A comparison of static optimization criteria for resolving the 3D muscle redundancy problem during human gait

In this paper, different approaches of static optimization for predicting muscle forces during human walking are investigated. In order to better reflect the true mechanics of the human body, a three-dimensional musculoskeletal model of a single leg is developed. The joint moments generated by muscles during walking are computed from inverse dynamics. The muscle force is estimated by different optimization criteria, each satisfying the moment constraints at all joints and the lower and upper muscle force constraints. Several polynomial and non-polynomial criteria frequently used in literature are studied. Then the results obtained from these calculations are compared with each other. This paper provides an overview of the effects of different optimization criteria on the 3D muscle force distribution problem during human walking. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study on feet forces' distributions,energy consumption and dynamic stability measure of hexapod robot during crab walking

This paper deals with the development of a dynamical model related to crab walking of a hexapod robot to determine the feet forces' distributions, energy consumption and dynamic stability measure considering the inertial effects of the legs on the system, which has not been attempted before. Both forward and inverse kinematic analyses of the robot are carried out with an assigned fixed global frame and subsequent local frames in the trunk body and joints of each leg. Coupled multi-body dynamic model of the robot is developed based on free-body diagram approach. Optimal feet forces and corresponding joint torques on all the legs are determined based on the minimization of the sum of the squares of joint torques, using quadratic programming (QP) method. An energy consumption model is developed to determine the minimum energy required for optimal values of feet forces. To ensure dynamically stable gaits, dynamic gait stability margin (DGSM) is determined from the angular momentum of the system about the supporting edges. Computer simulations have been carried out to test the effectiveness of the developed dynamic model with crab wave gaits on a banking surface. It is observed that when the swing leg touches the ground, impact forces (sudden shoot outs) are generated and their effects are also observed on the joints of the legs. The effects of walking parameters, namely trunk body velocity, body stroke, leg offset, body height, crab angle etc. on power consumption and stability during crab motion for duty factors (DFs) like 1/2, 2/3, 3/4 have also been studied.     

Studying Dynamical Principles of Human Locomotion using Inverse Optimal Control

Human movement, as for example human gait, can be considered as an optimal realization of some given task. However, the criterion for which the naturally performed human motion is optimal, is generally not known. In this article we formulate an inverse optimal control problem to study the relevance of four different optimization criteria in human locomotion. As a walking model we use an actuated three dimensional spring loaded inverted pendulum (3D-SLIP), which is able to mirror the typical shape of the center of mass trajectory in human gait. Using a direct all-at-once approach, the weighting of the optimization criteria and the position of the footsteps are optimized in such a way, that the center of mass trajectory of the resulting optimal state fits real motion capture data as good as possible. Numerical experiments show, that whereas the so called capture point seems to have a great impact on human walking, minimization of the vertical center of mass movement does not show any relevance at all. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximating the relationship among the degree of the reaction forces and the nodes on footprint during a stance phase

This study examined the foot biomechanics that are utilized when foot is in contact with the ground during a stance phase. The purpose of the study was to investigate the normalized ground reaction forces that impacted certain sections and points on the footprint, and to identify patterns in the degrees to which these forces occurred. Foot was modeled in such a manner that a vertex represented a bone and an edge represented a joint, and a graph that depicted the foot was created. Twelve nodes were marked on the footprint and these were linked together to create a gait path. By fusing the graph and the gait path and by manipulating the mathematical models, a profile for an ideal bipedal walking locomotion was developed. A male subject performed bipedal walking through a force plate system in order to obtain the profile that reflected actual bipedal walking. The actual and the proposed profiles were compared and there were significant similarities between the two profiles, with both exhibiting an double-bump pattern. It is therefore viable that the approximation techniques proposed in this work may provide an alternative means over the application of a force plate system to generate a profile for bipedal walking. However, the accuracy and reliability of the results yielded from this technique need further investigation.     

