Point Foot Research Articles

Control of stability in semi-passive robot based on RBF neural network

The stability control of passive walking has been a major challenge in the field of passive robots because of its significant nonlinear characteristics. Using the adaptive sliding mode control based on local approximation of Radial Basis Function Neural Network (RBFNN), the walking stability of the simplest point foot model of biped passive robot is investigated in this paper. Simulation results show that the passive robot with this control method could achieve stable periodic gait with fewer steps than the robot without the control. In addition, given different control target state functions according to the characteristics of passive walking gait, passive robot can stabilize to corresponding periodic walking state with small control errors under the adaptive sliding mode control based on RBFNN. Finally, the influences of the gain coefficients of weight updating formula of RBFNN and the robustness coefficients of adaptive sliding mode controller on the control error results are discussed. It is found that the error decreases when the parameters increase within a certain limit, and the control effect becomes less obvious when the parameter exceeds the limit range.

A novel kinematics and statics correction algorithm of semi-cylindrical foot end structure for 3-DOF LHDS of legged robots

In this paper, aiming at the problem that the ideal modeling point of the foot end deviates from the actual contact point due to the rolling effect of the semi-cylindrical foot end in leg hydraulics drive system (LHDS), a novel and relatively simple kinematics and statics correction algorithm is proposed. This algorithm can effectively improve the accuracy of LHDS kinematics and statics, and it is still applicable when the body and the contact surface are at different angles. Firstly, this paper deduces the kinematics and statics when the foot end of LHDS is regarded as the point foot, analyzes and calculates the deviation under common working conditions. Secondly, in view of this phenomenon, a kinematics correction algorithm based on virtual DOF and a statics correction algorithm based on translation theorem of forces are proposed respectively. Finally, the proposed algorithm is verified by LHDS performance test platform under various working conditions. The results show that after applying the kinematics correction algorithm, the trajectory deviation reduction rate of the hip joint is over 65%; after applying the statics correction algorithm, the deviation reduction rate of foot end contact force is over 43%. The related research results can be applied to any similar foot end, which has engineering application value.

Comparison of direct collocation optimal control to trajectory optimization for parameter identification of an ellipsoidal foot–ground contact model

Foot–ground contact models play an important role in the accuracy of predictive human gait simulations, and there is a need for a computationally-efficient dynamic contact model for predictive and evaluative studies. In this research, we generated symbolic dynamic equations for a 2D torque-driven 11-DOF human model with a 3D ellipsoidal volumetric foot–ground contact model. The main goal was to increase the prediction accuracy and decrease the computation time for human gait analyses compared to the previous studies that used numerical formulations and point foot–ground contact models. A data-tracking optimization was developed to identify the contact parameters of the human gait model using two optimization approaches: trajectory optimization and optimal control. The first approach is developed with a global search algorithm based on inverse dynamics. In this algorithm, a local optimizer is repeatedly run from multiple potential start points to select the best start point while satisfying the constraints and reaching the lowest cost function value. The second approach is developed using direct collocation based on implicit dynamics. In this method, the optimization problem is solved using a variable-order adaptive orthogonal collocation method along with sparse nonlinear programming. Optimal control was superior to trajectory optimization for identifying a large number of parameters; the simulated torques and ground reaction forces from the optimal control correlated better with the experimental data. For the optimal control, the root-mean-square errors of the resultant torques, tangential and normal ground reaction forces were 0.48 (N.m), 14.07 (N), and 26.44 (N), respectively. However, for the trajectory optimization, these errors were 15.19 (N.m), 36.51 (N), and 234.57 (N). Thus, the optimized contact model from the optimal control, which was developed symbolically and based on volumetric contact equations, is a suitable foot–ground contact model for predictive human gait simulations. Additionally, we demonstrated that optimal control could be used to predict the motion and torque for the metatarsal joints, which are not easily measurable in practice.

