Point Feet Research Articles

Enhancing speed recovery rapidity in bipedal walking with limited foot area using DCM predictions

The research on bipedal robots with limited foot area is gaining increasing attention. To tackle the challenge of dealing with unknown disturbances in the environment, the adjustment of footstep placement plays a vital role in maintaining stable motion during bipedal walking. This paper introduces an innovative approach based on the relationship between the Divergent Component of Motion (DCM) and footstep. It utilizes a DCM prediction model to optimize the optimal speed for recovering the foothold position. The goal is to enable quick and relevant footstep selection for bipedal robots, thereby facilitating the swift recovery of robot speed. The paper provides insights into the process of designing the desired DCM for achieving an optimal average walking speed without relying on predefined footstep sequences. By establishing a state equation between the DCM and footstep placement, this approach enables the prediction of multiple footstep positions within a fixed walking cycle, thereby facilitating the desired average motion speed. Extensive numerical simulations are conducted to compare the proposed method with various conventional footstep adjustment algorithms. The results emphasize our method’s ability to converge more rapidly to the target speed, even with minor step adjustments. To validate the feasibility and robustness of the algorithm, we conduct experiments on the bipedal robot BHR-B2. These experiments further confirm the algorithm’s effectiveness. Given its promising performance, this algorithm holds potential for applications in legged robots with point feet.

Control of Dynamic Biped Walking Robot

The objective of this article is to present control algorithms of biped dynamic walking robot. A mathematical model of the walking robot is compiled. The construction of the robot is based on minimalist design principles - absolutely solid body with two legs. Analytical dependencies between six coordinates of the body, coordinates of the left and right legs and absolute coordinates of the feet are defined. The block diagram of control system is presented. Differential equations of walking are compiled. The dynamic stability of biped walking robot near the required trajectory is provided by discrete control of the parameters: «when and where to put foot». To define these parameters, it is proposed to use an inverted mathematical pendulum as an ideal mechanism. Its linearized differential equations allow present the feet coordinates according to the measured initial and final parameters (at the begging and at the end of the step). The article paid particular attention to results of such control method with various walking modes. The coordinates of the robot body, its velocities and accelerations, angles of rotation were investigated. Calculations confirmed the small deviations of the proposed model of walking from the ideal one. The developed methodology allows improve the construction and control system of biped dynamic walking robots at the design stage. Some of the tasks, it can be used: design machines simulating human walking, with high speed and maneuverability, with point feet and synchronized with natural uncontrolled movements.

Trajectory-free dynamic locomotion using key trend states for biped robots with point feet

Trajectory-free dynamic locomotion using key trend states for biped robots with point feet

Traversing Steep and Granular Martian Analog Slopes With a Dynamic Quadrupedal Robot

Celestial bodies, such as the Moon and Mars are mainly covered by loose, granular soil, which is a notoriously challenging terrain to traverse with wheeled robots. Here, we present experimental work on traversing steep, granular slopes with the dynamically-walking quadrupedal robot SpaceBok. To adapt to the challenging environment, we developed passive-adaptive, planar feet and optimized studs to reduce sinkage and increase traction. Single-foot experiments revealed that a surface area of 110 cm2 per foot reduces sinkage to an acceptable level for the 22 kg robot, even on highly collapsible soil. Implementing several 12 mm studs increases traction by 22% to 66% on granular media compared to stud-less designs. Together with a terrain-adapting walking controller, we validate — for the first time — static and dynamic locomotion on Mars analog slopes of up to 25°(the maximum of the testbed). We evaluated the performance between point- and planar feet and static and dynamic gaits for safety, velocity, and energy consumption. We show that dynamic gaits are energetically more efficient than static ones, but are riskier on steep slopes. Our tests also revealed that energy consumption with planar feet increases drastically as slope inclination approaches the soil’s angle of repose. Point feet are less affected by slippage due to their excessive sinkage but, in turn, are prone to instabilities and tripping. Based on our findings, we present safe and energy-efficient, global, path-planning strategies for negotiating steep Martian topography.