Omnidirectional walking of legged robots with a failed leg

This paper studies omnidirectional walking of a hexapod robot with a locked joint failure by proposing crab gaits and turning gaits. Due to the reduced workspace of a failed leg, fault-tolerant gaits have limitations in their mobility. As for crab gaits, an accessible range of the crab angle is derived for a given configuration of the failed leg. As for turning gaits, the conditions on turning trajectories guaranteeing fault tolerance are derived for spinning gaits and circling gaits. Based on the principles of fault-tolerant gait planning, periodic crab gaits and turning gaits are proposed in which a hexapod robot realizes tripod walking after a locked joint failure, having a reasonable stride length and stability margin. The proposed fault-tolerant gaits are then applied to an obstacle avoidance problem of a hexapod robot with a locked joint failure. The kinematic constraints of fault-tolerant gaits should be considered in planning the robot trajectory.     

Virtual quadruped: Mechanical design,control, simulation,and experimentation

We consider a prototyped walking robot containing a platform and two double-link legs. Thus, it is a five-link mechanism. The front leg models identical motions of the quadruped’s two front legs, and the back leg models identical motions of the quadruped’s two back legs. The legs have passive (uncontrolled) feet that extend in the frontal plane. Because of this the robot is stable in the frontal plane. This robot can be viewed as a “virtual” quadruped. Four DC motors drive the mechanism. Its control system comprises a computer, hardware servo-systems, and power amplifiers. The locomotion of the prototype is planar curvet gait. In the double support our prototype is statically stable and overactuated. In the single support it is an unstable and underactuated system. There is no flight phase. We describe here the scheme of the mechanism, the characteristics of the drives, and the control strategy. The dynamic model of the planar walking is recalled for the double-and single-support phases and for the impact instant. The experiments give results that are close to those of the simulation. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 8, pp. 5–28, 2005.     

Sensitivity Analysis of Human Leg Metabolical Costs

The human walking is characterized by skeletal dynamics and muscle excitation patterns minimizing the metabolical energy. This criterion is applied to assess the performance of lower limb prosthetic devices, and to evaluate therapies for patients presenting gait disorders. It is desirable, therefore, to dispose models of the human normal and pathological gaits capable of estimating the metabolical energy expenditure. For the swing phase of normal and pathological gaits a musculoskeletal model of the lower limb is presented to estimate metabolical energy expenditure. The mechanical model has three degrees of freedom and is actuated by eight Hill-type muscle units, and the model for the metabolical costs is adopted from literature. In this paper a combination of inverse and direct dynamics is used, and a sensitivity analysis of the dynamical behavior and the corresponding metabolical costs estimations with respect to parametrized neural excitations is performed. The leg motions are based on experiments in a gait analysis laboratory. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulating Prosthetic Gait ‐ Lessons to Learn

Modern computer assisted above knee prostheses currently available on the market (e.g. C‐Leg from Otto‐Bock) allow the patients to choose their walking speed freely during level walking. Due to energy reasons it is only possible to change the passive mechanical characteristics of the prosthetic limb but no active actuators can be used to influence the knee joint movement. The control strategies for level walking act on the damping of the knee joint during swing phase of gait. During walking down ramps or descending stairs the control strategies are switched off in current designs. Based on a measured reference kinematics it should be possible to study the influence and behaving of technical devices in combination with the whole body biomechanical system. For this purpose we use a combined inverse‐forward‐dynamics approach. Kinematics parameters that are not critical in the inverse‐dynamics approach (leading to physiological reasonable forces and moments) and that are not influenced by the other parameters in the model are prescribed as in the classical inverse‐dynamics approach. To follow the other kinematics parameters (joint‐angles) control elements are used where the associated joint‐moments are determined by the goal trajectory and physiological boundary conditions. The so called “controlled joints” of the model and the applied technical device (prosthesis) are formulated as a forward‐dynamics system. In contrast to experimental studies a simulation study offers the advantage, that parameters can be varied in a wide range. Different ramp and stair inclinations can be implemented and different control strategies can be tested without any risk for the patient. The disadvantage lies in the fact, that there are only few reference sets for the kinematics of real patients. The modification of a reference kinematics for different situations (level walking, ramp or stair descent) is a big challenge and needs further investigation. On the other hand the combined inverse‐forward‐dynamics approach with its well balanced simplicity and complexity offers a flexible tool to reach this aim. This approach can also be used to investigate the interaction of the biomechanical system with other technical systems like sports equipment.     

