Bipedal Model Research Articles

Piezoelectric energy harvesting from walking motion of a passive biped robot model with flexible legs

Passive dynamic walking biped robots utilize the inherent dynamics of their structure to achieve walking motion without continuous actuation, enhancing energy efficiency and stability. Replacing conventional rigid legs with flexible elastic beams in the simplest passive walker will be associated with undesirable vibrations. Despite the positive effect of the damper in reducing vibrations, the current research has used the piezoelectric energy harvesting with the aim of reducing the wasted energy of the gait cycle and improving its stability range. For this purpose, the electromechanical Lagrange equations are determined by applying Hamilton's principle and the assumed mode method and then, the new definition of the step function is obtained through numerical methods, solving a boundary value problem to establish proper initial conditions for stable walking. Numerical simulations indicate that the piezoelectric energy harvester can create a stable period-one gait cycle by optimizing the length of the piezo layers attached to the undamped elastic legs despite the presence of small vibrations. Additional results are presented in bifurcation diagrams, investigating the effect of important physical and structural parameters such as slope angle, length and thickness of the piezo layer.

Simulation Analysis of a Passive Biped Robot

To more accurately understand the fundamental characteristics of the motion of a passive biped robot and to enhance the guidance provided by model research for the design of practical prototypes, we analyze the characteristics of this passive model and establish the corresponding dynamic model using the Lagrange method. Based on the characteristic that the stable walking cycle gait of the robot manifests as a limit cycle in the phase plane, we study the passive biped model with knee joints through co-simulation using Adams and Matlab. The process of simulating steady-state walking of the ideal model is demonstrated in detail, including the initial conditions required for the robot to achieve periodic steady-state walking, the motion characteristics, and the distribution, variation, and interconversion of kinetic and potential energy during the motion.

Modelling strategies supplemental to foot placement for frontal-plane stability in walking.

Walking is unstable and requires active control. Foot placement is the primary strategy to maintain frontal-plane balance with contributions from lateral ankle torques, ankle push-off and trunk postural adjustments. Because these strategies interact, their individual contributions are difficult to study. Here, we used computational modelling to understand these individual contributions to frontal-plane walking balance control. A three-dimensional bipedal model was developed based on linear inverted pendulum dynamics. The model included controllers that implement the stabilization strategies seen in human walking. The control parameters were optimized to mimic human gait biomechanics for typical spatio-temporal parameters during steady-state walking and when perturbed by mediolateral ground shifts. Using the optimized model as a starting point, the contributions of each stabilization strategy were explored by progressively removing strategies. The lateral ankle and trunk strategies were more important than ankle push-off, with their removal causing up to 20% worse balance recovery compared with the full model, while removing ankle push-off led to minimal changes. Our results imply a potential benefit of preferentially training these strategies in populations with poor balance. Moreover, the proposed model could be used in future work to investigate how walking stability may be preserved in conditions reflective of injury or disease.

A solvable walking model for a two-legged robot

We present a solvable biped walking model based on an inverted pendulum with two massless articulated legs capable of walking on uneven floors and inclined planes. The stride of the two-legged robot results from the pendular motion of a standing leg and the articulated motion of a trailing leg. Gaiting is possible due to the pendular motion conservation of energy and the alternating role of the legs, the standing and the trailing leg. The motion on uneven surfaces and inclined planes is possible by imposing the same maximal opening angle between the two legs in the transition between strides and the adaptability of the time of each stride. This model is solvable in closed form and is reversible in time, modelling the different types of biped motion. Several optimisation results for the speed of gaiting as a function of the robot parameters have been derived.

Bounding gait control of a parallel quadruped robot

PurposeThe computing power of the legged robot is not enough to perform high-frequency updates for the full-body model predictive control (MPC) of the robot, which is a common problem encountered in the gait research of the legged robot. The purpose of this paper is to propose a high-frequency MPC control method for the bounding gait of a parallel quadruped robot.Design/methodology/approachAccording to the bounding gait characteristics of the robot, the quadruped robot model is simplified to an equivalent plane bipedal model. Under the biped robot model, the forces between the robot’s feet and the ground are calculated by MPC. Then, the authors apply a proportional differential controller to distribute these forces to the four feet of the quadruped robot. The robot video can be seen at www.bilibili.com/video/BV1je4y1S7Rn.FindingsTo verify the feasibility of the controller, a prototype was made, and the controller was deployed on the actual prototype and then fully analyzed through experiments. Experiments show that the update frequency of MPC could be stabilized at 500 Hz while the robot was running in the bounding gait stably and efficiently.Originality/valueThis paper proposes a high-frequency MPC controller under the simplified model, which has a higher working efficiency and more stable control performance.

