Dynamic modelling for implementation of a right turn in bipedal walking

This paper deals with the development of a conceptual model for the control of a multilink biped during a turning maneuver. The skeletal model is a seven link biped for which the equations of motion are derived. A set of lower limb muscles are idealized by simple force actuators with no co-contraction of agonist-antagonist muscle pairs. A nonlinear control scheme is proposed to guide the model along the desired trajectory and to control ground reaction forces. The input to the system is a desired set of trajectories as functions of time and the patterns of desired ground reaction forces in a turn. One set of such inputs are inferred from the existing literature. With this input, the nonlinear control strategy allows computation of muscular forces needed for the turning maneuver.     

Initiation of walk and tiptoe of a planar nine-link biped

A nine-link planar biped model is studied. Its nonlinear differential equations are derived. Constraints due to the connections of the links and the contact between the model and the ground are analyzed, and forces of constraint are specified as functions of the state and inputs. With large external forces acting on the model, connection constraints are maintained by the ligaments and other soft tissue structures. It is shown that ligamentious structures contribute to the stability of the system and help maintain the integrity of the joint. By using linear feedback control, the nine-link model is stabilized around the vertical stance. The stable motion of the system in the vicinity of the vertical is studied by computer simulation of walking and tiptoe gaits.     

A computational human model for exploring the role of the feet in balance

Many studies concerning human balance use computational models that represent the body as a single, double, or triple inverted pendulum while ignoring the feet. Clinical research, however, has begun to more closely examine specific contributions of the feet in balance, leading to a disparity between the state of clinical research and the models used for simulation. Here, we expand the single inverted pendulum model by adding four additional rigid links to represent the feet. Model parameters, equations of motion, actuation based on human musculature, and control based on proprioception are discussed. Computation of ground reaction forces under the heel, forefoot, and toes is also addressed. Simulations focusing on the role of the toes and toe muscles in static balance and forward leaning are presented.     

Pattern of anterior cruciate ligament force in normal walking

The goal of this study was to calculate and explain the pattern of anterior cruciate ligament (ACL) loading during normal level walking. Knee-ligament forces were obtained by a two-step procedure. First, a three-dimensional (3D) model of the whole body was used together with dynamic optimization theory to calculate body-segmental motions, ground reaction forces, and leg-muscle forces for one cycle of gait. Joint angles, ground reaction forces, and muscle forces obtained from the gait simulation were then input into a musculoskeletal model of the lower limb that incorporated a 3D model of the knee. The relative positions of the femur, tibia, and patella and the forces induced in the knee ligaments were found by solving a static equilibrium problem at each instant during the simulated gait cycle. The model simulation predicted that the ACL bears load throughout stance. Peak force in the ACL (303 N) occurred at the beginning of single-leg stance (i.e., contralateral toe off). The pattern of ACL force was explained by the shear forces acting at the knee. The balance of muscle forces, ground reaction forces, and joint contact forces applied to the leg determined the magnitude and direction of the total shear force acting at the knee. The ACL was loaded whenever the total shear force pointed anteriorly. In early stance, the anterior shear force from the patellar tendon dominated the total shear force applied to the leg, and so maximum force was transmitted to the ACL at this time. ACL force was small in late stance because the anterior shear forces supplied by the patellar tendon, gastrocnemius, and tibiofemoral contact were nearly balanced by the posterior component of the ground reaction.     

An actuated dissipative spring-mass walking model: Predicting human-like ground reaction forces and the effects of model parameters

Simple models are widely used to understand the mechanics of human walking. The optimization-based minimal biped model and spring-loaded-inverted-pendulum (SLIP) model are two popular models that can achieve human-like walking patterns. However, ground reaction forces (GRF) from these two models still deviate from experimental data. In this paper, we proposed an actuated dissipative spring-mass model by integrating these two models to realize more human-like GRF patterns. We first explored the function of stiffness, damping, and weights of both energy cost and force cost in the objective function and found that these parameters have distinctly different influences on the optimized gait and GRF profiles. The stiffness and objective weight affect the number and size of peaks in the vertical GRF and stance time. The damping changes the relative size of the peaks but has little influence on stance time. Based on these observations, these parameters were manually tuned at three different speeds to approach experimentally measured vertical GRF and the highest correlation coefficient can reach 0.983. These results indicate that the stiffness, damping, and proper objective functions are all important factors in achieving human-like motion for this simple walking model. These findings can facilitate the understanding of human walking dynamics and may be applied in future biped models.     

