Ground Contact Model Research Articles

A novel rigid Foot-Ground contact model for Predicting ground reaction forces and center of pressure during normal gait

Ground reaction forces (GRFs) and center of pressure (COP) are essential for understanding human motion and evaluating biomechanical parameters, but measuring them with force plates is often limited in many scenarios. In this study, we propose a novel methodology for estimating GRFs and COP during normal gait based on a rigid foot–ground contact model, referred to as the COP phase transition continuity model (COP-PTCM). The GRFs and COP are calculated based on the Newton-Euler Equations during the single support phase (SSP). Considering the spatiotemporal continuity of the COP trajectory during normal gait, the COP data for the double support phase (DSP) is obtained by an improved logistic function fitted using the COP data from the SSP. GRFs during the DSP are optimized using the minimum energy hypothesis. The COP-PTCM method is used to estimate the GRFs and COP of ten participants during normal gait, and the results are compared with simultaneously measured force plate data, yielding the relative root mean square error (rRMSE) between measured and estimated GRFs in the anterior-posterior, vertical, and medial–lateral directions are 10.90 ± 2.09 %, 4.73 ± 1.44 %, and 15.17 ± 1.69 %, respectively. Additionally, the rRMSE between measured and estimated COP in the anterior-posterior direction is 11.23 ± 0.03 %. The above comparison validates the effectiveness and accuracy of the proposed method.

Design and implementation of a hardware-in-the-loop simulation platform for a tail-sitter UAV

Purpose A high-fidelity simulation platform helps to verify the feasibility of the controller and reduce the cost of subsequent experiments. Therefore, this paper aims to design a high-fidelity hardware-in-the-loop (HIL) simulation platform for the tail-sitter vehicles. Design/methodology/approach The component breakdown approach is used to develop a more reliable model. Thruster dynamics and ground contact force are also modeled. Accurate aerodynamic coefficients are obtained through wind tunnel tests. This simulation system adopts a mode transition method to achieve continuous simulation for all flight modes. Findings Simulation results are in good agreement with the flight log and successfully predict the state of the vehicle. Originality/value First, the effects of the propeller slipstream are considered. Second, most researchers ignore the parasitic drag caused by the landing gear and other appendages, which is discussed in this study. Third, a ground contact model is implemented to allow a realistic simulation of the takeoff and landing phases. Fourth, complete wind tunnel tests are conducted to obtain more accurate aerodynamic coefficients. Finally, a mode transition method is deployed in the HIL simulation system to achieve continuous simulation for all flight modes.

One necessary condition for passive all-wheel attachment of a wheeled planetary rover

A planetary rover is designed to traverse rough, unpaved terrain. The all-wheel-attachment property, i.e., that each rover wheel maintains firm contact with the terrain, is considered crucial in modern rover suspension design. This paper proposes one necessary condition associating the DOF of the suspension with the number of wheels for the all-wheel-attachment property. The paper first describes an equivalent single wheel–ground contact model and then the whole rover model, through which the mobility value of 3 was calculated for the all-wheel-attachment condition. The necessary condition is finally acquired through the fact that in the all-wheel-attachment condition, mobility should equal the difference of DOF of the whole rover and constraints. Furthermore, a type synthesis is proposed for the rovers with passive all-wheel-attachment property using the necessary condition. The necessary condition was further verified and interpreted by case studies of various excellent rovers by different institutes and the simulation of newly proposed rovers.

Development and Validation of a Framework for Predictive Simulation of Treadmill Gait.

Treadmill training is a common intervention to promote healthy walking function for individuals with pathological gait. However, because of the heterogeneity of many patient populations, determining how an individual will respond to new treadmill protocols may require extensive trial and error, causing increased patient fatigue. The purpose of this study was to develop and validate a framework for predictive simulation of treadmill gait, which may be used in the design of treadmill training protocols. This was accomplished through three steps: predict motion of a simple model of a block relative to a treadmill, create a predictive framework to estimate gait with a two-dimensional (2D) lower limb musculoskeletal model on a treadmill, and validate the framework by comparing predicted kinematics, kinetics, and spatiotemporal parameters across three belts speeds and between speed-matched overground and treadmill predictive simulations. Predicted states and ground reaction forces for the block-treadmill model were consistent with rigid body dynamics, and lessons learned regarding ground contact model and treadmill motion definition were applied to the gait model. Treadmill simulations at 0.7, 1.2, and 1.8 m/s belt speeds resulted in predicted sagittal plane joint angles, ground reaction forces, step length, and step time that closely matched experimental data at similar speeds. Predicted speed-matched overground and treadmill simulations resulted in small root-mean-square error (RMSE) values within standard deviations for healthy gait. These results suggest that this predictive simulation framework is valid and can be used to estimate gait adaptations to various treadmill training protocols.