Dynamic Optimization of Mechanism Parameters of Bipedal Robot Considering Full-Range Walking Energy Efficiency

Mechanism parameters of bipedal robots are crucial for achieving efficient locomotion in complex environments. Inspired by the human energy-efficient walking style, this paper proposes a novel concept of full-range walking energy efficiency and explores the optimal linkage mechanism within certain ranges of step length and walking speed for bipedal robots. First, a bipedal model incorporating an upper body is established for dynamic analysis. Next, an optimal walking gait subject to walking constraints is solved by considering the full-range energy efficiency. Further, an optimal linkage mechanism is investigated, and the influence of dynamic parameters on energy efficiency is analyzed. Finally, the push-off impulse, minimum ground support force, and walking torque features are discussed. It shows that the full-range walking energy efficiency can be lowered by reducing the ratio of leg mass, concentrating mass at the hip joint, decreasing the length of the upper body, or increasing the center of mass of the leg. In addition, efficient walking motion can be achieved by designing the coordination of positive hip joint torque and push-off impulse at the ankle. This paper can be used to guide the mechanism parameter optimization and efficient walking gait design of bipedal robots.

A parallel heterogeneous policy deep reinforcement learning algorithm for bipedal walking motion design.

Considering the dynamics and non-linear characteristics of biped robots, gait optimization is an extremely challenging task. To tackle this issue, a parallel heterogeneous policy Deep Reinforcement Learning (DRL) algorithm for gait optimization is proposed. Firstly, the Deep Deterministic Policy Gradient (DDPG) algorithm is used as the main architecture to run multiple biped robots in parallel to interact with the environment. And the network is shared to improve the training efficiency. Furthermore, heterogeneous experience replay is employed instead of the traditional experience replay mechanism to optimize the utilization of experience. Secondly, according to the walking characteristics of biped robots, a biped robot periodic gait is designed with reference to sinusoidal curves. The periodic gait takes into account the effects of foot lift height, walking period, foot lift speed and ground contact force of the biped robot. Finally, different environments and different biped robot models pose challenges for different optimization algorithms. Thus, a unified gait optimization framework for biped robots based on the RoboCup3D platform is established. Comparative experiments were conducted using the unified gait optimization framework, and the experimental results show that the method outlined in this paper can make the biped robot walk faster and more stably.

Dynamic Posture Stabilization Of Humanoid Robot NAO Using 3D-Multilinked Dual Spring-Loaded Inverted Pendulum Model for Uneven and Inclined Floor

Gait pattern performance, for its crucial significance in humanoid robot stabilization, has attracted the attention of researchers worldwide. Although simplified models highlight major features, bipedal walking has bewildered the researchers. Therefore, for a precise understanding of the bipedal model, a state-of-the-art, simplified model has been proposed in this paper which comprises a 3D-multilinked dual spring-loaded inverted pendulum (3D-MDSLIP) while acknowledging the vertical fluctuations of the center of mass (CoM). In addition, the model considers upper body movement and its effects on the stabilization of the humanoid robot. The mathematical modeling of a humanoid walking over the obstacle and slope is demonstrated to precisely understand the problem. The tuning process of the parameters and postures in a humanoid robot is complex and time-consuming. For proper walking of a robot over uneven terrains and slopes, tuning of the PID controller is achieved using converged teaching-learning based optimization (CTLBO) technique for a central pattern generator (CPG) gait, as introduced in the paper. The optimal gait angles are applied to the experimental and simulated NAO to successfully navigate the provided terrain. Thus, the experimental and simulation results jointly show that the proposed CPG-CTLBO gait learning technique is feasible for finding an optimal gait pattern for the humanoid robot within a deviation of 5%. The energy efficiency of the proposed controller is compared with the default controller of NAO based on the average electronic current in sagittal and lateral movement. Further, it is examined for the energy consumption for several slopes, and the results obtained are acceptable, showing the controller is efficient. Additionally, it has been compared with an existing technique for walking a humanoid robot on uneven terrains. The graph obtained using the proposed technique demonstrates the superiority of the proposed technique.

Does joint impedance improve dynamic leg simulations with explicit and implicit solvers?

