Mathematical modeling of human running is a challenging problem from analytical and computational points of view. Purpose of the present research is to develop and study formulations and computational procedures for simulation of natural human running. The human skeletal structure is modeled as a mechanical system that includes link lengths, mass moments of inertia, joint torques, and external forces. The model has 55 degrees of freedom, 49 for revolute joints and 6 for global translation and rotation. Denavit-Hartenberg method is used for kinematics analysis and recursive Lagrangian formulation is used for the equations of motion. The dynamic stability is achieved by satisfying the zero moment point (ZMP) condition during the ground contact phase. B-spline interpolation is used for discretization of the joint angle profiles. The joint torque square, impulse at the foot strike, and yawing moment are included in the performance measure. A minimal set of constraints is imposed in the formulation of the problem to simulate natural running motion. Normal running with arm fixed, slow jog along curves, and running with upper body motion are formulated. Simulation results are obtained for various cases and discussed. The cases are running with different foot locations, running with backpack, and running with different running speeds. Also, extreme cases are performed. Each case gives reasonable cause and effect results. Furthermore, sparsity of the formulation is studied. The results obtained with the formulation are validated with the experimental data. The proposed formulation is robust and can predict natural motion of human running.

Recent advances in predictive dynamics allow the user to not only predict physics based human motion simulations but also determine the actuation torques required to achieve those motions. The predictive dynamics approach uses optimization to predict motion while using many task based, physics based, and environment based constraints including the equations of motion. Many tasks have been simulated using this new method of predicting and simulating digital human motion, e.g. walking, running, stair climbing, and box lifting. In this research, we develop a method to predict the motion as well as effect of external equipment hanging on the digital human. The proposed method is tested on a simple case of a two degree of freedom serial chain mechanism with a simple passive system to behave as external equipment. In particular, the passive mass is assumed to be attached to the two links system with a spring and damper. The results of the proposed method are compared with the results obtained by integrating the equations of motion of the full three degree of freedom system.

Design of heavy earthmoving equipment is based primarily on feedback from drivers. Most design studies on ingress and egress focus on the motion itself and rely heavily on experimental data. This process requires physical construction of expensive (in terms of time and money) mockups before any feedback can be obtained. Post-feedback design changes and the analysis of those changes are again expensive processes. Although the design of heavy vehicles requires consideration of human safety and comfort, very little attention has been given to simulating ingress and egress movement for these vehicles. This thesis describes the development of a virtual model to perform ingress and egress motions for heavy equipment and its applications to study the responses of operators with different anthropometries to different cab designs. Different performance measures are suggested and used with predictive dynamics to study human performance since human motion is not governed by a single performance measure. Optimizing multiple performance measures allows the full range of motion for all 55 degrees of freedom to be considered for simulating the task. Once the relevant performance measure was established, case studies were performed on seven different cab designs and digital human models with three different anthropometries. Finally, several different cab design metrics for propensity of injury, comfort, and accessibility were proposed. These design metrics were evaluated for each of the case studies. Finally, each cab design was ranked based on the design metrics to identify the best design for a range of anthropometries. These results help designers make decisions and plan further design changes.

One seminal question that faces a vehicle's driver (either human or computer) is predicting the capability of the vehicle as it encounters upcoming terrain. A Location-Aware Adaptive Vehicle Dynamics (LAAVD) System is being developed to assist the driver in maintaining vehicle handling capabilities through various driving maneuvers. In contrast to current active safety systems, this system is predictive, not reactive. The LAAVD System employs a predictor-corrector method in which the driver's input commands (throttle, brake, steering) and upcoming driving environment (terrain, traffic, weather) are predicted. An Intervention Strategy uses a novel measure of handling capability, the Performance Margin (PM), to assess the need to intervene. The driver's throttle and brake control are modulated to affect desired changes to the PM in a manner that is minimally intrusive to the driver's control authority. This system depends heavily on an understanding of the interplay between the vehicle's longitudinal, lateral, and vertical forces, as well as their resulting moments. These vehicle dynamics impact the PM metric and ultimately the point at which the Intervention Strategy will modulate the throttle and brake controls. Real-time implementation requires the development of computationally efficient predictive models of the vehicle dynamics. In this work, a method for predicting future vehicle states, based on current states and upcoming terrain, is developed using perturbation theory. An analytical relationship between the change in the spindle forces and the resulting change in the PM is derived, and the inverse relationship, between change in PM and resulting changes in longitudinal forces, is modeled. This model is implemented in the predictor-corrector algorithm of the Intervention Strategy. Corrections to the predicted states are made at each time step using a detailed, full, non-linear vehicle model. This model is run in real-time and is intended to be replaced with a drive-by-wire vehicle. Finally, the impact of this work on the automotive industry is discussed and recommendations for future work are given. / Master of Science