Contribution of Leg Flexibility, Limb Length, Leg Power for the Split Leap Skills of Rhythmic Gymnastics Athletes

This study examined the association between leg flexibility, leg length, jump height, and split leap movement scores at various levels of rhythmic gymnasts. Fifty-two young rhythmic gymnasts (age: 10.63 ± 2.9 years) were divided into two groups (qualifying, n = 32 and non-qualifying, n = 20) based on age and regional championship level. The gymnast underwent a series of fitness tests in the form of leg flexibility and leg explosive power as well as a split jump performance which was judged by 2 national and international certified judges. There was a significant difference and correlation between qualification and non-qualification in the split leap score (p = 0.00), body weight (p = 0.00; r = 0.351), limb length (p = 0.00; r = 0.420), High Jump (p = 0.01; r = 0.279), raised straight legs (p = 0.021; r = -0.279). There was no difference found in point feet but positively related at split leap score (p = 0.386; r = 0.373). The overall multiple regression analysis of all novice athletes revealed that Limb length, point feet, and high jump accounted for a medium part (32%) of the split leap score. In conclusion, the level of the gymnast (non-qualification), weight, Limb length, and arm length had a greater effect on the implementation of the split leap, whereas at the junior level (qualification) the leg explosiveness and flexibility of the leg effectively contributed to the split leap movement. Overall, the athlete's flexibility, body composition, and the explosive power of the limb variables effectively contribute to the split leap movement in youth rhythmic gymnastics.

The validation of new phase-dependent gait stability measures: a modelling approach.

Identification of individuals at risk of falling is important when designing fall prevention methods. Current measures that estimate gait stability and robustness appear limited in predicting falls in older adults. Inspired by recent findings on changes in phase-dependent local stability within a gait cycle, we devised several phase-dependent stability measures and tested for their usefulness to predict gait robustness in compass walker models. These measures are closely related to the often-employed maximum finite-time Lyapunov exponent and maximum Floquet multiplier that both assess a system's response to infinitesimal perturbations. As such, they entail linearizing the system, but this is realized in a rotating hypersurface orthogonal to the period-one solution followed by estimating the trajectory-normal divergence rate of the swing phases and the foot strikes. We correlated the measures with gait robustness, i.e. the largest perturbation a walker can handle, in two compass walker models with either point or circular feet to estimate their prediction accuracy. To also test for the dependence of the measures under state space transform, we represented the point feet walker in both Euler–Lagrange and Hamiltonian canonical form. Our simulations revealed that for most of the measures their correlation with gait robustness differs between models and between different state space forms. In particular, the latter may jeopardize many stability measures' predictive capacity for gait robustness. The only exception that consistently displayed strong correlations is the divergence of foot strike. Our results admit challenges of using phase-dependent stability measures as objective means to estimate the risk of falling.

A Case Study on Influence of Utilizing Hill-Type Muscles on Mechanical Efficiency of Biped Running Gait

The presence of compliant elements in biped running mechanisms generates a smoother motion and decreases the impact forces. Biological creatures that have a complicated actuation system with parallel and series elastic elements in their muscles demonstrate very efficient and robust bipedal gaits. The main difficulty of implementing these systems is duplicating their complicated dynamics and control. This paper studies the effects of an actuation system, including Hill-type muscles on the running efficiency of a kneed biped robot model with point feet. In this research, we implement arbitrary trajectories compatible with the initial condition of the robot, and we calculate the necessary muscle forces using an analytical inverse dynamics model. To verify the results, we execute the direct dynamics of the robot with the calculated control inputs to generate the robot’s trajectory. Finally, we calculate the contractile element force of the muscles and its cost of transport, and we investigate the effects of the muscles’ elements on reducing or increasing the cost of transport of the gait and maximum actuating forces.

