Lower limb exoskeletons and exosuits have shown promise in augmenting human physical capabilities, with applications ranging from rehabilitation to performance enhancement. Accurate evaluation of their impact on metabolic energy expenditure is crucial for optimizing design and control strategies. While experimental measurement of metabolic cost via indirect calorimetry provides direct assessment, it is often impractical outside laboratory settings. Computational models offer an alternative, but their effectiveness in predicting metabolic cost changes induced by assistive devices remains underexplored. This study investigates the impact of incorporating different levels of complexity and sensory information, as well as various metabolic cost models, on estimating muscle metabolic cost during walking with a passive biarticular thigh exosuit. We compare three modeling approaches: joint-space dynamics, musculoskeletal simulation with effort minimization, and EMG-informed musculoskeletal simulation, each employing several metabolic models. Results show that EMG-informed musculoskeletal simulation, particularly using the Uchida (2016) metabolic model, provides the highest accuracy in predicting metabolic cost changes. Musculoskeletal simulation with effort minimization also shows promise, offering a viable alternative without the need for EMG data. These findings highlight the potential of computational models in evaluating and optimizing assistive devices.

The virtual pivot point (VPP), a theoretical convergence point of ground reaction forces during gait, has gained attention for its potential to uncover underlying locomotor control strategies. Here, we present the first investigation of VPP in individuals with unilateral above-knee amputation, using a publicly available dataset of 18 participants. Subjects were categorized into K2 (walking speeds 0.4–0.8m/s) and K3 (0.6–1.4m/s) functional levels. Our findings show that both groups demonstrate high sagittal-plane VPP quality, comparable to that of healthy individuals, with R2> 95%, indicating a strong relationship between VPP formation and sagittal plane dynamics. Conversely, in the frontal plane, VPP analysis reveals greater variability and lower quality, indicating the absence of a well-defined pivot during gait. Notably, frontal-plane VPP quality deteriorates with increasing walking speed, particularly in K3 ambulators. While this speed-dependency is observed in healthy individuals as well, the rate of decline is significantly steeper in amputees. Additionally, spatial analysis of VPP positions reveals a consistent elevation of the amputated leg’s VPP compared to the intact leg. These findings emphasize the importance of frontal plane dynamics in amputee gait and suggest improvements in prosthetic design to enhance control and promote more symmetrical, natural gait.

Human locomotion exhibits extraordinary adaptability and robustness, yet the mechanisms by which lower limbs adjust to sudden environmental disruptions remain poorly understood. To address this, we employed the bioinspired human-sized EPA-Hopper II robot to examine how lower-limb joints recover from an abrupt drop in ground height, mimicking unexpected perturbations encountered in natural settings. Our study investigates the roles of the monoarticular soleus (SOL) and biarticular gastrocnemius (GAS) muscle configurations, focusing on how their compliance influences the robot’s hopping stability. Experiments reveal that a coordinated interplay between SOL and GAS markedly improves recovery from disturbances, enhancing energy distribution and joint synchronization. Detailed kinematic and power analyses show that GAS facilitates energy transfer across joints, while SOL’s spring-like properties support rapid recovery. These results highlight how bioinspired muscle arrangements enable robust locomotion through intrinsic mechanical interactions. By leveraging a robotic platform to probe these dynamics, this work deepens our understanding of biological locomotion and informs the design of bioinspired bipedal robots and prosthetics capable of thriving in unpredictable environments.

Legged robots, particularly quadrupeds, excel at navigating rough terrains, yet their performance under vertical ground perturbations, such as those from oscillating surfaces, remains underexplored. This study introduces a novel approach to enhance quadruped locomotion robustness by training the Unitree Go2 robot on an oscillating bridge—a 13.24-meter steel-and-concrete structure with a 2.0 Hz eigenfrequency designed to perturb locomotion. Using Reinforcement Learning (RL) with the Proximal Policy Optimization (PPO) algorithm in a MuJoCo simulation, we trained 15 distinct locomotion policies, combining five gaits (trot, pace, bound, free, default) with three training conditions: rigid bridge and two oscillating bridge setups with differing height regulation strategies (relative to bridge surface or ground). Domain randomization ensured zero-shot transfer to the real-world bridge. Our results demonstrate that policies trained on the oscillating bridge exhibit superior stability and adaptability compared to those trained on rigid surfaces. Our framework enables robust gait patterns even without prior bridge exposure. These findings highlight the potential of simulation-based RL to improve quadruped locomotion during dynamic ground perturbations, offering insights for designing robots capable of traversing vibrating environments.