A Viscoelastic Contact Analysis of the Ground Reaction Force Differentiation in Walking and Running Gaits Realized in the Simplified Horse Leg Model Focusing on the Hoof—Ground Interaction

In the present study, the systematic method for the forward dynamics associated with the ground contact model was introduced to be able to consider the viscoelastic effect when contacting with the ground. In particular, we focused on the hoof-ground interaction in the simplified horse leg model because walking and running gaits are known to be different in trajectories; however, the force analysis still remains as unsolved issues. The computational experiments in Matlab, elastic and inelastic impact with the ground was resolved by using the dissipative contact force model proposed by Lankarani and Nikravesh and the ground reaction force was clearly examined in four different conditions from the combination of walking/running and elastic/inelastic contact. As result, two peaks during the stance phase in the walking condition were realized as well as the human gait and a single peak was newly observed in running with a time gap in elastic and inelastic condition. The proposed method contributes to the establishment of the detail time course analysis of the ground reaction force for animal and human gaits in a consistent manner.

Virtual Testing of Counterbalance Forklift Trucks: Implementation and Experimental Validation of a Numerical Multibody Model

This study investigates the dynamic behavior of a recently developed counterbalance forklift truck. The final objective is creating virtual testing tools based on numerical multibody models to evaluate the dynamic stresses experienced by the forklift family of interest during a reference operating cycle, defined by the manufacturer’s testing protocols. This work aims at defining sufficiently accurate and easy-to-implement modelling approaches and validation procedures. It focuses on a specific test, namely the passage of a speed-bump-like obstacle at high velocity, which represents one of the most severe conditions within the reference cycle. Indeed, unlike most of the other wheeled vehicles, forklifts typically do not have advanced suspension systems and their dynamic response is significantly affected by ground irregularities. To this end, a preliminary model of the complete forklift, featuring rigid bodies and a simplified tire–ground contact model, is implemented with a commercial software. Experimental tests are conducted on the forklift to measure the vehicle vibrations when running on the obstacle, for model validation purposes. After model updating, the results provided by the numerical simulations match the experimental data satisfactorily. Hence, the modelling and validation strategies are proven viable and effective.

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 Quick Turn of Foot: Rigid Foot-Ground Contact Models for Human Motion Prediction.

Computer simulation can be used to predict human walking motions as a tool of basic science, device design, and for surgical planning. One the challenges of predicting human walking is accurately synthesizing both the movements and ground forces of the stance foot. Though the foot is commonly modeled as a viscoelastic element, rigid foot-ground contact models offer some advantages: fitting is reduced to a geometric problem, and the numerical stiffness of the equations of motion is similar in both swing and stance. In this work, we evaluate two rigid-foot ground contact models: the ellipse-foot (a single-segment foot), and the double-circle foot (a two-segment foot). To evaluate the foot models we use three different comparisons to experimental data: first we compare how accurately the kinematics of the ankle frame fit those of the model when it is forced to track the measured center-of-pressure (CoP) kinematics; second, we compare how each foot affects how accuracy of a sagittal plane gait model that tracks a subjects walking motion; and third, we assess how each model affects a walking motion prediction. For the prediction problem we consider a unique cost function that includes terms related to both muscular effort and foot-ground impacts. Although the ellipse-foot is superior to the double-circle foot in terms of fit and the accuracy of the tracking OCP solution, the predictive simulation reveals that the ellipse-foot is capable of producing large force transients due to its geometry: when the ankle quickly traverses its u-shaped trajectory, the body is accelerated the body upwards, and large ground forces result. In contrast, the two-segment double-circle foot produces ground forces that are of a similar magnitude to the experimental subject because the additional forefoot segment plastically contacts the ground, arresting its motion, similar to a human foot.

Multibody simulation of a tracked vehicle with deformable ground contact model

In this paper, the realisation of a multibody model of a tracked machine is described. A new compact modelling of the tracks–soil interaction is presented and soil mechanics laws for terrain response are implemented. Tracked vehicles can be used in different fields such as agriculture, military and construction. The conditions of the terrain on which they operate may vary a lot, in terms of soil composition, slope and roughness. For this reason, performance of tracked vehicles is difficult to predict without a great number of field tests. The model is developed in a multibody code that makes it possible to investigate its dynamic and kinematic behaviour in several operating conditions. A specific routine is implemented in the multibody model in order to simulate the behaviour of the tracked vehicle on deformable terrains. The main hypothesis of this paper is that the terrain deformation could be in a narrow zone affected by the vehicle. Thus, the deformation of the soil is kinematically correlated to the vehicle. Soil mechanics equations are implemented on each track portion and solved only for track links in contact with the soil. The latter is modelled as a rigid body and terrain stress or deformation are not directly computed, thus simplifying solution and terrain modelling despite obtaining coherent results in terms of vehicle traction force, slip and sinkage. Results are reported pointing out performance of the tracked machine on different ground conditions.