Period-three route to chaos induced by a cyclic-fold bifurcation in passive dynamic walking of a compass-gait biped robot

This paper presents a study of the passive dynamic walking of a compass-gait biped robot as it goes down an inclined plane. This biped robot is a two-degrees-of-freedom mechanical system modeled by an impulsive hybrid nonlinear dynamics with unilateral constraints. It is well-known to possess periodic as well as chaotic gaits and to possess only one stable gait for a given set of parameters. The main contribution of this paper is the finding of a window in the parameters space of the compass-gait model where there is multistability. Using constraints of a grazing bifurcation on the basis of a shooting method and the Davidchack–Lai scheme, we show that, depending on initial conditions, new passive walking patterns can be observed besides those already known. Through bifurcation diagrams and Floquet multipliers, we show that a pair of stable and unstable period-three gait patterns is generated through a cyclic-fold bifurcation. We show also that the stable period-three orbit generates a route to chaos.     

Solving the Probabilistic TSP with Ant Colony Optimization

In this paper, we describe new ways to apply Ant Colony Optimization (ACO) to the Probabilistic Traveling Salesperson Problem (PTSP). PTSP is a stochastic extension of the well known Traveling Salesperson Problem (TSP), where each customer will require a visit only with a certain probability. The goal is to find an a priori tour visiting all customers with minimum expected length, customers not requiring a visit simply being skipped in the tour.We show that ACO works well even when only an approximative evaluation function is used, which speeds up the algorithm, leaving more time for the actual construction. As we demonstrate, this idea can also be applied successfully to other state-of-the-art heuristics. Furthermore, we present new heuristic guidance schemes for ACO, better adapted to the PTSP than what has been used previously. We show that these modifications lead to significant improvements over the standard ACO algorithm, and that the resulting ACO is at least competitive to other state-of-the-art heuristics.     

Expected waiting time in symmetric polling systems with correlated walking times

Polling systems have been extensively studied, and have found many applications. They have often been used for studying wired local area networks such as token passing rings and wireless local area networks such as bluetooth. In this contribution we relax one of the main restrictions on the statistical assumptions under which polling systems have been analyzed. Namely, we allow correlation between walking times. We consider (i) the gated regime where a gate closes whenever the server arrives at a queue. It then serves at that queue all customers who were present when the gate closes. (ii) The exhaustive regime in which the server remains at a queue till it empties. Our analysis is based on stochastic recursive equations related to branching processes with migration with a random environment. In addition to our derivation of expected waiting times for polling systems with correlated walking times, we set the foundations for computing second order statistics of the general multi-dimensional stochastic recursions.      

Dynamics of children with torsional anomalies of the lower limb joints

In this study we used the techniques of nonlinear dynamics to analyze the stability of normal and pathological gait in children. We based the analysis on the assumption that a human at steady-state locomotion can be represented as a nonlinear periodic system. Kinematic data for the lower limb joints were used to construct phase plane portraits and first return maps for the hip, the knee and the ankle joints. Anomalies in the joint rotations of pathological individuals were graphically depicted by comparing the phase plane portraits and first return maps. Using the Floquet theory, an index of dynamic stability was used to compare normal and pathological gait.     

The Effect of Clone Template Parameters on the Spreading Speeds in CNNs

The aim of this paper is to investigate the effect of clone template parameters on the spreading speeds in cellular neural networks(CNNs). According to the property analysis of spreading speeds of monotone semiflows developed by Yu and Zhang [{\it European Journal of Applied Mathematics}, {\bf 31} (2020), 369-384], we investigate the sign of spreading speeds, continuity and limit cases with no propagation phenomena for CNNs with general output functions where each cell interacts with its 2-neighborhood cell.     