A Geometric Strategy Algorithm for Orthogonal Projection onto a Parametric Surface

In this paper, we investigate how to compute the minimum distance between a point and a parametric surface, and then to return the nearest point (foot point) on the surface as well as its corresponding parameter, which is also called the point projection problem of a parametric surface. The geometric strategy algorithm (hereafter GSA) presented consists of two parts as follows. The normal curvature to a given parametric surface is used to find the corresponding foot point firstly, and then the Taylor’s expansion of the parametric surface is employed to compute parameter increments and to get the iteration formula to calculate the orthogonal projection point of test point to the parametric surface. Our geometric strategy algorithm is essentially dependent on the geometric property of the normal curvature, and performs better than existing methods in two ways. Firstly, GSA converges faster than existing methods, such as the method to turn the problem into a root-finding of nonlinear system, subdividing methods, clipping methods, geometric methods (tangent vector and geometric curvature) and hybrid second-order method, etc. Specially, it converges faster than the classical Newton’s iterative method. Secondly, GSA is independent of the initial iterative value, which we prove in Theorem 1. Many numerical examples confirm GSA’s robustness and efficiency.

Analysis of Behaviors Observed During Mechanical Nociceptive Threshold Testing in Donkeys and Horses

The aims of the study were to analyze and compare behaviors in horses and donkeys observed during nociceptive threshold tests with a mechanical stimulus applied to the limb. The purpose was to identify end point behaviors suggesting the animals had perceived the stimulus to be noxious. Six male castrated horses (aged 3–4 years, weighing 415–503 kg) and eight castrated male donkeys (aged 4–9 years, weighing 152.5–170.5 kg) were studied. Video data recorded during mechanical nociceptive threshold test were analyzed by a single observer. Behaviors were classified into short-duration event behaviors and longer duration activity/state behaviors. Frequency of behaviors within a test (event behaviors) and percentage time spent during the test (activity/state behaviors) were calculated. Data were compared between horses and donkeys using Mann–Whitney tests (nonparametric data) or t-test (parametric data). Significance was taken as P < .05. Behaviors during the tests were observed which could indicate the animals perceived the stimulus as noxious. These included flattening ears back against the head, and turning the head (horses) and chewing (donkeys) although these were not consistent across both species. Foot lifts were often preceded by other behaviors which suggests that the foot lift was not purely a reflex withdrawal response. A shift in weight toward the contralateral limb was a consistent prodromal sign for an end point foot lift.

Dynamic and Reactive Walking for Humanoid Robots Based on Foot Placement Control

This paper presents a novel online walking control that replans the gait pattern based on our proposed foot placement control using the actual center of mass (COM) state feedback. The analytic solution of foot placement is formulated based on the linear inverted pendulum model (LIPM) to recover the walking velocity and to reject external disturbances. The foot placement control predicts where and when to place the foothold in order to modulate the gait given the desired gait parameters. The zero moment point (ZMP) references and foot trajectories are replanned online according to the updated foothold prediction. Hence, only desired gait parameters are required instead of predefined or fixed gait patterns. Given the new ZMP references, the extended prediction self-adaptive control (EPSAC) approach to model predictive control (MPC) is used to minimize the ZMP response errors considering the acceleration constraints. Furthermore, to ensure smooth gait transitions, the conditions for the gait initiation and termination are also presented. The effectiveness of the presented gait control is validated by extensive disturbance rejection studies ranging from single mass simulation to a full body humanoid robot COMAN in a physics based simulator. The versatility is demonstrated by the control of reactive gaits as well as reactive stepping from standing posture. We present the data of the applied disturbances, the prediction of sagittal/lateral foot placements, the replanning of the foot/ZMP trajectories, and the COM responses.

Comparison of point foot, collisional and smooth rolling contact models on the bifurcations and stability of bipedal walking

Traditional biped walkers based on passive dynamic walking usually have flat or circular feet. This foot contact may be modelled with an effective rocker – represented as a roll-over shape – to describe the function of the knee–ankle–foot complex in human ambulation. Mahmoodi et al. has represented this roll-over shape as a polygon with a discretised set of collisions. In this paper point foot, collisional and smooth rolling contact models are compared. An approach based on the Lagrangian mechanics is used to formulate the equations for the swing phase that conserves mechanical energy. Qualitative insight can be gained by studying the bifurcation diagrams of gait descriptors such as average velocity, step period, mechanical energy and inter-leg angle for different gain and length values for the feet, as well as different mass and length ratios. The results from the three approaches are compared and discussed. In the case of a rolling disk, the collisional contact model gives a negligible energy loss; inco...