The fear of falling due to changes in gait leads to a decrease in quality of life in Parkinson's patients. Also, Parkinson's patients require medical treatment due to falling each year. However, the reasons for the changed walking style still remain unknown. The goal of this study is the evaluation of possible reasons for the changed walking pattern in Parkinson's disease. A pilot study is conducted, which includes patient experiments, data analysis, and biomechanical modeling. Differences between Parkinsonian and healthy gait are detected and replicated by the model. The model represents simplified body dynamics and is optimized for healthy and Parkinsonian gait, respectively. Comparison measures are ground reaction forces, joint torques, and the virtual pivot point (VPP) location. The VPP is the intersection point of all forces throughout the gait cycle and is closely correlated to human balancing and stability. Parkinsonian gait showed different force and torque curves compared to healthy walking and a VPP below the center of mass location (negative VPP). The model represents healthy walking well. Specific Parkinsonian behavior can be explained by the changed modulation of the model. However, a negative VPP location turns the model unstable as, after two steps, the trunk tilts more than 90 degrees forward. Our modeling with negative VPP shows instability effects observed in Parkinson's patients walking who struggle with frequent stumbles and falls. Such modeling approaches could be used for developing new rehabilitation techniques and gait assistance devices.

The lower limb morphology of biological locomotors is abundant in muscle-tendon units. Yet, not much is known about how these actuation units contribute to the output performance and energy economy of movements. In this work, we investigate the functionality of four of the important lower limb muscles - Vastus, Popliteus, Soleus, and Gastrocnemius - in a hopping task at different frequencies (1.5-3.5 Hz). These muscles are implemented as pneumatic artificial muscles (PAMs) on the EPA-Hopper-II robot, which is a human-sized 3-segmented leg co-actuated by electrical motors and PAMs. A bioinspired reflex-based Force Modulated Control (FMC) is also implemented on the robot to achieve hopping at different frequencies. The results show that the Vastus contributes the most to energy-efficient hopping at low to mid frequencies. The biarticular Gastrocnemius also helps increase efficiency at low frequencies. Further, it is found that the Gastrocnemius synchronizes the knee-ankle motion and mitigates lateral knee motion. The outcomes of this work add further evidence to hypotheses regarding human lower-limb actuation and proper recruitment of muscles for building more efficient robots.

There is a long history demonstrating humans' tendency to create artificial copies of living creatures. For moving machines called robots, actuators play a key role in developing human-like movements. Among different types of actuation, PAMs (pneumatic artificial muscles) are known as the most similar ones to biological muscles. In addition to similarities in force generation mechanism (tension based), the well-accepted argumentation from Klute et al., states that the PAM force-length (fl) behavior is close to biological muscles, while the force-velocity (fv) pattern is different. Using the multiplicative formulation of the pressure (as an activation term), fland fvbeside an additive passive parallel elastic element, we present a new model of PAM. This muscle-based model can predict PAM dynamic behaviors with high precision. With a second experiment on a two-segmented leg, the proposed model is verified to predict the generated forces of PAMs in an antagonistic arrangement. Such a dynamic muscle-like model of artificial muscles can be used for the design and control of legged robots to generate robust, efficient and versatile gaits.

Balancing or postural stability is one of important locomotor subfunctions in bipedal gaits. The inverted pendulum and virtual pivot point (VPP) are common modeling approaches to analyze balance control in human and robot walking. In this paper, we employ the VPP concept to investigate posture control in the frontal plane. The outcomes demonstrate that unlike posture control in the sagittal plane, the VPP in the frontal plane is place below center of mass. This finding explains a novel hybrid strategy for lateral stability in human walking. The here proposed model shows that switching between unstable inverted virtual pendulums generate stable posture control in the frontal plane. This outcome is consistent within a group of seven human subjects walking at normal and slow speeds.