Walking Control Based on Step Timing Adaptation

Step adjustment can improve the gait robustness of biped robots; however, the adaptation of step timing is often neglected as it gives rise to nonconvex problems when optimized over several footsteps. In this article, we argue that it is not necessary to optimize walking over several steps to ensure gait viability and show that it is sufficient to merely select the next step timing and location. Using this insight, we propose a novel walking pattern generator that optimally selects step location and timing at every control cycle. Our approach is computationally simple compared to standard approaches in the literature, yet guarantees that any viable state will remain viable in the future. We propose a swing foot adaptation strategy and integrate the pattern generator with an inverse dynamics controller that does not explicitly control the center of mass nor the foot center of pressure. This is particularly useful for biped robots with limited control authority over their foot center of pressure, such as robots with point feet or passive ankles. Extensive simulations on a humanoid robot with passive ankles demonstrate the capabilities of the approach in various walking situations, including external pushes and foot slippage, and emphasize the importance of step timing adaptation to stabilize walking.

Variational-Based Optimal Control of Underactuated Balancing for Dynamic Quadrupeds

This paper presents a control strategy for quadruped balancing that enables postural control in underactuated contact configurations (e.g., when standing on two point feet). Underactuated balancing has received considerable attention with prototype control models such as the cart pendulum or acrobot. Yet, when attempting to transition these solutions to balance in legged robots, technical challenges related to friction-limited contacts and the underlying manifold structure of the configuration space prevent straightforward application. This paper presents a new balance control framework that combines constrained optimal control strategies with recent variational-based linearization approaches to solve the balancing problem for a common simplified quadruped model. The controller is implemented as a convex quadratic program (QP) that uses an unconstrained optimal control solution to approximate a friction-constrained optimal policy. Unlike state-of-the-art QP-based balance controllers, the method is able to handle balance in underactuated regimes. Via comparison to model-predictive control strategies, the proposed formulation is highly compact, requiring less computation, while still showing the ability to handle extreme friction limitations. Simulation and hardware results with the MIT Mini Cheetah demonstrate the capabilities of the controller to exploit body angular momentum for disturbance recovery on two feet, and to recover from cases where the center of mass exits the support polygon. These results and the generality of the formulation suggest exploration for further application to bipeds and humanoids.

Robust compound control of dynamic bipedal robots

This paper presents a robust compound control strategy to produce a stable gait in dynamic bipedal robots under random perturbations. The proposed control strategy consists of two interactive loops: an adaptive trajectory generator and a robust trajectory tracking controller. The adaptive trajectory generator produces references for the robot controlled joints without a-priori knowledge of the terrain features and minimizes the effects of disturbances and model uncertainties during the gait, particularly during the support-leg exchange. The trajectory tracking controller is a non-switching robust multivariable generalized proportional integral (GPI) controller. The GPI controller rejects external disturbances and uncertainties faced by the robot during the swing walking phase. The proposed control strategy was evaluated on the numerical model of a five-link planar bipedal robot with one degree of under-actuation, four actuators, and point feet. The results showed robust performance and stability under external disturbances and model parameter uncertainties on uneven terrain with uphills and downhills. The stability of the gait was proven through the computation of a Poincaré return map for a hybrid zero dynamics with uncertainties (HZDU) model, which shows convergence to a bounded neighborhood of a nominal orbital periodic behavior.

Fuzzy control of bipedal running with variable speed and apex height

In this paper we propose a fuzzy-based control scheme to generate stable planar biped running gaits with variable apex height and velocity. The considered biped robot model includes five links with locked torso angles, point feet, and four actuators at the hip and knees. The controller includes two separate levels: upper-level and lower-level. The lower-level part is composed of a state machine, where the trajectory of running sub-phases and their switching time are controlled. The upper-level part includes an event-based fuzzy logic controller that is called at the apex of each flight phase. We use an offline fuzzy training process for designing fuzzy rules before controlling the robot. Fuzzy training is an iterative computational process that is repeated until convergence. Outputs of the fuzzy controller are fed into the state machine to control the running gaits. Simulation results show that the proposed control strategy generates stable gaits with controllable apex height and velocity in each step. Finally, the effects of apex height and velocity in running efficiency are investigated and optimum height is calculated as a function of running velocity.

