological gaiting.

Application of Big Data Analysis and Internet of Things to the Intelligent Active Robotic Prosthesis for Transfemoral Amputees

With the advent and rising usage of Internet of Things (IoT) eco-systems, there is a consequent, parallel rise in opportunities where technology can find its place to improve a number of human conditions. However, this is nothing new - we have been perfecting the usage of tools to aid our daily living throughout history. The true evolution lies in the interaction between us and the tools we create. Tools are now smart devices, yielding an opportunity where human-device interaction is giving us the very knowledge on how to improve that particular synthesis. From improving our fitness to detecting bradycardia and response of traumatic brain injury patient, we have come to a point where we are able to gain actionable insight into a lot of aspects of our health and condition. This creates a certain autonomy in understanding the unique make-up of every single person, in addition to yielding information that can be used by health practitioners to help in diagnosis, determination of medical approach and right recovery and follow-up methods. All of this supported by two major factors: IoT platforms and Big Data Analysis (BDA). This paper takes a deep dive into exemplary set-up of IoT platform and BDA framework necessary to support the improvement of human condition. Our SmartLeg prosthetic device integrates advanced prosthetic and robotic technology with the state-of-the-art machine learning algorithms capable of adapting the working of the prosthesis to the optimal gait and power consumption patterns, which provide means to customize the device to a particular user.

Вплив засобів фізичної терапії на якість ходьби та показники електроміографії у студентів 17–19 років з плоскостопістю і порушеннями постави

Робота присвячена розгляду біометричних параметрів ходьби студентів 17–19 років зі зниженням висоти склепіння стопи за даними системи SIGMA XL та ознаками функціонального сколіозу. Розглянуто такі часові параметри ходьби, як тривалість одного циклу кроку, одиночної опори, середня нормалізована швидкість. Проведено аналіз інтегрованого показника якості ходьби FAP. Мета. Оцінити динаміку та особливості часових параметрів ходьби до та після впровадження авторської програми корекції плоскостопості і функціональних порушень постави у студентів 17–19 років. Методи. Проаналізовано параметри ходьби 120 студентів з гіпогіпертонусом м’язів, які входять до складу різних міофасціальних ланцюгів. Студенти були розподілені на дві групи: основну (ОГ) та контрольну (КГ) по 60 чол. у кожній. Студенти ОГ займались за авторською програмою, яка передбачала застосування засобів фізичної терапії, передбачених методикою І. Д. Ловейко [7], в модифікації О. В. Пешкової зі співавт. [12]. Крім цього, додатково проводили заняття модифікованими видами спорту у воді (поло, баскетбол, волейбол, імпровізовані ігри тощо) – температура води 25 о С, глибина басейну до 1,2 м. Студенти КГ займалися тільки за програмою І. Д. Ловейко. Обстеження проводили на початку дослідження і через 12 і 24 міс. після застосування відповідних програм фізичної терапії. Результати. За результатами проведенного статистичного дослідження було виявлено деякі закономірності для студентів, у яких плантографічним методом визначалися ознаки плоскостопості і функціонального сколіозу (КГ) та для студентів, у яких постава залишалася без зміни (ОГ). До лікування студенти незалежно від групи дослідження за параметрами ходьби були однаковими, тобто у них простежувалися всі ознаки спотворення ходьби внаслідок плоскостопості. Через два роки після впровадження обох програм параметри ходьби відновлювалися, хоча їх нормалізація за програмою для КГ не досягала середньостатистичної референтної норми. Після лікування за авторською програмою спостерігалося значне покращення параметрів ходьби у студентів ОГ – практично відновлювалася симетрія ходьби. Висновки. Зменшення тонусу і дисбаланс м’язів гомілки і спини є об’єктивною причиною втрати навичок якісної ходьби, що студенти показували до впровадження авторської програми. Тобто тривале несиметричне навантаження м’язів призводить до втрати оптимальних показників ходьби, зменшення опорної спроможності стопи, що виражається збільшенням часу опори на стопу із порушенням склепінчастого апарату стопи і збільшенням тривалості кроку. Наслідком цих змін є розвиток та поступове прогресування сколіотичної хвороби. Застосування у програмі фізичної терапії у студентів ОГ модифікованих ігрових видів фізичних вправ у воді сприяє підвищенню частотно-амплітудних характеристик м’язів окремих міофасціальних кінематичних ланцюгів, а зменшення дисбалансу між ними викликає покращення показників, що характеризують якість ходьби.