Several modeling studies, which address neuromuscular control in impaired unperturbed gaits, were performed to predict human strategies to cope with lateral asymmetries in the body. Experimental studies show different step length and stance time relations between limbs in walking of stroke patients. By extension of a bipedal SLIP (spring-loaded inverted pendulum) based model and the corresponding controllers to 3D space, we focus on different features of the pathologic gaits. The introduced model is based on an extension of the FMCH (force modulated compliant hip) and VBLA (velocity based leg adjustment) model to 3D space. With the proposed model, asymmetric leg and control parameters can result in similar gait patterns as observed in experiments. These parameters comprise hip stiffness and rest angles in FMCH models and the tuning parameter of VBLA for foot placement. It is shown that asymmetries in muscle properties (e.g. stiffness) and leg adjustment can play an important role in generating pathologic gaits.

Walking with 5-link model has been achieved by HZD (Hybrid Zero Dynamics) controller based on virtual constraints. These holonomic constraints are obtained by optimizing a set of virtual relations (e.g., Beziér polynomial) between system states which mostly do not have physical interpretations. In this paper, the virtual constraints are designed using human walking experiment data. Inspiring from human locomotion, different polynomials are extracted to mimic human joint angles patterns during walking. The virtual leg angle is the increasing variable which synchronize the joints angles and defines the virtual constraints. Simulation results show that stable locomotion with leg and upper-body behavior similar to human experiment data is achieved for a wide range of speeds and body configuration parameters. VPP (Virtual Pivot Point) concept, a significant balancing feature found in human/animal locomotion, is investigated for different gait speeds as a performance index to compare the kinetic behavior of the simulated and human walking. Hence, we present human-like posture control as an outcome of motion control achieved by HZD with human inspired virtual constraints.

Spring loaded inverted pendulum (SLIP) model used simple spring mass mechanism to explain leg function and ground reaction force in legged locomotion. Balancing the upper body can be addressed by addition of a rigid trunk to this template model. The resulting model is not conservative and needs hip torque to keep the trunk upright during locomotion, like humans. Leg force modulated compliant hip (FMCH) is our new model for postural control in walking which employs the leg force feedback to adjust the hip compliance. Such an application of positive force feedback presents a new template for neuromuscular model. This method provides stable and robust walking in simulations and also mimics human-like kinetic behavior. Analyzing human walking experiment shows that FMCH can explain the hip torque-angle relation for different walking speeds. Finally, this approach may physically implement the virtual pendulum (VP) concept, observed in human/animal locomotion.

The design of gaits and corresponding control policies for bipedal walkers is a key challenge in robot locomotion. Even when a viable controller parametrization already exists, finding near-optimal parameters can be daunting. The use of automatic gait optimization methods greatly reduces the need for human expertise and time-consuming design processes. Many different approaches to automatic gait optimization have been suggested to date. However, no extensive comparison among them has yet been performed. In this paper, we present some common methods for automatic gait optimization in bipedal locomotion, and analyze their strengths and weaknesses. We experimentally evaluated these gait optimization methods on a bipedal robot, in more than 1800 experimental evaluations. In particular, we analyzed Bayesian optimization in different configurations, including various acquisition functions.

Swing leg adjustment, repulsive leg function and balance are key elements in the control of bipedal locomotion. In simple gait models like spring-loaded inverted pendulum (SLIP), swing leg control can be applied to achieve stable running. The aim of this study is to investigate the ability of pendulum like swing leg motion for stabilizing running and reproducing a desired (human like) gait pattern. The employed running model consists of two sub-models: SLIP model for the stance phase and a pendulum based control for the swing phase. It is shown that with changing the pendulum length at each step, stable running gaits with widely different performances are achieved. The body vertical speed at take off is utilized as feedback information to tune the pendulum length as the control parameter. In particular, the effect of the pendulum length adjustment on the motion characteristics like horizontal speed, apex height and the stabilized system energy will be investigated. With this method key features of the human like swing leg motion e.g. leg retraction can be reproduced. Higher speeds correspond larger angular motion of each leg which is in agreement with experimental results in previous studies. The presented model also explains the swing-leg to stance-leg interaction mechanism which was not addressed in the underlying SLIP model. This conceptual model can be considered as a functional mechanical template for legged locomotion and can be used to build more complex models, e.g. having segmented legs or an upper body.