CPG Control for Biped Hopping Robot in Unpredictable Environment

A CPG control mechanism is proposed for hopping motion control of biped robot in unpredictable environment.Based on analysis of robot motion and biological observation of animal's control mechanism,the motion control task is divided into two simple parts:motion sequence control and output force control.Inspired by a two-level CPG model,a two-level CPG control mechanism is constructed to coordinate the drivers of robot joint,while various feedback information are introduced into the control mechanism.Interneurons within the control mechanism are modeled to generate motion rhythm and pattern promptly for motion sequence control; motoneurons are modeled to control output forces of joint drivers in real time according to feedbacks.The control system can perceive changes caused by unknown perturbations and environment changes according to feedback information,and adapt to unpredictable environment by adjusting outputs of neurons.The control mechanism is applied to a biped hopping robot in unpredictable environment on simulation platform,and stable adaptive motions are obtained.     

ASSESSMENT OF EXTERNAL AND INTERNAL LOADS IN THE TRIPLE JUMP VIA INVERSE DYNAMICS SIMULATION

The triple jump is a demanding athletics event that, after an approach run, consists of three consecutive phases: the hop, the bound, and the jump. During the involved three take-off actions a jumper is exposed to increased risk of injury due to the high impact forces from the ground and powerful muscle/tendon efforts, which are further reflected in the internal loads of the lower limb joints. While external ground reactions can possibly be measured using force platforms, in vivo measurements of the internal loads are practically not feasible. The purpose of the paper is to present the development of an effective formulation for the inverse dynamics simulation of the triple jump, based on the jumper dynamical model and non-invasive kinematic recordings of the movement. The developed simulation model serves for the analysis of all the triple jump phases, irrespective of whether the jumper is in flight or in contact with the ground with one of his feet, and is focused on effective assessment of the external reactions on the supporting leg as well as the muscle forces and joint reaction forces in the leg. Some numerical results of inverse dynamics simulation of the triple jump are reported.     

Steady state kinetics of an enzyme reaction with one substrate and one modifier

This study examines the steady state kinetics of a reaction involving an enzyme, a substrate and a modifier when the reaction follows Michaelis-Menten kinetics. Conditions for Michaelis-Menten kinetics are deduced, and it is shown that an analogue of detailed balance determines the complexity of the rate equations in these cases. A scheme to distinguish many cases of Michaelis-Menten kinetics is presented. It is shown that steady state kinetics are, in general, insufficient to specify the mechanism of a reaction, since different effects of a modifier can give identical steady state kinetic data.     

Stability in legged locomotion

Stability is a key element in a gait synthesis. Static stability margins are widely adopted in crawlers, while no similar approach has been developed for dynamically stable systems. Utilizing an analytical approach, we developed a set of easy-to-calculate stability indices to describe instantaneous static and dynamic (In)stability for a certain group of walking systems. The analysis is based on a thorough analysis of the interaction between ground reaction forces and the walking system. The indices are applicable to walking systems regardless of the number of legs or mechanical/biological design. We show that static and dynamic stability are independent of each other. We suggest a possible categorization of gait modes based on stability. Stability characteristics are analyzed in a healthy and highly pathological human gait. Finally, we discuss the applicability of the proposed methods.     