Optimal Strokes of Low Reynolds Number Linked-Sphere Swimmers

Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of linked-spheres that can change their separation and/or their sizes. We examine the dynamics of three existing linked-sphere types of modeling swimmers in low Reynolds number Newtonian fluids using asymptotic analysis, and obtain their optimal swimming strokes by solving the Euler–Lagrange equation using the shooting method. The numerical results reveal that (1) with the minimal 2 degrees of freedom in shape deformations, the model swimmer adopting the mixed shape deformation modes strategy is more efficient than those with a single-mode of shape deformation modes, and (2) the swimming efficiency mostly decreases as the number of spheres increases, indicating that more degrees of freedom in shape deformations might not be a good strategy in optimal gait design in low Reynolds number locomotion.

Gait modeling and optimization for the perturbed Stokes regime

Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the "Stokesian" (viscous; zero Reynolds number) limit, the motion is governed by a reduced order "connection" model that describes how body shape change produces motion for the body frame with respect to the world. In the "perturbed Stokes regime" where inertial forces are still dominated by viscosity, but are not negligible (low Reynolds number), we show that motion is still governed by a functional relationship between shape velocity and body velocity, but this function is no longer linear in shape change rate. We derive this model using results from singular perturbation theory, and the theory of noncompact normally hyperbolic invariant manifolds (NHIMs). Using the theoretical properties of this reduced-order model, we develop an algorithm that estimates an approximation to the dynamics near a cyclic body shape change (a "gait") directly from observational data of shape and body motion. This extends our previous work which assumed kinematic "connection" models. To compare the old and new algorithms, we analyze simulated swimmers over a range of inertia to damping ratios. Our new class of models performs well on the Stokesian regime, and over several orders of magnitude outside it into the perturbed Stokes regime, where it gives significantly improved prediction accuracy compared to previous work. In addition to algorithmic improvements, we thereby present a new class of models that is of independent interest. Their application to data-driven modeling improves our ability to study the optimality of animal gaits, and our ability to use hardware-in-the-loop optimization to produce gaits for robots.

The Geometry of Optimal Gaits for Drag-Dominated Kinematic Systems

In this paper, we present a set of geometric principles for understanding and optimizing the gaits of drag-dominated kinematic locomoting systems. For systems with two shape variables, the dynamics of gait optimization are analogous to the process by which internal pressure and surface tension combine to produce the shape and size of a soap bubble. The internal pressure on the gait curve is provided by the flux of the curvature of the system constraints passing through the surface bounded by the gait, and surface tension is provided by the cost associated with executing the gait, which when executed at optimal (constant-power) pacing is proportional to its pathlength measured under a Riemannian metric. We extend these principles to work on systems with three and then more than three shape variables. We demonstrate these principles on a variety of system geometries (including Purcell's swimmer) and for optimization criteria that include maximizing displacement and efficiency of motion for both translation and turning motions. We also demonstrate how these principles can be used to simultaneously optimize a system's gait kinematics and physical design.

Dynamic optimization of Gait with a Generalized Lower-Limb Prosthesis Model.

Predictive simulation of gait is a promising tool for robotic lower limb prosthesis design, but has been limited in its application to models of existing design types. We propose a modeling approach to find optimal prosthesis dynamics in gait simulations without constraining the prosthesis to follow kinematics allowed by a specific joint mechanism. To accomplish this, we render a transtibial prosthetic device as the composition of its resultant forces and moments as they act upon the prosthetic foot and socket and allow3 degree-of-freedom planar motion. The model is implemented into a human musculoskeletal model and used to solve dynamic optimizations of muscle and prosthesis controls to minimize muscle effort and loading on the residual limb during walking. The emphasis on muscle effort vs. limb loading is varied in the minimization objective and the resulting optimal prosthesis dynamics are compared. We found that muscle effort and socket loading measures were reduced for our prosthesis model compared to a revolute joint prosthesis model. We interpret large displacements in the linear axes to transfer energy to the plantarflexion action before toe-off and reduce loading at the socket-limb interface. Our results suggest this approach could assist in the design of non-biomimetic prostheses but requires experimental validation to assess our modeling assumptions, as well as progress toward increased fidelity of predictive simulation approaches more generally.