This study develops theorems which generalize or improve the existing predictive dynamics method and implements them to simulate several motion tasks of a human model. Specifically, the problem of determination of contact forces (non-adhesive) between the environment and the digital human model is addressed. Determination of accurate contact forces is used in the calculation of joint torques and is important to account for human strength limitations in simulation of various tasks. It is shown that calculation of the contact forces based on the distance of the contact areas from the Zero Moment Point (ZMP) leads to unrealistic values for some of the forces. This is the approach that has been used in the past. In this work, necessary and sufficient constraints for modeling the non-adhesiveness of a contact area are presented through the definition of NCM (Normal Contact Moment) concepts. NCM point, constraints and stability margins are the new theoretical concepts introduced. When there is only one contact area between the body and the environment, the ZMP and the NCM point coincide. In this case, the contact forces and moments are deterministic. When there are more than one contact areas, the contact forces and moments are indeterminate. In this case, an optimization problem is defined based on the NCM constraints where contact forces and moments are treated as the unknown design variables. Here, kinematics of the motion is assumed to be known. It is shown that this approach leads to more realistic values for the contact forces and moments for a human motion task as opposed to the ZMP based approach. The proposed approach appears to be quite promising and needs to be fully integrated into the predictive dynamics approach of human motion simulation. Some other insights are obtained for the predictive dynamics approach of human motion simulation. For example, it is mathematically proved and also validated that there is a need for an individual constraint to ensure that the normal component of the resultant global forces remains compressive for non-adhesive contacts between the body and the environment. Also, the ZMP constraints and stability margins are applicable for the problems where all the contacts between the environment and the body are in one plane; however, the NCM constraints and stability margins are applicable for all types of arbitrary contacts between the body and the environment. The ZMP and NCM methods are used to model the motion of a human (soldier) performing several military tasks: Aiming, Kneeling, Going Prone and Aiming in Prone Position. New collision avoidance theorems are also presented and used in these simulations.

Simulating realistic human behavior on a virtual avatar presents a difficult task. Because the simulated environment does not adhere to the same scientific principles that we do in the existent world, the avatar becomes capable of achieving infeasible postures. In an attempt to obtain realistic human simulation, real world constraints are imposed onto the non-sentient being. One such constraint, and the topic of this thesis, is self-collision avoidance. For the purposes of this topic, a posture will be defined solely as a collection of angles formed by each joint on the avatar. The goal of self-collision avoidance is to eliminate the formation of any posture where multiple body parts are attempting to occupy the exact same space. My work necessitates an extension of this definition to also include collision avoidance with objects attached to the body, such as a backpack or armor. In order to prevent these collisions from occurring, I have implemented an effort-based approach for correcting afflicted postures. This technique specifically pertains to postures that are sequenced together with the objective of animating the avatar. As such, the animation's coherence and defining characteristics must be preserved. My approach to this problem is unique in that it strategically blends the concept of keyframe interpolation with an optimization-based strategy for posture prediction. Although there has been considerable work done with methods for keyframe interpolation, there has been minimal progress towards integrating a realistic collision response strategy. Additionally, I will test this optimization-based approach through the use of a complex kinematic human model and investigate the use of the results as input to an existing dynamic motion prediction system.