A closed-loop cadaveric foot and ankle loading model

Investigations of human foot and ankle biomechanics rely chiefly on cadaver experiments. The application of proper force magnitudes to the cadaver foot and ankle is essential to obtain valid biomechanical data. Data for external ground reaction forces are readily available from human motion analysis. However, determining appropriate forces for extrinsic foot and ankle muscles is more problematic. A common approach is the estimation of forces from muscle physiological cross-sectional areas and electromyographic data. We have developed a novel approach for loading the Achilles and posterior tibialis tendons that does not prescribe predetermined muscle forces. For our loading model, these muscle forces are determined experimentally using independent plantarflexion and inversion angle feedback control. The independent (input) parameters -- calcaneus plantarflexion, calcaneus inversion, ground reaction forces, and peroneus forces -- are specified. The dependent (output) parameters -- Achilles force, posterior tibialis force, joint motion, and spring ligament strain -- are functions of the independent parameters and the kinematics of the foot and ankle. We have investigated the performance of our model for a single, clinically relevant event during the gait cycle. The instantaneous external forces and foot orientation determined from human subjects in a motion analysis laboratory were simulated in vitro using closed-loop feedback control. Compared to muscle force estimates based on physiological cross-sectional area data and EMG activity at 40% of the gait cycle, the posterior tibialis force and Achilles force required when using position feedback control were greater.     

A model of the basal ganglia in voluntary movement and postural reactions

A basal ganglia central pattern generator (CPG) is developed and its role in voluntary movements on the ground and postural reactions on a disturbed platform are studied and analysed by simulation. Biped dynamics and platform kinematics are utilised. The effects of agonist–antagonist muscular co-activation and joint stiffness are formulated. The implementation of the necessary counter-manoeuvres for maintaining balance and postural stability is studied. A control strategy, applicable to large systems, is formulated. The biped manoeuvres and transitions terminate in pre-specified intervals of time. Gravity is included and compensated for. Certain voluntary and postural adjustment strategies are the same but are initiated differently. Further experimental/computational research may identify the central nervous system and sensory paths that lead to the CPG. All actuator forces linearly evolve in time from their original values to their terminal values. There are no central continuous feedback loops present. Monitoring and sensing, however, are ongoing. The counter-manoeuvres are based on learned human-like voluntary movements that are triggered by the disturbance. The required central inputs to the musculoskeletal system are designed in the CPG. A functional structure for the CPG is proposed. The effect of certain disorders and malfunctions of the CPG are studied by simulation.     

The deformation of an adherent leukocyte under steady shear flow: a numerical study

Leukocyte adhesion is a pathophysiological process in which the balance between hemodynamic and adhesion forces (molecular bonds) plays a key role. In this work, we studied the deformation of an adherent leukocyte and calculated the forces exerted on it. Three model cells were proposed, considering the leukocyte as a single drop, a compound drop, and a nucleus drop, representing a cell without nucleus, a cell with a nucleus, and a nucleus only, respectively. These model cells were supposedly adherent to a smooth substrate under steady shear flow. Our numerical results showed that all three model cells deformed in function of the initial contact angle, capillary number, and Reynolds number. The single drop was the most deformable, while the nucleus drop was the most resistant to the external flow. Each of the model cells showed maximum cell deformation at a high Reynolds number. The distribution of pressure on the cell confirmed the existence of a high-pressure region downstream of the drop, which retarded further deformation of the cell and provided a positive lift force on the drop. The consideration of a highly viscous nucleus can correct the over evaluation of the cell deformation in a flow.     