Investigating Balancing Control of a Standing Bipedal Robot With Point Foot Contact

Abstract: Comparing with wheeled or tracked moving machines, legged robots have potential advantages, especially when considering moving on discontinuous or rough terrain. For many bipedal robots, balance in the standing position is easy to maintain by having sufficient contact area with the ground. For some bipedal robots, the Zero Moment Point (ZMP) control method has been successfully implemented in which the center of mass is aligned above the support area. However, the balancing issue while standing becomes challenging when the contact area is very small. This paper presents a controller which is developed to balance a bipedal robot with coupled legs which have point foot contact. It is necessary to investigate the non-linear characteristics of the system. A pole-placement control method is used, and noise issues with sensing higher motion derivatives are investigated. The simulation-based evaluation indicates limitations that need to be addressed before experimental implementation.

Stability and agility: biped running over varied and unknown terrain

We tackle the problem of a biped running over varied and unknown terrain. Running is a necessary skill for a biped moving fast, but it increases the challenge of dynamic balance, especially when a biped is running on varied terrain without terrain information (due to the difficulty and cost of obtaining the terrain information in a timely manner). To address this issue, a new dynamic indicator called the sustainable running criterion is developed. The main idea is to sustain a running motion without falling by maintaining the system states within a running-feasible set, instead of running on a periodic limit cycle gait in the traditional way. To meet the precondition of the criterion, the angular moment about the center of gravity (COG) is restrained close to zero at the end of the stance phase. Then to ensure a small state jump at touchdown on the unknown terrain, the velocity of the swing foot is restrained within a specific range at the end of the flight phase. Finally, the position and velocity of the COG are driven into the running-feasible set. A five-link biped with underactuated point foot is considered in simulations. It is able to run over upward and downward terrain with a height difference of 0.15 m, which shows the effectiveness of our control scheme.

Online Biped Walking Pattern Generation with Contact Consistency

In this paper, a novel online biped walking gait pattern generating method with contact consistency is proposed. Generally, it’s desirable that there is no foot-ground slipping during biped walking. By treating the hip of the biped robot as a linear inverted pendulum (LIP), a foot placement controller that takes the contact consistency into account is proposed to tracking the desired orbit energy. By selecting the hip’s horizontal locomotion as the parameter, the trajectories in task space for walking are planned. A task space controller without calculating the inversion of inertial matrix is presented. Simulation experiments are implemented on a virtual 5-link point foot biped robot. The results show the effectiveness of the walking pattern generating method which can realize a stable periodic gait cycle without slipping and falling even suffering a sudden disturbance.

Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models

This two-part paper discusses the analysis and control of legged locomotion in terms of N-step capturability: the ability of a legged system to come to a stop without falling by taking N or fewer steps. We consider this ability to be crucial to legged locomotion and a useful, yet not overly restrictive criterion for stability. In this part (Part 1), we introduce a theoretical framework for assessing N-step capturability. This framework is used to analyze three simple models of legged locomotion. All three models are based on the 3D Linear Inverted Pendulum Model. The first model relies solely on a point foot step location to maintain balance, the second model adds a finite-sized foot, and the third model enables the use of centroidal angular momentum by adding a reaction mass. We analyze how these mechanisms influence N-step capturability, for any N > 0. Part 2 will show that these results can be used to control a humanoid robot.

Prediction of Bodyweight and Energy Expenditure Using Point Pressure and Foot Acceleration Measurements

Bodyweight (BW) is an essential outcome measure for weight management and is also a major predictor in the estimation of daily energy expenditure (EE). Many individuals, particularly those who are overweight, tend to underreport their BW, posing a challenge for monitors that track physical activity and estimate EE. The ability to automatically estimate BW can potentially increase the practicality and accuracy of these monitoring systems. This paper investigates the feasibility of automatically estimating BW and using this BW to estimate energy expenditure with a footwear-based, multisensor activity monitor. The SmartShoe device uses small pressure sensors embedded in key weight support locations of the insole and a heel-mounted 3D accelerometer. Bodyweight estimates for 9 subjects are computed from pressure sensor measurements when an automatic classification algorithm recognizes a standing posture. We compared the accuracy of EE prediction using estimated BW compared to that of using the measured BW. The results show that point pressure measurement is capable of providing rough estimates of body weight (root-mean squared error of 10.52 kg) which in turn provide a sufficient replacement of manually-entered bodyweight for the purpose of EE prediction (root-mean squared error of 0.7456 METs vs. 0.6972 METs). Advances in the pressure sensor technology should enable better accuracy of body weight estimation and further improvement in accuracy of EE prediction using automatic BW estimates.