Changes in the gait characteristics caused by external load,ground slope and velocity variation

The complexity of the human gait manifests itself by lots of parameters that can evoke different changes in the walking manner. They can be divided into two groups: inherent, like anthropometric features or peculiar psychomotor type, and those related to the external conditions. The aim of the paper is to analyze the influence of three parameters, i.e. external load, ground slope and gait velocity, on the locomotion characteristics and the gait stability. Within the framework of investigations for different values of the mentioned parameters a film registration of the trajectories of selected kinematic nodes during some gait cycles has been carried out. The obtained data was a subject of numerical calculation aimed at extracting the essential properties of the principal gait characteristics.     

A template for the exploration of chaotic locomotive patterns

Inverted pendulum and spring-mass models have been successfully used to explore the dynamics of the lower extremity for animal and human locomotion. These models have been classified as templates that describe the biomechanics of locomotion. A template is a simple model with all the joint complexities, muscles and neurons of the locomotor system removed. Such templates relate well to the observed locomotive patterns and provide reference points for the development of more elaborate dynamical systems. In this investigation, we explored if a passive dynamic double pendulum walking model, that walks down a slightly sloped surface (γ<0.0189 rad), can be used as a template for exploring chaotic locomotion. Simulations of the model indicated that as γ was increased, a cascade of bifurcations were present in the model's locomotive pattern that lead to a chaotic attractor. Positive Lyapunov exponents were present from 0.01839 rad <γ<0.0189 rad (Lyapunov exponent range=+0.002 to +0.158). Hurst exponents for the respective γ confirmed the presence of chaos in the model's locomotive pattern. These results provide evidence that a passive dynamic double pendulum walking model can be used as a template for exploring the biomechanical control parameters responsible for chaos in human locomotion.     

On Evolving Social Systems: Communication, Speciation and Symbiogenesis

In this paper we introduce three enhancements for evolutionary computing techniques in social environments. We describe the use of the genetic algorithm to evolve communicating rule-based systems, where each rule-based system represents an agent in a social/multi-agent environment. It is shown that the evolution of multiple cooperating agents can give improved performance over the evolution of an equivalent single agent, i.e. non-social, system. We examine the performance of two social system configurations as approaches to the control of gait in a wall climbing quadrupedal robot, where each leg of the quadruped is controlled by a communicating agent. We then introduce two social-level operators&2014;speciation and symbiogenesis&2014;which aim to reduce the amount of knowledge required a priori by automatically manipulating the system&2018;s social structure and describe their use in conjunction with the communicating rule-based systems. The reasons for implementing these kinds of operators are discussed and we then examine their performance in developing the controller of the wall-climbing quadruped. We find that the use of such operators can give improved performance over static population/agent configurations.     

The Logic with Truth and Falsehood Operators from a Point of View of Universal Logic

The logic with independent truth and falsehood operators TFL is proposed. In TFL(→) standard truth-conditions for the implication are adopted. Nevertheless the laws of classical logic are not valid. In this language more then 10⁷ different binary connectives can be defined. So this logic can be treated as universal logic relatively to the class of sentential logics.     

Force control of a fluidic muscle driven parallel platform

In this paper a new method for the force control of a parallel platform consisting of six fluidic-muscles of type RRPS is presented. Fluidic muscles require that the gas model as well as the rubber nonlinearities are included in the control scheme. Moreover, the control law for the gas flow in the proportional directional control valve in 3/3-way function needs to be taken into account. The present paper describes the basic dynamic models as well as testbed results for the existing fluidic-muscle parallel platform “HexaSpine” [3]. Here each leg is equipped with a force sensor, a pressure sensor and a magnetostrictive position encoder. The control scheme for the platform comprises six control loops for the six operated actuators with a model based force control each. It is shown that the aforementioned control scheme leads to a stable force control of the platform driven by fluidic muscles. As an application, the device will be employed in fields of biomechanics, as well as in general environments requiring physical simulation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)