Control of microtubule assembly by extracellular matrix and externally applied strain

A number of studies have suggested that externally applied mechanical forces and alterations in the intrinsic cell-extracellular matrix (ECM) force balance equivalently induce changes in cell phenotype. However, this possibility has never been directly tested. To test this hypothesis, we directly investigated the response of the microtubule (MT) cytoskeleton in smooth muscle cells to both mechanical signals and alterations in the ECM. A tensile force that resulted in a positive 10% step change in substrate strain increased MT mass by 34 +/- 10% over static controls, independent of the cell adhesion ligand and tyrosine phosphorylation. Conversely, a compressive force that resulted in a negative 10% step change in substrate strain decreased MT mass by 40 +/- 6% over static controls. In parallel, increasing the density of the ECM ligand fibronectin from 50 to 1,000 ng/cm(2) in the absence of any applied force increased the amount of polymeric tubulin in the cell from 59 +/- 11% to 81 +/- 13% of the total cellular tubulin. These data are consistent with a model in which MT assembly is, in part, controlled by forces imposed on these structures, and they suggest a novel control point for MT assembly by altering the intrinsic cell-ECM force balance and applying external mechanical forces.     

Planning and Control for Passive Dynamics Based Walking of 3D Biped Robots

Efficient walking is one of the main goals of research on biped robots.Passive Dynamics Based Walking (PDBW) has been proven to be an efficient pattern in numerous previous approaches to 2D biped walking.The goal of this study is to develop a feasible method for the application of PDBW to 3D robots.First a hybrid control method is presented,where a previously proposed two-point-foot walking pattern is employed to generate a PDBW gait in the sagittal plane and,in the frontal plane,a systematic balance control algorithm is applied including online planning of the landing point of the swing leg and feedback control of the stance foot.Then a multi-space planning structure is proposed to implement the proposed method on a 13-link 3D robot.Related kinematics and planning details of the robot are presented.Furthermore,a simulation of the 13-link biped robot verifies that stable and highly efficient walking can be achieved by the proposed control method.In addition,a number of features of the biped walking,including the transient powers and torques of the joints are explored.     

A microcomputer-based video vector system for clinical gait analysis

A microcomputer-based video vector system has been developed to display the resultant ground reaction force vector on a television image of the subject in real-time. For each television field the force platform signals are acquired and processed and the resultant force vector superimposed on the video image of the walking subject. The force platform results are stored on disc and the composite video signals recorded on video tape for further analysis. The system is easy to set up and use and the results can be readily interpreted. The external moments produced at the joint centres by the ground reaction forces can be observed visually and, if required, quantification of the external moments can be achieved following data collection. The spatial resolution of the system is 0.342% vertically and 0.156% horizontally. The force vector visualization technique has routine applications in orthotics and prosthetics. It is also a useful technique for the teaching of biomechanics.     

Muscle contributions to whole-body sagittal plane angular momentum during walking

Walking is a complex dynamic task that requires the regulation of whole-body angular momentum to maintain dynamic balance while performing walking subtasks such as propelling the body forward and accelerating the leg into swing. In human walking, the primary mechanism to regulate angular momentum is muscle force generation. Muscles accelerate body segments and generate ground reaction forces that alter angular momentum about the body’s center-of-mass to restore and maintain dynamic stability. In addition, gravity contributes to whole-body angular momentum through its contribution to the ground reaction forces. The purpose of this study was to generate a muscle-actuated forward dynamics simulation of normal walking to quantify how individual muscles and gravity contribute to whole-body angular momentum in the sagittal plane. In early stance, the uniarticular hip and knee extensors (GMAX and VAS), biarticular hamstrings (HAM) and ankle dorsiflexors (TA) generated backward angular momentum while the ankle plantar flexors (SOL and GAS) generated forward momentum. In late stance, SOL and GAS were the primary contributors and generated angular momentum in opposite directions. SOL generated primarily forward angular momentum while GAS generated backward angular momentum. The difference between muscles was due to their relative contributions to the horizontal and vertical ground reaction forces. Gravity contributed to the body’s angular momentum in early stance and to a lesser extent in late stance, which was counteracted primarily by the plantar flexors. These results may provide insight into balance and movement disorders and provide a basis for developing locomotor therapies that target specific muscle groups.     