Altered Disease Course after Initiation of Self-Monitoring of Blood Glucose in Noninsulin-Treated Type 2 Diabetes (ROSSO 3)

Patients with noninsulin-treated type 2 diabetes were documented from diagnosis to determine whether patients taking up self-monitoring of blood glucose (SMBG) are distinct by baseline characteristics, exhibit a different natural disease course, and are treated differently. The German multicenter, retrospective cohort study (ROSSO) followed 3268 persons from diagnosis of type 2 diabetes for a mean of 6.5 years. During follow-up, 1912 persons received oral antidiabetic agents (OAD) for at least 1 year, but no insulin. Data were retrieved from patient files of randomly contacted primary care practices. During follow-up, 742 patients (38.8%) began with SMBG prior to an end point. Initiation of SMBG was followed by improved glycemic control. Patients in the SMBG cohort were treated more often by an internist, younger by a mean of 3 years, and more often male (p < 0.001, each). A higher percentage of persons in the SMBG cohort were treated with metformin (74.7% vs 65.0%, p < 0.001) or changed OAD therapy (66.3% of patients vs 48.3% of patients, p < 0.001). SMBG was not accompanied by more comedication. In the SMBG cohort, 68 persons had a clinical end point (myocardial infarction, stroke, foot amputation, blindness, hemodialysis, or all-cause mortality) (9.2%) compared to 155 persons (13.2%) in the cohort without SMBG (p = 0.04 after multivariate adjustments). This first large documentation of OAD-treated persons from diagnosis for 6.5 years indicates that the use of SMBG is associated with younger age at diagnosis, a higher prescription rate of metformin, more frequent changes of oral therapy, and a lower risk of a clinical end point.

The Onset of Ventricular Isovolumic Contraction as Reflected in the Carotid Artery Distension Waveform

The blood pressure waveform carries information about the cardiac contraction and the impedance characteristics of the vascular bed. Here, we demonstrate that the start of isovolumic ventricular contraction is persistently reflected as an inflection point in the pressure wave as recorded in the aortic root (TP IC) as well as in the carotid artery distension waveform (TD IC) as it travels down the arterial tree. In a group of six patients with normal pressure gradients across the aortic valve after valve replacement, the TP IC had a small delay with respect to the onset of isovolumic ventricular contraction (<10 ms). In a group ( n = 21) of young presumably healthy volunteers, the inflection point occurred persistently in the carotid distension waveform, as recorded by means of ultrasound, before the systolic foot (intersubject delay between inflection point and systolic foot: mean ± SD = 40.0 ± 9.4 ms, intrasubject SD 4.6 ms). Retrograde coronary blood flow during isovolumic ventricular contraction may be the origin of the persistent end-diastolic pressure and distension perturbation. This study shows that the duration of the isovolumic contraction can be reliably extracted from the carotid artery distension waveform. (E-mail: A.Hoeks@BF.Unimaas.nl)

The onset of ventricular isovolumetric contraction as reflected in the carotid artery distension waveform

The blood pressure waveform carries information about the cardiac contraction and the impedance characteristics of the vascular bed. Here, we demonstrate that the start of isovolumic ventricular contraction is persistently reflected as an inflection point in the pressure wave as recorded in the aortic root (TPIC) as well as in the carotid artery distension waveform (TDIC) as it travels down the arterial tree. In a group of six patients with normal pressure gradients across the aortic valve after valve replacement, the TPIC had a small delay with respect to the onset of isovolumic ventricular contraction (<10 ms). In a group (n = 21) of young, presumably healthy, volunteers, the inflection point occurred persistently in the carotid distension waveform, as recorded by means of ultrasound, before the systolic foot (intersubject delay between inflection point and systolic foot: mean ± SD = 40.0 ± 9.4 ms, intrasubject SD 4.6 ms). Retrograde coronary blood flow during isovolumic ventricular contraction may be the origin of the persistent end-diastolic pressure and distension perturbation. This study shows that the duration of the isovolumic contraction can be reliably extracted from the carotid artery distension waveform. Figure 1