Bipedal locomotion can be divided into primitive tasks, namely repulsive leg behavior (bouncing against gravity), leg swing (protraction and retraction) and body alignment (balancing against gravity). In the bipedal spring-mass model for walking and running, the repulsive leg function is described by a linear prismatic spring. This paper adopts two strategies for swinging and bouncing control from conceptual models for the human-inspired musculoskeletal BioBiped robot. The control approach consists of two layers, velocity based leg adjustment (VBLA) and virtual model control to represent a virtual springy leg between toe and hip. Additionally, the rest length and stiffness of the virtual springy leg are tuned based on events to compensate energy losses due to damping. In order to mimic human locomotion, the trunk is held upright by physical constraints. The controller is implemented on the validated detailed simulation model of BioBiped. In-place as well as forward hopping and switching between these two gaits are easily achieved by tuning the parameters for the leg adjustment, virtual leg stiffness and injected energy. Furthermore, it is shown that the achieved motion performance of in-place hopping agrees well with that of human subjects.

Bouncing, balancing and swinging the leg forward can be considered as three basic control tasks for bipedal locomotion. Defining the trunk by an unstable inverted pendulum, balancing as being translated to trunk stabilization is the main focus of this paper. The control strategy is to generate a hip torque to have upright trunk to achieve robust hopping and running. It relies on the Virtual Pendulum (VP) concept which is recently proposed for trunk stabilization, based on human/animal locomotion analysis. Based on this concept, a control approach, named Virtual Pendulum Posture control (VPPC) is presented, in which the trunk is stabilized by redirecting the ground reaction force to a virtual support point. The required torques patterns generated by the controller, could partially be exerted by elastic structures like hip springs. Hybrid Zero Dynamics (HZD) control approach is also applied as an exact method of keeping the trunk upright. Stability of the motion which is investigated by Poincaré map analysis could be achieved by hip springs, VPPC and HZD. The results show that hip springs, revealing muscle properties, could facilitate trunk stabilization. Compliance in hip produces acceptable performance and robustness compared with VPPC and HZD, while it is a passive structure.

Elastic elements in prosthetic devices can help to reduce peak power (PP) and energy requirements (ER) for the actuators. Calculations showed that it is impossible with current commercial motor technology to mimic human ankle behavior in detail for higher walking and running speeds with single motor solutions using a Serial Elastic Actuator (SEA). Concerning this result we checked the requirements of a parallel elastic actuator (PEA) and a combination of serial and parallel (SE+PEA) springs. We found that a PEA can reduce PP additionally in comparison to the SEA by pre-loading the spring in the flight phase. This reduces also peak torque. But this loading needs additional energy so that the ER increase in comparison to the SEA. The SE+PEA concept can further decrease PP. With that, the ER are less than the PEA but higher than for the SEA. The results show less benefit for the PEA and the SE+PEA when a constant stiffness and a fixed parallel spring slack length is used for both gaits and all speeds. All concepts show that mimicking human ankle joint behavior in running and walking at higher speeds is still challenging for single motor devices.

Legged locomotion is one of the most versatile forms of mobility. However, despite the importance of legged locomotion and the large number of legged robotics studies, no biped or quadruped matches the agility and versatility of their biological counterparts to date. Approaches to designing controllers for legged locomotion systems are often based on either the assumption of perfectly known dynamics or mechanical designs that substantially reduce the dimensionality of the problem. The few existing approaches for learning controllers for legged systems either require exhaustive real-world data or they improve controllers only conservatively, leading to slow learning. We present a data-efficient approach to learning feedback controllers for legged locomotive systems, based on learned probabilistic forward models for generating walking policies. On a compass walker, we show that our approach allows for learning gait policies from very little data. Moreover, we analyze learned locomotion models of a biomechanically inspired biped. Our approach has the potential to scale to high-dimensional humanoid robots with little loss in efficiency.