Estimating the complete ground reaction forces with pressure insoles in walking

This study presented a method to estimate the complete ground reaction forces from pressure insoles in walking. Five male subjects performed 10 walking trials in a laboratory. The complete ground reaction forces were collected during a right foot stride by a force plate at 1000Hz. Simultaneous plantar pressure data were collected at 100Hz by a pressure insole system with 99 sensors covering the whole plantar area. Stepwise linear regressions were performed to individually reconstruct the complete ground reaction forces in three directions from the 99 individual pressure data until redundancy among the predictors occurred. An additional linear regression was performed to reconstruct the vertical ground reaction force by the sum of the value of the 99 pressure sensors. Five other subjects performed the same walking test for validation. Estimated ground reaction forces in three directions were calculated with the developed regression models, and were compared with the real data recorded from force plate. Accuracy was represented by the correlation coefficient and the root mean square error. Results showed very good correlation in anterior-posterior (0.928) and vertical (0.989) directions, and reasonable correlation in medial-lateral direction (0.719). The root mean square error was about 12%, 5% and 28% of the peak recorded value. Future studies should aim to generalize the methods or to establish specific methods to other subjects, patients, motions, footwear and floor conditions. The method gives an extra option to study an estimation of the complete ground reaction forces in any environment without the constraints from the number and location of force plates.     

Quantitative assessment of gait determinants during single stance via a three-dimensional model--Part 1. Normal gait

In this two-part paper, a variety of three-dimensional, dynamical models are constructed for simulating the single support phases of normal and pathological human gait. A major objective of this work is to quantify the influence of individual gait determinants on the ground reaction forces generated during normal, level walking. To this end, Part 1 presents a three-dimensional, seven degree-of-freedom model incorporating five of the six fundamental determinants of gait. On the basis of crude muscle-force and/or joint-moment trajectories, body-segmental motions and ground reaction forces are synthesized open loop. Through a quantitative comparison with experimental gait data, the model's predictions are evaluated. Our simulation results suggest that pelvic list is not as dominant a dynamical determinant as either stance knee flexion-extension or foot and knee interaction. Transverse pelvic rotation, however, makes an important contribution by limiting the magnitude of the horizontal ground reaction prior to opposite heel-strike.     

Determining the centre of pressure during walking and running using an instrumented treadmill

In this paper, a new method of determining spatial and temporal gait parameters by using centre of pressure (CoP) data is presented. A treadmill is used which was developed to overcome limitations of regular methods for the analysis of spatio-temporal gait parameters and ground reaction forces during walking and running. The design of the treadmill is based on the use of force transducers underneath a separate left and right plate, which together form the treadmill walking surface. The results of test procedures and measurements show that accurate recordings of vertical ground reaction force can be obtained. These recordings enable a separate analysis of vertical ground reaction forces during double support phases in walking, and the analysis of changes in the centre of pressure (CoP) position during subsequent foot placements. From the CoP data, temporal gait parameters (e.g. duration of left/right support and swing phases) and spatial gait parameters (i.e. left/right step lengths and widths) can be derived.     

A treadmill-mounted force platform

Muscle, bone, and tendon forces; the movement of the center of mass, and the spring properties of the body during terrestrial locomotion can be measured using ground-mounted force platforms. These measurements have been extremely time consuming because of the difficulty in obtaining repeatable constant speed trials (particularly with animals). We have overcome this difficulty by mounting a force platform directly under the belt of a motorized treadmill. With this arrangement, vertical force can be recorded from an unlimited number of successive ground contacts in a much shorter time. With this treadmill-mounted force platform it is possible to accurately make the following measurements over the full range of steady speeds and under various perturbations of normal gait: 1) vertical ground reaction force over the course of the contact phase; 2) peak forces in bone, muscle, and tendon; 3) the vertical displacement of the center of mass; and 4) contact time for the limbs. In our treadmill-force platform design, belt forces and frictional forces cause no measurable cross-talk problem. Natural frequency (160 Hz), nonlinearity (less than 5%), and position independence (less than 2%) are all quite acceptable. Motor-caused vibrations are greater than 150 Hz and thus can be easily filtered.