[pt] A simulação do movimento do corpo humano é uma ferramenta valiosa para diferentes campos, como robótica e biomecânica. Mesmo com o crescente número de pesquisas, ainda existem poucos grupos no Brasil que trabalham desenvolvendo modelos de movimento humano. Tal simulação tem sido um problema desafiador do ponto de vista de modelagem e computacional. Esta dissertação traz uma revisão bibliográfica de conceitos de dinâmica estrutural e dos principais determinantes da dinâmica do caminhar humano. Quatro modelos bidimensionais de crescente complexidade encontrados na literatura são inicialmente analisados para entender a influência dos diversos elementos e graus de liberdade na qualidade dos resultados obtidos. Antes de introduzir estes modelos, uma investigação de algumas variáveis cinemáticas, conhecidas como determinantes da caminhada, é realizada para a fase de apoio simples. O modelo mais simples considera um pêndulo invertido e, em seguida, articulações são adicionadas para simular o quadril, joelho, tornozelo/pé e, finalmente, todo o mecanismo de perna é substituído por uma mola. Os efeitos das adições sucessivas de graus de liberdade são analisados e os resultados são comparados com os resultados experimentais de Winter para torques e forças de reação. Com base nestas análises este trabalho propõe um modelo bidimensional do caminhar humano durante a fase de apoio simples (SSP) com sete graus de liberdade. As forças resultantes das ações musculares são representadas por torques em cada articulação. Todas as massas de segmentos corporais superiores são agrupadas. O modelo é baseado na dinâmica inversa, sendo os deslocamentos angulares interpolados por B-splines de 5º grau e a cinemática do corpo é calculada usando a formulação robótica de Denavit-Hartenberg (DH). As equações de movimento são obtidas com base em uma formulação Lagrangiana recursiva, em virtude de sua eficiência computacional. Um problema de otimização é estabelecido para obter os pontos de controle das B-splines, onde a função objetivo é definida pelo o esforço dinâmico. As restrições impostas ao movimento são de dois tipos: as restrições dependentes do tempo (limites de torque/ângulo e estabilidade dinâmica definida pelo critério do Zero Moment Point) e as restrições independentes do tempo (estado inicial e final). Os resultados do modelo são favoravelmente comparados com os dados experimentais de Winter, em particular as forças de reação do solo. / [en] The simulation of human body movement is a valuable tool for different fields such as robotics and biomechanics. Even with the growing number of researches, there are still few groups in Brazil that work on developing models of human movement. Such simulation has been a challenging problem from a modeling and computational point of view. This dissertation brings a bibliographical review of concepts of structural dynamics and the main determinants of the dynamics of human walking. Four two-dimensional models of increasing complexity found in the literature are initially analyzed to understand the influence of the various elements and degrees of freedom on the quality of the obtained results. Before introducing these models, an investigation of some kinematic variables, known as determinants of walking, is performed for the simple support phase. The simpler model considers an inverted pendulum, and then joints are added to simulate the hip, knee, ankle/foot, and finally the entire leg mechanism is replaced by a spring. The effects of successive additions of degrees of freedom are analyzed and the results are compared with Winter s experimental results for torques and reaction forces. Based on these analyzes, this work proposes a two-dimensional model of human walking during the simple support phase (SSP) with seven degrees of freedom. The forces resulting from muscular actions are represented by torques at each joint. All masses of upper body segments are grouped. The model is based on inverse dynamics, with angular displacements being interpolated by 5th degree B-splines and the body kinematics is calculated using the Denavit-Hartenberg (DH) robotic formulation. The equations of motion are obtained based on a recursive Lagrangian formulation, due to its computational efficiency. An optimization problem is established to obtain the B-splines control points, where the objective function is defined by the dynamic effort. The constraints imposed on movement are of two types: the time-dependent constraints (torque/angle limits and dynamic stability defined by the Zero Moment Point criterion) and the independent time constraints (initial and final state). The results of the model are favorably compared with Winter s experimental data, in08:22 23/07/2019 particular the ground reaction forces.