The nervous system predicts and executes complex motion of body segments actuated by the coordinated action of muscles. When a stroke or other traumatic injury disrupts neural processing, the impeded behavior has not only kinematic but also kinetic attributes that require interpretation. Biomechanical models could allow medical specialists to observe these dynamic variables and instantaneously diagnose mobility issues that may otherwise remain unnoticed. However, the real-time and subject-specific dynamic computations necessitate the optimization these simulations. In this study, we explored the effects of intrinsic viscoelasticity, choice of numerical integration method, and decrease in sampling frequency on the accuracy and stability of the simulation. The bipedal model with 17 rotational degrees of freedom (DOF)-describing hip, knee, ankle, and standing foot contact-was instrumented with viscoelastic elements with a resting length in the middle of the DOF range of motion. The accumulation of numerical errors was evaluated in dynamic simulations using swing-phase experimental kinematics. The relationship between viscoelasticity, sampling rates, and the integrator type was evaluated. The optimal selection of these three factors resulted in an accurate reconstruction of joint kinematics (err < 1%) and kinetics (err < 5%) with increased simulation time steps. Notably, joint viscoelasticity reduced the integration errors of explicit methods and had minimal to no additional benefit for implicit methods. Gained insights have the potential to improve diagnostic tools and accurize real-time feedback simulations used in the functional recovery of neuromuscular diseases and intuitive control of modern prosthetic solutions.

Backstepping-based control for a new semi-passive biped model

In this work, we propose a new Semi-Passive Biped (SPB) Model and a Center of Gravity Shift (CGS) control method of this model. The passing friction between the swing leg and the ground of passive robots locomotion consumes robots energy, resulting in the model cant walk passively. In order to analyze this problem in a more practical way, we propose a new SPB Model and analyze its energy consumption. Also, we suggest a CGS control method, which can make the proposed new SPB model walk stable. Finally, an illustrative experiment is presented to verify the SPB model and the effectiveness of the CGS control method.

A biped model to predict a wide range of gait and posture results

While human locomotion involves complex interactions of the body musculoskeletal structure, many aspects of this behavior can be predicted and examined using simplified mathematical models. This study investigates a realistically simple biped model to study the interaction between lower limbs and trunk with different trunk postures, which is still relatively unexplored, although the trunk makes up about two thirds of the body weight. The results of this study demonstrate that a simple mathematical model is capable of predicting a number of results of posture and gait that align with the reported experimental results in the literature. Additionally, the study reveals significant adaptations in the kinetic and kinematics gait parameters of the lower limbs to compensate for various normal and abnormal trunk conditions.

Predicting fall risk using multiple mechanics-based metrics for a planar biped model.

For both humans and robots, falls are undesirable, motivating the development of fall prediction models. Many mechanics-based fall risk metrics have been proposed and validated to varying degrees, including the extrapolated center of mass, the foot rotation index, Lyapunov exponents, joint and spatiotemporal variability, and mean spatiotemporal parameters. To obtain a best-case estimate of how well these metrics can predict fall risk both individually and in combination, this work used a planar six-link hip-knee-ankle biped model with curved feet walking at speeds ranging from 0.8 m/s to 1.2 m/s. The true number of steps to fall was determined using the mean first passage times from a Markov chain describing the gaits. In addition, each metric was estimated using the Markov chain of the gait. Because calculating the fall risk metrics from the Markov chain had not been done before, the results were validated using brute force simulations. Except for the short-term Lyapunov exponents, the Markov chains could accurately calculate the metrics. Using the Markov chain data, quadratic fall prediction models were created and evaluated. The models were further evaluated using differing length brute force simulations. None of the 49 tested fall risk metrics could accurately predict the number of steps to fall by themselves. However, when all the fall risk metrics except the Lyapunov exponents were combined into a single model, the accuracy increased substantially. These results suggest that multiple fall risk metrics must be combined to obtain a useful measure of stability. As expected, as the number of steps used to calculate the fall risk metrics increased, the accuracy and precision increased. This led to a corresponding increase in the accuracy and precision of the combined fall risk model. 300 step simulations seemed to provide the best tradeoff between accuracy and using as few steps as possible.