Theoretical Analysis and Numerical Optimization of a Wearable Spring-Clutch Mechanism for Reducing Metabolic Energy Cost During Human Walking

Abstract There is a growing interest in assistive wearable devices for laden walking, with applications to civil hiking or military soldiers carrying heavy loads in outdoor rough terrains. While the solution of powered exoskeleton is known to be heavy and energy consuming, recent works presented wearable light-weight (semi-)passive elements based on elastic springs engaged by timed clutches. In this work, we theoretically study the dynamics of a five-link model of a human walker with point feet, using numerical simulations. We propose a novel mechanism of a spring and two triggered clutches, which enables locking the spring with stored energy while the device's length can change freely. For a given gait of joint angles trajectories, we numerically optimize the spring parameters and clutch timing for minimizing the metabolic energy cost. We show that a cleverly designed device can, in theory, lead to a drastic reduction in metabolic energy expenditure.

Humanoid Dynamic Synchronization Through Whole-Body Bilateral Feedback Teleoperation

This paper presents a method to achieve human and legged robot dynamic synchronization through bilateral feedback teleoperation. Our study shows how we can explore the interplay between human Extrapolated Center of Mass and the contact forces with the environment in order to transmit to the robot the underlying balancing and stepping strategy. All the necessary key equations for the frontal plane coupled dynamics are presented along with the human feedback law derived from the proposed state normalization in length and time. Here, we pay special attention to how the natural frequency of each system influences the resulting motion and analyze how the coupled system responds to various robot sizes. Experiments in which a human operator controls a simulated bipedal robot show how the Balance Feedback Interface force varies according to different scales and responds to external disturbances. Finally, we show the method's robustness to uneven terrain and how we can allow the point feet robot to synchronously take steps with the operator. This is an introductory study that aims to grant legged robots motor capabilities for power manipulation comparable to humans.

EXPERIMENTAL VALIDATION OF A CONTROL METHOD FOR UNDERACTUATED BIPEDAL WALKING ON COMPLIANT GROUND

This paper presents the experimental validation of an adaptive feed-forward control (AFC) method for underactuated bipedal walkingon compliant ground using UBbot, a four-link planar robot proto-type composed of two legs with knees and unactuated point feet.

Discrete sliding mode control to stabilize running of a biped robot with compliant kneed legs

This paper investigates performance of two event-based controllers applied to an underactuated biped robot to stabilize its running gait in presence of uncertainties. Mechanism of the biped robot includes four links leg, one point mass at the hip, point feet, and three motors parallel to rotational springs. So it has one degree of underactuation during stance phase and three degrees of underactuation during flight phase. A discrete sliding mode controller (DSMC) in comparison with a discrete linear-quadratic regulator (DLQR) is examined in order to stabilize the fixed point of the corresponding Poincare map. Using numerical simulations, it is concluded that DSMC has a better performance regarding basin of attraction and convergence speed compared to DLQR, especially in presence of disturbances.

Control of Walking for an Exoskeleton with the Use of Information about the Programmatic Torques