This paper presents a new control approach to achieve robust hopping with upright trunk in the sagittal plane. It relies on an innovative concept for trunk stabilization, called Virtual Pendulum concept, recently proposed, based on experimental finding in animal locomotion. With this concept, the trunk is stabilized by redirecting the ground reaction force to a virtual support point, named Virtual Pivot Point (VPP). This concept is combined with a new leg adjustment scheme to induce stable hopping when an extended trunk is added to SLIP model. The stability is investigated by Poincaré map analysis. With fixed VPP position, stability, disturbance rejection and moderate robustness are achieved, but with low convergence speed. To improve the performances and attain higher robustness, event based control of VPP position is introduced, using feedback of the system state at apex. Dead beat control and Discrete LQR are alternatively considered to adjust the feedback gains. In both cases, considerable enhancements with respect to stability, convergence speed and robustness against perturbations are achieved.

During walking and running, passive foot prostheses can only do positive work by releasing elastic energy stored in compliant structures. This limited ability to generate positive work can be improved in devices which actively support the push-off. Here, we estimate the peak power and energy requirements of a simulated serial elastic actuator (SEA) for walking and running and compare it with a direct drive setup. The simulations indicate that a serial spring can highly reduce peak power and the energy. Results suggest that optimizing SEA stiffness to obtain minimal peak power is the more general approach as it needs similar energy requirements as observed in optimizing for minimal energy. In contrast, optimization for minimal energy results in clearly higher peak power requirements. For both gaits, the predicted optimal spring stiffness suitable for minimizing peak power increases with speed. For optimizing energy, the stiffness decreases with walking speed and remains nearly constant across speeds in running. A constant stiffness for both gaits is possible. It should be chosen based on the optimized peak power solution for the highest desired speed, where the peak power requirements are most critical.

In ankle-foot prostheses a serial spring can assist the motor to reduce peak power (PP) and energy requirements (ER) during locomotion. Similar benefits can be expected for an active knee prosthesis. We compare the situation of a direct drive with a series elastic actuator optimized for minimal ER or for minimal PP. The simulations indicate that at the knee joint a serial spring can highly reduce ER and PP in running and fast walking. Around preferred walking speed (1.3m/s) only a reduction in ER is found. The optimal stiffness changes with speed and gait. Still it is possible to use one constant stiffness for a huge range of walking and running speeds with only moderate increases of ER and PP in comparison to speed and gait optimized values.

Bipedal walking could be implemented into a robot by mimicking spring-like leg behaviour. The fundamental model, describing human-like leg function in walking is the bipedal spring-mass model which was investigated in this study. We identified several types of walking patterns, e.g. symmetric and asymmetric walking, that accounts for high variability of gait. The aim of this study is the identification of a stiffness range which allows for stable walking with comparatively large robustness against perturbations. Walking with compliant legs was tested with the bipedal PogoWalker, demonstrating advantages of the underlying leg mechanics, i.e. walking without the necessity of precise leg adjustments, and acceptable impact forces.

In human and animal running spring-like leg behavior is found, and similar concepts have been demonstrated by various robotic systems in the past. In general, a spring-mass model provides self-stabilizing characteristics against external perturbations originated in leg-ground interactions and motor control. Although most of these systems made use of linear spring-like legs. The question addressed in this paper is the influence of leg segmentation (i.e. the use of rotational joint and two limb-segments) to the self-stability of running, as it appears to be a common design principle in nature. This paper shows that, with the leg segmentation, the system is able to perform self-stable running behavior in significantly broader ranges of running speed and control parameters (e.g. control of angle of attack at touchdown, and adjustment of spring stiffness) by exploiting a nonlinear relationship between leg force and leg compression. The concept is investigated by using a two- segment leg model and a robotic platform, which demonstrate the plausibility in the real world.

Passive dynamics plays an important role in legged locomotion of the biological systems. The use of passive dynamics provides a number of advantages in legged locomotion such as energy efficiency, self-stabilization against disturbances, and generating gait patterns and behavioral diversity. Inspired from the theoretical and experimental studies in biomechanics, this paper presents a novel bipedal locomotion model for walking and running behavior which uses compliant legs. This model consists of three-segment legs, two servomotors, and four passive joints that are constrained by eight tension springs. The self-organization of two gait patterns (walking and running) is demonstrated in simulation and in a real-world robot. The analysis of joint kinematics and ground reaction force explains how a minimalistic control architecture can exploit the particular leg design for generating different gait patterns. Moreover, it is shown how the proposed model can be extended for controlling locomotion velocity and gait patterns with the simplest control architecture.