A 3D ellipsoidal volumetric foot–ground contact model for forward dynamics

Foot–ground contact models are an important part of forward dynamic biomechanic models, particularly those used to model gait, and have many challenges associated with them. Contact models can dramatically increase the complexity of the multibody system equations, especially if the contact surface is relatively large or conforming. Since foot–ground contact has a large potential contact area, creating a computationally efficient model is challenging. This is particularly problematic in predictive simulations, which may determine optimal performance by running a model simulation thousands of times. An ideal contact model must find a balance between accuracy for large, conforming surfaces, and computational efficiency. Volumetric contact modelling is explored as a computationally efficient model for foot–ground contact. Previous foot models have used volumetric contact before, but were limited to 2D motion and approximated the surfaces as spheres or 2D shapes. The model presented here improves on current work by using ellipsoid contact geometry and considering 3D motion and geometry. A gait experiment was used to parametrise and validate the model. The model ran over 100 times faster than real-time (in an inverse simulation at 128 fps) and matched experimental normal force and centre of pressure location with less than 7% root-mean-square error. In most gait studies, only the net reaction forces, centre of pressure, and body motions are recorded and used to identify parameters. In this study, contact pressure was also recorded and used as a part of the identification, which was found to increase parameter optimisation time from 10 to 164 s (due to the additional time needed to calculate the pressure distribution) but helped the results converge to a more realistic model. The model matched experimental pressures with 33–45% root-mean-square error, though some of this was due to measurement errors. The same parametrisation was done with friction included in the foot model. It was determined that the velocity-based friction model that was used was inappropriate for use in an inverse-dynamics simulation. Attempting to optimise the model to match experimental friction resulted in a poor match to the experimental friction forces, inaccurate values for the coefficient of friction, and a poorer match to the experimental normal force.

Model validation of a hexapod walker robot

SUMMARYOur complete dynamical simulation-model realistically describes the real low-cost hexapod walker robot Szabad(ka)-II within prescribed tolerances under nominal load conditions. This validated model is novel, described in detail, for it includes in a single study: (a) digital controllers, (b) gearheads and DC motors, (c) 3D kinematics and dynamics of 18 Degree of Freedom (DOF) structure, (d) ground contact for even ground, (e) sensors and battery model. In our model validation: (a) kinematical-, dynamical- and digital controller variables were simultaneously compared, (b) differences of measured and simulated curves were quantified and qualified, (c) unknown model parameters were estimated by comparing real measurements with simulation results and applying adequate optimization procedures. The model validation helps identifying both model's and real robot's imperfections: (a) gearlash of the joints, (b) imperfection of approximate ground contact model, (c) lack of gearhead's internal non-linear friction in the model. Modeling and model validation resulted in more stable robot which performed better than its predecessors in terms of locomotion.

Foot–ground contact modeling within human gait simulations: from Kelvin–Voigt to hyper-volumetric models

This study describes the development of a multibody foot–ground contact model consisting of spherical volumetric models for the surfaces of the foot. The developed model is two-dimensional and consists of two segments, the hind-foot, mid-foot, and fore-foot as one rigid body and the phalanges collectively as the second rigid body. The model has four degrees of freedom: ankle $x$ and $y$ , foot orientation, and metatarsal-phalangeal joint angle. Three different types of contact elements are targeted: Kelvin–Voigt, linear volumetric, and hyper-volumetric. The models are kinematically driven at the ankle and the metatarsal joints, and simulated horizontal and vertical ground reaction forces as well as center of pressure location are compared against experimental quantities acquired from barefoot measurements during a human gait cycle. Parameter identification is performed for finding optimal contact parameters and locations of the contact elements. The hyper-volumetric foot–ground contact model was found to be a suitable choice for foot/ground interaction modeling within human gait simulations; this model showed 75 % and 62 % improvement on the matching quality over the point contact and linear volumetric models, respectively.