A Novel Low-Cost ZMP Estimation Method for Humanoid Gait using Inertial Measurement Devices: Concept and Experiments

Estimation and control of zero-moment point (ZMP) is a widely used concept for planning the locomotion of bipedal robots and is commonly measured using integrated joint angle encoders and foot force sensors. Contemporary methods for ZMP measurement involve built-in contact sensors such as joint encoders or instrumented foot force sensors. This paper presents a novel approach for computing ZMP for a humanoid robot using inertial sensor-based wireless foot sensor modules (WFSMs). The developed WFSMs, strapped at different limb segments of a bipedal robot, measure lower limb joint angles in real time. The joint angle trajectories, further transformed into Cartesian position coordinates, are used for estimating the ZMP positions of humanoid robots using the planar biped model. The whole framework is presented through experimental studies for different real-life walking scenarios. Since the modules work based on the limb motion and inclination, any ground unevenness would be automatically reflected in the module output. Hence, this measurement process can be a convenient method for applications requiring humanoid control on uneven surfaces/outdoor terrains. To compare the performance of the proposed model, ZMP is simultaneously measured from inbuilt foot force sensors and joint encoders of the robot. Statistical tests exhibit a high linear correlation between the proposed method with integrated encoders and foot force sensors (Pearson’s coefficient, [Formula: see text]). Results indicate that ZMP estimated by WFSM is a viable method to monitor the dynamic gait balance of a humanoid robot and has potential application in outdoor and uneven terrains.

Multimodal bipedal locomotion generation with passive dynamics via deep reinforcement learning.

Generating multimodal locomotion in underactuated bipedal robots requires control solutions that can facilitate motion patterns for drastically different dynamical modes, which is an extremely challenging problem in locomotion-learning tasks. Also, in such multimodal locomotion, utilizing body morphology is important because it leads to energy-efficient locomotion. This study provides a framework that reproduces multimodal bipedal locomotion using passive dynamics through deep reinforcement learning (DRL). An underactuated bipedal model was developed based on a passive walker, and a controller was designed using DRL. By carefully planning the weight parameter settings of the DRL reward function during the learning process based on a curriculum learning method, the bipedal model successfully learned to walk, run, and perform gait transitions by adjusting only one command input. These results indicate that DRL can be applied to generate various gaits with the effective use of passive dynamics.

The energetic effect of hip flexion and retraction in walking at different speeds: a modeling study.

In human walking, power for propulsion is generated primarily via ankle and hip muscles. The addition of a 'passive' hip spring to simple bipedal models appears more efficient than using only push-off impulse, at least, when hip spring associated energetic costs are not considered. Hip flexion and retraction torques, however, are not 'free', as they are produced by muscles demanding metabolic energy. Studies evaluating the inclusion of hip actuation costs, especially during the swing phase, and the hip actuation's energetic benefits are few and far between. It is also unknown whether these possible benefits/effects may depend on speed. We simulated a planar flat-feet model walking stably over a range of speeds. We asked whether the addition of independent hip flexion and retraction remains energetically beneficial when considering work-based metabolic cost of transport (MCOT) with different efficiencies of doing positive and negative work. We found asymmetric hip actuation can reduce the estimated MCOT relative to ankle actuation by up to 6%, but only at medium speeds. The corresponding optimal strategy is zero hip flexion and some hip retraction actuation. The reason for this reduced MCOT is that the decrease in collision loss is larger than the associated increase in hip negative work. This leads to a reduction in total positive mechanical work, which results in an overall lower MCOT. Our study shows how ankle actuation, hip flexion, and retraction actuation can be coordinated to reduce MCOT.

Occurrence of Complex Behaviors in the Uncontrolled Passive Compass Biped Model

It is widely known that an appropriately built unpowered bipedal robot can walk down an inclined surface with a passive steady gait. The features of such gait are determined by the robot's geometry and inertial properties, as well as the slope angle. The energy needed to keep the biped moving steadily comes from the gravitational potential energy as it descends the inclined surface. The study of such passive natural motions could lead to ideas for managing active walking devices and a better understanding of the human locomotion. The major goal of this study is to further investigate order, chaos and bifurcations and then to demonstrate the complexity of the passive bipedal walk of the compass-gait biped robot by examining different bifurcation diagrams and also by studying the variation of the eigenvalues of the Poincaré map's Jacobian matrix and the variation of the Lyapunov exponents. We reveal also the exhibition of some additional results by changing the inertial and geometrical parameters of the bipedal robot model.