Manipulability Based Hierarchical Control of Perturbed Walking

In this paper, a novel manipulability based three-level hierarchical approach is suggested for control of perturbed bipedal walking. An appropriate postural strategy is selected to restore stability if a perturbation occurs during steady-state human walking. Previous experimental studies on the human walking suggest that the selection of stabilizing strategies can be related to the kinematic manipulability of swing foot. The proposed three-level structure consists of a low, middle, and high levels. The manipulability is at the high-level layer. Therefore, in case of disturbance it determines to lengthen the step (elevating strategy) or shorten the step length (lowering strategy). The middle-level layer determines the optimal desired trajectories for joints. Finally, a low-level controller tracks the desired optimal trajectory to maintain stability. The results show the success of the manipulability based adapted control scheme against pushing perturbation. A comparison between the optimal gait patterns obtained with and without consideration of manipulability is also presented in this study. The results show that the manipulability improves disturbance rejection capability. Positioning the manipulability in the high-level of our proposed method mitigates the possibility of singularity occurrence and configuration limits during postural response.

Knee and torso kinematics in generation of optimum gait pattern based on human-like motion for a seven-link biped robot

Gait pattern affects the quality of a walking robot. In this paper, an optimum human-like gait generation method is proposed for a seven-link biped robot. This method utilizes kinematic constraints based on human-like motion. At first, the constraints are parameterized with unknown parameters. Then, an optimization problem is defined with an objective function and the kinematic constraints. The objective function includes the energy consumption and walking stability. Unknown parameters appearing in the constraints are determined by solving the optimization problem. Joint variables are obtained by integrating a velocity form of the kinematic constraints. This approach is carried out for gait planning of the seven-link biped robot and its results are presented. This method allows studying some effective parameters on the gait such as constant knee angle duration, and torso inclination is optimized for different speeds. Our studies indicate that as walking speed increases the knee should extend and the torso should lean forward further in order to maintain better stability. Moreover, energy consumption increases as the torso leans forward.

Autonomous Optimization of Swimming Gait in a Fish Robot With Multiple Onboard Sensors

Autonomous gait optimization is an essential survival ability for mobile robots. However, it remains a challenging task for underwater robots. This paper addresses this problem for the locomotion of a bio-inspired robotic fish and aims at identifying fast swimming gait autonomously by the robot. Our approach for learning locomotion controllers mainly uses three components: 1) a biological concept of central pattern generator to obtain specific gaits; 2) an onboard sensory processing center to discover the environment and to evaluate the swimming gait; and 3) an evolutionary algorithm referred to as particle swarm optimization. A key aspect of our approach is the swimming gait of the robot is optimized autonomously, equivalent to that the robot is able to navigate and evaluate its swimming gait in the environment by the onboard sensors, and simultaneously run a built-in evolutionary algorithm to optimize its locomotion all by itself. Forward speed optimization experiments conducted on the robotic fish demonstrate the effectiveness of the developed autonomous optimization system. The latest results show that our robotic fish attained a maximum swimming speed of 1.011 BL/s (40.42 cm/s) through autonomous gait optimization, faster than any of the robot’s previously recorded speeds.

Energetically optimal stride frequency is maintained with fatigue in trained ultramarathon runners

ObjectivesAt a given running speed, humans naturally endeavor to achieve an optimal stride frequency that minimizes metabolic cost. Research has suggested that runners select this near optimal stride frequency in some process of self-optimization even during fatiguing tasks up to 1-h of high-intensity running. Here, we studied whether runners demonstrate a similar self-optimizing capability after an ultramarathon of 6 h. DesignControlled pre-post study. MethodWe collected temporal stride kinematics and metabolic data in nine (experimental group) male runners before and after 6 h of running and in six (control group) male ultramarathon runners who did not run, but stayed awake and performed normal, daily physical activities avoiding strenuous exercises over the 6-h period. For each participant, preferred and optimal stride frequencies were measured, where stride frequency was systematically varied above and below PSF (±4% and ±8%). ResultsPreferred and optimal stride frequencies across time and group showed no significant differences (p ≥ 0.276). Furthermore, neither the overall relationship between metabolic cost and stride frequency, nor the energetically optimal stride frequency changed substantially after several hours of running. ConclusionsSimilar dynamics of stride frequency adjustments in the experimental group occurred as those found in a non-fatigued state. This suggests that after an ultramarathon of 6 h, runners were still able to optimize their gait, and automatically adjust it in order to converge on the energetically optimal gait.