A dynamic model of the motion in the sagittal plane of the lower limbs of the exoskeleton, integrated with a human operator, was created with account of its lean on rigid weightless crutches. This model describes a mockup of the exoskeleton, which is a 5-link system incorporating the knee and hip drives, as well as massless hand supports. The dynamic model is based on the Lagrange equations of the second kind, which, alongside with the kinematic parameters, also includes the reaction support forces of the point feet and weightless crutches. When the parameters of the mathematical model were set, the inertial mass of the body characteristics of the resulting statistical processing of the tomography slices of a certain number of subjects were taken into account. In the model, the crutches are considered as an extension of the human hands, so the force application points of the crutches are the shoulders of the operator. Human reaction in the shoulder joint to the torque of the crutches is considered irrelevant. The model also takes into account the dynamics of the DC electrical drives. The synthesis is based on the method of solving the inverse tasks of the dynamics. Synthesis of the control system was carried out on the example of a flat, single support for comfortable walking. Since it is assumed that an operator has a weakened musculoskeletal system, but workable hands, it is considered that the given influences on the control system of the exoskeleton are the required torques in the hip and knee joints, viewed as a time function, while a person is assigned the function of providing power to the crutches. As a result, an analytical law motion control exoskeleton was designed, which provided locomotion to the hip and knee joints in accordance with the selected desired mode. The synthesized algorithms were applied to the constructed mathematical models and a numerical study of them was conducted. The article presents the results of the numerical simulation and of the investigated precision control.

An asymptotic solution to a passive biped walker model

We consider a simple model of a passive dynamic biped robot walker with point feet and legs without knee. The model is a switched system, which includes an inverted double pendulum. Robot’s gait and its stability depend on parameters such as the slope of the ramp, the length of robot’s legs, and the mass distribution along the legs. We present an asymptotic solution of the model. The first correction to the zero order approximation is shown to agree with the numerical solution for a limited parameter range.

Optimized 3D stable walking of a bipedal robot with line-shaped massless feet and sagittal underactuation

This paper seeks to provide a method for optimizing 3D bipedal walking with satisfactory energy efficiency, provable stability and one degree of underactuation. Following the studies of the planar biped RABBIT, we propose a 3D robot with massless line feet which serve as sagittal rotation axes when lying flat on the ground. Using this configuration and the control method based on virtual constraints and feedback linearization, the walking stability can be verified by the restricted scalar Poincaré map of the zero dynamics of the system, and periodic gaits can be obtained analytically as in the case of planar bipeds with point feet. A line-foot contact model is adopted to ensure one degree of underactuation. Unlike most published contact models of bipedal walking, this model also prevents possible yaw movements of the feet on the ground. In addition, we adopt an output function named “symmetry outputs” with the desired outputs parameterized by Bézier coefficients and postural parameters, and the gait optimization is performed using a SQP algorithm. According to the results obtained from a bipedal model with a height of 1.5 m and a weight of 39 kg, the optimization program is capable of calculating stable periodic gaits with a speed between 0.2 m/s and 1.5 m/s.

Compliant Biped Walking on Uneven Terrain with Point Feet

In this paper, we aim to realize compliant biped walking on uneven terrain with point feet. A control system is designed for a 5-link planar biped walker. According to the role that each leg plays, the control system is decomposed into two parts: the swing leg control and the support leg control. The trajectory of the swing foot is generated in real-time to regulate the walking speed. By considering the reaction torque of the swing leg's hip joint as disturbance, a sliding model controller is implemented at the support leg's hip joint to control the torso's posture angle. In order to make sure the landing foot does not rebound after impact, the vertical contact force control is set as the internal loop of the hip's height control. In simulation, the control system is tested on a virtual 5-link planar biped walker in Matlab. Finally, stable biped walking is realized on uneven terrain with roughness up to 2cm.

Interactive design of 3D-printable robotic creatures

We present an interactive design system that allows casual users to quickly create 3D-printable robotic creatures. Our approach automates the tedious parts of the design process while providing ample room for customization of morphology, proportions, gait and motion style. The technical core of our framework is an efficient optimization-based solution that generates stable motions for legged robots of arbitrary designs. An intuitive set of editing tools allows the user to interactively explore the space of feasible designs and to study the relationship between morphological features and the resulting motions. Fabrication blueprints are generated automatically such that the robot designs can be manufactured using 3D-printing and off-the-shelf servo motors. We demonstrate the effectiveness of our solution by designing six robotic creatures with a variety of morphological features: two, four or five legs, point or area feet, actuated spines and different proportions. We validate the feasibility of the designs generated with our system through physics simulations and physically-fabricated prototypes.