Spatio-temporal point processes, partial likelihood, foot and mouth disease

Spatio-temporal point process data arise in many fields of application. An intuitively natural way to specify a model for a spatio-temporal point process is through its conditional intensity at location x and time t, given the history of the process up to time t. Often, this results in an analytically intractable likelihood. Likelihood-based inference then relies on Monte Carlo methods which are computationally intensive and require careful tuning to each application. A partial likelihood alternative is proposed, which is computationally straightforward and can be applied routinely. The method is applied to data from the 2001 foot and mouth epidemic in the UK, using a previously published model for the spatio-temporal spread of the disease.

Equine Dentistry

The aims of the study were to analyze and compare behaviors in horses and donkeys observed during nociceptive threshold tests with a mechanical stimulus applied to the limb. The purpose was to identify end point behaviors suggesting the animals had perceived the stimulus to be noxious. Six male castrated horses (aged 3–4 years, weighing 415–503 kg) and eight castrated male donkeys (aged 4–9 years, weighing 152.5–170.5 kg) were studied. Video data recorded during mechanical nociceptive threshold test were analyzed by a single observer. Behaviors were classified into short-duration event behaviors and longer duration activity/state behaviors. Frequency of behaviors within a test (event behaviors) and percentage time spent during the test (activity/state behaviors) were calculated. Data were compared between horses and donkeys using Mann–Whitney tests (nonparametric data) or t-test (parametric data). Significance was taken as P < .05. Behaviors during the tests were observed which could indicate the animals perceived the stimulus as noxious. These included flattening ears back against the head, and turning the head (horses) and chewing (donkeys) although these were not consistent across both species. Foot lifts were often preceded by other behaviors which suggests that the foot lift was not purely a reflex withdrawal response. A shift in weight toward the contralateral limb was a consistent prodromal sign for an end point foot lift.

A mathematical taxonomy to evaluate the biomechanical quality of the human foot

The relationship between a functional disorder of the foot and the geometric configuration of its anatomical structure has been a subject of continuing interest among clinicians who are concerned with the various biomechanical disabilities of the foot. A survey of the literature shows that various geometric criteria and models have been proposed to arrive at a diagnosis and select an appropriate plan of treatment. Although these models have been used in biomechanical evaluation with varying degrees of success, their verbal descriptions and measurements are considered as oversimplifications with respect to both classification and discrimination. A more realistic model should induce a classification of sufficient refinement to produce a differential diagnosis among clinically significant variations in the biostructure of the foot. Based on a rationale of anatomical, physiological and clinical considerations, the one-quarter ellipsoid is selected as the model. Mathematical methods are used to classify human feet into a continuum of points representing the entire range of variations in foot shape. There is located an optimal point (foot) from which every other point is measured by means of a distance function. Each numerical deviation of a particular foot reflects the biomechanical quality of that foot. The concept of a biomechanically optimal foot which has ideal function as opposed to normal function offers the practitioner a quantitative rationale for the diagnosis and treatment of mechanical foot disorders.

A mathematical taxonomy to evaluate the biomechanical quality of the human foot

The relationship between a functional disorder of the foot and the geometric configuration of its anatomical structure has been a subject of continuing interest among clinicians who are concerned with the various biomechanical disabilities of the foot. A survey of the literature shows that various geometric criteria and models have been proposed to arrive at a diagnosis and select an appropriate plan of treatment. Although these models have been used in biomechanical evaluation with varying degrees of success, their verbal descriptions and measurements are considered as over-simplifications with respect to both classification and discrimination. A more realistic model should induce a classification of sufficient refinement to produce a differential diagnosis among clinically significant variations in the biostructure of the foot.Based on a rationale of anatomical, physiological, and clinical considerations, the one-quarter ellipsoid is selected as the model. Mathematical methods are used to classify human feet into a continuum of points representing the entire range of variations in foot shape. There is located an optimal point (foot) from which every other point is measured by means of a distance function. Each numerical deviation of a particular foot reflects the biomechanical quality of that foot.The concept of a biomechanically optimal foot which has ideal function as opposed to normal function offers the practitioner a quantitative rationale for the diagnosis and treatment of mechanical foot disorders.