Leg Trajectory Planning for Quadruped Robots with High-Speed Trot Gait

In this paper, a single leg platform for quadruped robots is designed based on the motivation of high-speed locomotion. The leg is designed for lightweight and low inertia with a structure of three joints by imitating quadruped animals. Because high acceleration and extensive loadings will be involved on the legs during the high-speed locomotion, the trade-off between the leg mass and strength is specifically designed and evaluated with the finite element analysis. Moreover, quadruped animals usually increase stride frequency and decrease contact time as the locomotion speed increases, while maintaining the swing duration during trot gait. Inspired by this phenomenon, the foot-end trajectory for quadruped robots with a high-speed trot gait is proposed. The gait trajectory is planned for swing and stance phase; thus the robot can keep its stability with adjustable trajectories while following a specific gait pattern. Especially for the swing phase, the proposed trajectory can minimize the maximum acceleration of legs and ensure the continuity of position, speed, and acceleration. Then, based on the kinematics analysis, the proposed trajectory is compared with the trajectory of Bézier curve for the power consumption. Finally, a simulation with Webots software is carried out for verifying the motion stability with two trajectory planning schemes respectively. Moreover, a motion capture device is used for evaluating the tracking accuracy of two schemes for obtaining an optimal gait trajectory suitable for high-speed trot gait.

Research on gait recognition algorithm based on multiinformation perception

With the collected multi-information, through the information preprocessing, feature vector extraction, analysis and fusion, the recognition model based on BP neural network, genetic algorithm optimization BP neural network, the extreme learning machine and support vector machine are established. We have accurately identified five gait modes: flat walking, upstairs, downstairs, uphill, and downhill. The highest average recognition rate is 96.5%, and the recognition time is 0.156 s. By analyzing the advantages and disadvantages of the four recognition models, the optimal gait recognition algorithm can be obtained.

Utilizing the Correlation Between Constraints and Objective Function for Constrained Evolutionary Optimization

When solving constrained optimization problems by evolutionary algorithms, the core issue is to balance constraints and objective function. This paper is the first attempt to utilize the correlation between constraints and objective function to keep this balance. First of all, the correlation between constraints and objective function is mined and represented by a correlation index. Afterward, a weighted sum updating approach and an archiving and replacement mechanism are proposed to make use of this correlation index to guide the evolution. By the above process, a novel constrained optimization evolutionary algorithm is presented. Experiments on a broad range of benchmark test functions indicate that the proposed method shows better or at least competitive performance against other state-of-the-art methods. Moreover, the proposed method is applied to the gait optimization of humanoid robots.

Is natural variability in gait sufficient to initiate spontaneous energy optimization in human walking?

In new walking contexts, the nervous system can adapt preferred gaits to minimize energetic cost. During treadmill walking, this optimization is not usually spontaneous but instead requires experience with the new energetic cost landscape. Experimenters can provide subjects with the needed experience by prescribing new gaits or instructing them to explore new gaits. Yet in familiar walking contexts, people naturally prefer energetically optimal gaits: the nervous system can optimize cost without an experimenter's guidance. Here we test the hypothesis that the natural gait variability of overground walking provides the nervous system with sufficient experience with new cost landscapes to initiate spontaneous minimization of energetic cost. We had subjects walk over paths of varying terrain while wearing knee exoskeletons that penalized walking as a function of step frequency. The exoskeletons created cost landscapes with minima that were, on average, 8% lower than the energetic cost at the initially preferred gaits and achieved at walking speeds and step frequencies that were 4% lower than the initially preferred values. We found that our overground walking trials amplified gait variability by 3.7-fold compared with treadmill walking, resulting in subjects gaining greater experience with new cost landscapes, including frequent experience with gaits at the new energetic minima. However, after 20 min and 2.0 km of walking in the new cost landscapes, we observed no consistent optimization of gait, suggesting that natural gait variability during overground walking is not always sufficient to initiate energetic optimization over the time periods and distances tested in this study. NEW & NOTEWORTHY While the nervous system can continuously optimize gait to minimize energetic cost, what initiates this optimization process during every day walking is unknown. Here we tested the hypothesis that the nervous system leverages the natural variability in gait experienced during overground walking to converge on new energetically optimal gaits created using exoskeletons. Contrary to our hypothesis, we found that participants did not adapt toward optimal gaits: natural variability is not always sufficient to initiate spontaneous energy optimization.