Parameter identification method for a three-dimensional foot–ground contact model

A new parameter identification method for a three-dimensional foot–ground contact model is presented. The model is used to reproduce the relationship between the contact forces and the relative foot–ground displacements and velocities. The parameters of the contact model are estimated using the optimization method known as covariance matrix adaptation evolution strategy. An extended Kalman filter is implemented as a controller to compute a forward dynamic analysis of the foot motion using body segment parameters and the ankle joint wrench as input data. The aim of this work is to adjust the position and size of the contact elements (spheres) and the model parameters in order to obtain both, a predicted motion provided by forward dynamics as faithful as possible to the captured motion and a resultant foot–ground wrench (obtained through the foot–ground contact model) as close as possible to the measured foot–ground reactions. The results show that the obtained motion is really similar to the captured one and, moreover, the vertical force and the moments in the horizontal plane are in agreement with the experimental mesurments. However, the bristle friction model used for tangential forces provides lower level of agreement with the experimental data.

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.

Total dynamic response of a PSS vehicle negotiating asymmetric road excitations

A planar suspension system (PSS) is a novel automobile suspension system in which an individual spring–damper strut is implemented in both the vertical and longitudinal directions, respectively. The wheels in a vehicle with such a suspension system can move back and forth relative to the chassis. When a PSS vehicle experiences asymmetric road excitations, the relative longitudinal motion of wheels with respect to the chassis in two sides of the same axle are not identical, and thus the two wheels at one axle will not be aligned in the same axis. The total dynamic responses, including those of the bounce, pitch and the roll of the PSS vehicle, to the asymmetric road excitation may exhibit different characteristics from those of a conventional vehicle. This paper presents an investigation into the comprehensive dynamic behaviour of a vehicle with the PSS, in such a road condition, on both the straight and curved roads. The study was carried out using an 18 DOF full-car model incorporating a radial-spring tyre–ground contact model and a 2D tyre–ground dynamic friction model. Results demonstrate that the total dynamic behaviour of a PSS vehicle is generally comparable with that of the conventional vehicle, while PSS exhibits significant improvement in absorbing the impact forces along the longitudinal direction when compared to the conventional suspension system. The PSS vehicle is found to be more stable than the conventional vehicle in terms of the directional performance against the disturbance of the road potholes on a straight line manoeuvre, while exhibiting a very similar handling performance on a curved line.

Performance comparison of a planar bipedal robot with rigid and compliant legs

AbstractThe purpose of this work is to study the effect of placing passive storage elements (springs) along the robot legs on its performance. We first present the model of a planar passive dynamic walker with compliant ground contact model, then replace its rigid legs with compliant legs. Simulation results validate the effectiveness of compliant legs in improving the performance (robustness and velocity) of the robot.

Measuring Lateral Tire Performance on Winter Surfaces

Abstract The Army has approved and funded an Army Technology Objective (ATO) entitled “High Fidelity Ground Platform and Terrain Mechanic Modeling.” This ATO is being jointly performed by the Engineer Research and Development Center (ERDC) along with the U.S. Army Tank Automotive Research, Development and Engineering Center (TARDEC) and the Army Research Laboratory (ARL). Two of the ERDC laboratories are participating in the ATO: The Cold Regions Research and Engineering Laboratory (CRREL) in Hanover, NH, and the Geotechnical and Structures Laboratory in Vicksburg, MS. One of CRREL’s major milestones for the ATO is to extend two-dimensional ground contact models for the TARDEC Real-time Simulator to full three-dimensional functionality by including the lateral forces. Central to that requirement is an understanding of lateral forces on all-seasons terrain. While modeling of vehicle tire lateral force interactions for typical hard paved surfaces is well understood, there is a need to translate that understanding in a consistent manner into off-road terrain and low-friction surfaces. The experimental work described in this paper is fundamental to gaining the required understanding. The experimental work, performed with instrumented vehicles, was accomplished via a contract with the Nevada Automotive Test Center. The testing included both lateral and longitudinal traction tests on winter surfaces. The surfaces included ice, packed snow, and disaggregated snow. The two principal tires tested were an all-season LT235/75R15 that has been the subject of many tests on the CRREL instrumented vehicle, and a tire used on the military’s HMMWV, size 37×12.50R16.5. For each tire and surface, tests at a minimum of two inflation pressures were conducted. For each surface/tire/inflation variant a minimum of ten replicate data sets were obtained. This paper reports the results of the tests and the analysis conducted to date.

The Role of Beam Flexibility and Ground Contact Model in the Clattering of Deformable Beams

It has been shown in previous research that, relative to (the usually considered case of) a single impact, multiple impacts (clattering) of rigid casings can greatly enhance the probability of failure of fragile components mounted on or inside them. This paper addresses the important issues of the roles of casing flexibility and contact model in the above situation. A finite element analysis of clattering of a Timoshenko beam is carried out here. Dependence of the maximum change in average velocity due to impact, on the beam stiffness and coefficient of restitution, are studied here.