Evaluation of Inverted-Pendulum-with-Rigid-Legs Walking Locomotion Models for Civil Engineering Applications

Bipedal models for walkers, originally developed in the research field of biomechanics, have been identified as potential candidates for modelling pedestrians in structural engineering applications. These models provide insight into both the kinetics and kinematics of walking locomotion and are considered to have a significant potential to improve the vibration serviceability assessment of civil engineering structures. Despite this notion, the ability of the bipedal models to represent the key features of the walking gait and natural variability within the pedestrian population are still under-researched. This paper critically evaluates the performance of two bipedal models with rigid legs to realistically both reproduce key features of an individual pedestrian’s walking gait and represent a wide range of individuals. The evaluation is performed for walking on a rigid, rather than vibrating, structure due to the availability of experimental data and expectation that successful modelling on rigid surfaces is a necessary condition for progressing towards modelling on the vibrating structures. Ready-to-use equations are provided and the ability of the models to represent the kinematics and kinetics of individual pedestrians as well as the inter-subject variability typical of the human population is critically evaluated. It was found that the two models could generate realistic combinations of the gait parameters and their correlations, but are less successful in reproducing genuine kinetic and kinematics profiles.

Predicting ground reaction forces of human gait using a simple bipedal spring-mass model.

Aircraft design must be lightweight and cost-efficient on the condition of aircraft certification. In addition to standard load cases, human-induced loads can occur in the aircraft interior. These are crucial for optimal design but difficult to estimate. In this study, a simple bipedal spring-mass model with roller feet predicted human-induced loads caused by human gait for use within an end-to-end design process. The prediction needed no further experimental data. Gait movement and ground reaction force (GRF) were simulated by means of two parameter constraints with easily estimable input variables (gait speed, body mass, body height). To calibrate and validate the prediction model, experiments were conducted in which 12 test persons walked in an aircraft mock-up under different conditions. Additional statistical regression models helped to compensate for bipedal model limitations. Direct regression models predicted single GRF parameters as a reference without a bipedal model. The parameter constraint with equal gait speed in experiment and simulation yielded good estimates of force maxima (error 5.3%), while equal initial GRF gave a more reliable prediction. Both parameter constraints predicted contact time very well (error 0.9%). Predictions with the bipedal model including full GRF curves were overall as reliable as the reference.

Feasible Wrench Set Computation for Legged Robots

During locomotion, legged robots interact with the ground by sequentially establishing and breaking contact. The interaction wrenches that arise from contact are used to steer the robot Center of Mass (CoM) and reject perturbations that make the system deviate from the desired trajectory and often make them fall. The feasibility of a given control target (desired CoM wrench or acceleration) is conditioned by the contact point distribution, ground friction, and actuation limits. In this work, we develop a method to compute the set of feasible wrenches that a legged robot can exert on its CoM through contact. The presented method can be used with any amount of non-co-planar contacts and takes into account actuation limits and limitations based on an inelastic contact model with Coulomb friction. This is exemplified with a planar biped model standing with the feet at different heights. Exploiting assumptions from the contact model, we explain how to compute the set of wrenches that are feasible on the CoM when the contacts remain in position as well as the ones that are feasible when some of the contacts are broken. Therefore, this method can be used to assess whether a switch in contact configuration is feasible while achieving a given control task. Furthermore, the method can be used to identify the directions in which the system is not actuated (i.e. a wrench cannot be exerted in those directions). We show how having a joint be actuated or passive can change the non-actuated wrench directions of a robot at a given pose using a spatial model of a lower-extremity exoskeleton. Therefore, this method is also a useful tool for the design phase of the system. This work presents a useful tool for the control and design of legged systems that extends on the current state of the art.

Passive walking biped robot model with flexible viscoelastic legs

To simulate the complex human walking motion accurately, a suitable biped model has to be proposed that can significantly translate the compliance of biological structures. In this way, the simplest passive walking model is often used as a standard benchmark for making the bipedal locomotion so natural and energy efficient. This paper is devoted to a presentation of the application of internal damping mechanism to the mathematical description of the simplest passive walking model with flexible legs. This feature can be taken into account by using the viscoelastic legs, which are constituted by the Kelvin–Voigt rheological model. Then, the update of the impulsive hybrid nonlinear dynamics of the simplest passive walker is obtained based on the Euler–Bernoulli’s beam theory and using a combination of Lagrange mechanics and the assumed mode method, along with the precise boundary conditions. The main goal of this study is to develop a numerical procedure based on the new definition of the step function for enforcing the biped start walking from stable condition and walking continuously. In our previous work, it was shown that the period-one gait cycle can be produced by adding the proportional damping model with high damping ratio to the elastic legs. The present paper overcomes the practical limitations of this damping model and similarly demonstrates the stable period-one gait cycles for the viscoelastic legs. The study of the influence of various system parameters is carried out through bifurcation diagrams, highlighting the region of stable period-one gait cycles. Numerical simulations clearly prove that the overall effect of viscoelastic leg on the passive walking is efficient enough from the viewpoint of stability and energy dissipation.