Planar Multi-Link Swimmers: Experiments and Theoretical Investigation using “Perfect Fluid” Model

SummaryRobotic swimmers are currently a subject of extensive research and development for several underwater applications. Clever design and planning must rely on simple theoretical models that account for the swimmer’s hydrodynamics in order to optimize its structure and control inputs. In this work, we study a planar snake-like multi-link swimmer by using the “perfect fluid” model that accounts for inertial hydrodynamic forces while neglecting viscous drag effects. The swimmer’s dynamic equations of motion are formulated and reduced into a first-order system due to symmetries and conservation of generalized momentum variables. Focusing on oscillatory inputs of joint angles, we study optimal gaits for 3-link and 5-link swimmers via numerical integration. For the 3-link swimmer, we also provide a small-amplitude asymptotic solution which enables obtaining closed-form approximations for optimal gaits. The theoretical results are then corroborated by experiments and motion measurement of untethered robotic prototypes with three and five links floating in a water pool, showing a reasonable agreement between the experiments and the theoretical model.

Altered muscle activation patterns (AMAP): an analytical tool to compare muscle activity patterns of hemiparetic gait with a normative profile

BackgroundStroke survivors often have lower extremity sensorimotor impairments, resulting in an inability to sufficiently recruit muscle activity at appropriate times in a gait cycle. Currently there is a lack of a standardized method that allows comparison of muscle activation in hemiparetic gait post-stroke to a normative profile.MethodsWe developed a new tool to quantify altered muscle activation patterns (AMAP). AMAP accounts for spatiotemporal asymmetries in stroke gait by evaluating the deviations of muscle activation specific to each gait sub-phase. It also recognizes the characteristic variability within the healthy population. The inter-individual variability of normal electromyography (EMG) patterns within some sub-phases of the gait cycle is larger compared to others, therefore AMAP penalizes more for deviations in a gait sub-phase with a constant profile (absolute active or inactive) vs variable profile. EMG data were collected during treadmill walking, from eight leg muscles of 34 stroke survivors at self-selected speeds and 20 healthy controls at four different speeds. Stroke survivors’ AMAP scores, for timing and amplitude variations, were computed in comparison to healthy controls walking at speeds matched to the stroke survivors’ self-selected speeds.ResultsAltered EMG patterns in the stroke population quantified using AMAP agree with the previously reported EMG alterations in stroke gait that were identified using qualitative methods. We defined scores ranging between ±2.57 as “normal”. Only 9% of healthy controls were outside “normal” window for timing and amplitude. Percentages of stroke subjects outside the “normal” window for each muscle were, Soleus = 79%; 73%, Medial Gastrocnemius = 62%; 79%, Tibialis Anterior = 62%; 59%, and Gluteus Medius = 48%; 51% for amplitude and timing component respectively, alterations were relatively smaller for the other four muscles. Paretic-propulsion was negatively correlated to AMAP scores for the timing component of Soleus. Stroke survivors’ self-selected walking speed was negatively correlated with AMAP scores for amplitude and timing of Soleus but only amplitude of Medial gastrocnemius (p < 0.05).ConclusionsOur results validate the ability of AMAP to identify alterations in the EMG patterns within the stroke population and its potential to be used to identify the gait phases that may require more attention when developing an optimal gait training paradigm.Trial registrationClinicalTrials.govNCT00712179, Registered July 3rd 2008