Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Development of a planar multi-body model of the human knee joint

The aim of this work is to develop a dynamic model for the biological human knee joint. The model is formulated in the framework of multibody systems methodologies, as a system of two bodies, the femur and the tibia. For the purpose of describing the formulation, the relative motion of the tibia with respect to the femur is considered. Due to their higher stiffness compared to that of the articular cartilages, the femur and tibia are considered as rigid bodies. The femur and tibia cartilages are considered to be deformable structures with specific material characteristics. The rotation and gliding motions of the tibia relative to the femur can not be modeled with any conventional kinematic joint, but rather in terms of the action of the knee ligaments and potential contact between the bones. Based on medical imaging techniques, the femur and tibia profiles in the sagittal plane are extracted and used to define the interface geometric conditions for contact. When a contact is detected, a continuous non-linear contact force law is applied which calculates the contact forces developed at the interface as a function of the relative indentation between the two bodies. The four basic cruciate and collateral ligaments present in the knee are also taken into account in the proposed knee joint model, which are modeled as non-linear elastic springs. The forces produced in the ligaments, together with the contact forces, are introduced into the system’s equations of motion as external forces. In addition, an external force is applied on the center of mass of the tibia, in order to actuate the system mimicking a normal gait motion. Finally, numerical results obtained from computational simulations are used to address the assumptions and procedures adopted in this study.Fundação para a Ciência e a Tecnologia (FCT

Quasi optimal sagittal gait of a biped robot with a new structure of knee joint

The design of humanoid robots has been a tricky challenge for several years. Due to the kinematic complexity of human joints, their movements are notoriously difficult to be reproduced by a mechanism. The human knees allow movements including rolling and sliding, and therefore the design of new bioinspired knees is of utmost importance for the reproduction of anthropomorphic walking in the sagittal plane. In this article, the kinematic characteristics of knees were analyzed and a mechanical solution for reproducing them is proposed. The geometrical, kinematic and dynamic models are built together with an impact model for a biped robot with the new knee kinematic. The walking gait is studied as a problem of parametric optimization under constraints. The trajectories of walking are approximated by mathematical functions for a gait composed of single support phases with impacts. Energy criteria allow comparing the robot provided with the new rolling knee mechanism and a robot equipped with revolute knee joints. The results of the optimizations show that the rolling knee brings a decrease of the sthenic criterion. The comparisons of torques are also observed to show the difference of energy distribution between the actuators. For the same actuator selection, these results prove that the robot with rolling knees can walk longer than the robot with revolute joint knees.ANR R2A

Dynamics simulation of human box delivering task

Thesis (M.S.) University of Alaska Fairbanks, 2018The dynamic optimization of a box delivery motion is a complex task. The key component is to achieve an optimized motion associated with the box weight, delivering speed, and location. This thesis addresses one solution for determining the optimal delivery of a box. The delivering task is divided into five subtasks: lifting, transition step, carrying, transition step, and unloading. Each task is simulated independently with appropriate boundary conditions so that they can be stitched together to render a complete delivering task. Each task is formulated as an optimization problem. The design variables are joint angle profiles. For lifting and carrying task, the objective function is the dynamic effort. The unloading task is a byproduct of the lifting task, but done in reverse, starting with holding the box and ending with it at its final position. In contrast, for transition task, the objective function is the combination of dynamic effort and joint discomfort. The various joint parameters are analyzed consisting of joint torque, joint angles, and ground reactive forces. A viable optimization motion is generated from the simulation results. It is also empirically validated. This research holds significance for professions containing heavy box lifting and delivering tasks and would like to reduce the chance of injury.Chapter 1 Introduction -- Chapter 2 Skeletal Human Modeling -- Chapter 3 Kinematics and Dynamics -- Chapter 4 Lifting Simulation -- Chapter 5 Carrying Simulation -- Chapter 6 Delivering Simulation -- Chapter 7 Conclusion and Future Research -- Reference

Suspension parameters analysis for different track conditions

Dissertação de mestrado integrado em Engenharia Mecânica (área de especialização em Sistemas Mecatrónicos)Este trabalho, aqui apresentado, tem como objetivo o estudo do comportamento do sistema de suspensão de um veículo ao atravessar estradas com obstáculos, como lombas ou buracos. Para atingir este objetivo, uma vasta revisão literária foi feita. Sendo este um tópico extenso, três tipos de revisão foram feitos. Primeiro, a um estudo global à tecnologia usava hoje em dia em pneus e nos sistemas de suspensão de veículos foi compilado. Uma breve menção à cinemática de veículos é empreendida. De seguida, a dinâmica do contacto pneu/solo é sistematicamente explanada, para compreender os diversos modelos de pneu (força) existentes. Adicionalmente, os conceitos fundamentais da análise da dinâmica multicorpo são expostos para justificar a modelação do veículo como um sistema multicorpo. Com toda a teoria apresentada, os conceitos previamente explicados são aplicados na prática para a formulação de um método que visa estimar a trajetória de um veículo atravessando uma qualquer estrada. O primeiro passo a executar é a escolha do modelo de pneu a utilizar. Percebe-se que se deve usar modelos matemáticos, culminando na escolha da Magic Formula. Os passos seguintes consistem na introdução de uma metodologia, que estima o contacto entre um pneu e o solo, para simular as dinâmicas pneu/solo de um veículo. Dois métodos diferentes são expostos: o primeiro para estradas completamente planas, sem obstáculos; o segundo, para estradas com obstáculos, como lombas ou buracos. Este modelo é posteriormente inserido num programa de análise das dinâmicas multicorpo, MUBODYNA3D, e diversas simulações são realizadas. Estas simulações começam pela definição do veículo como um sistema multicorpo, com corpos conectados por juntas cinemáticas. As primeiras simulações são realizadas numa estrada plana para validar os modelos e metodologias previamente criadas. O integrador, que integra os resultados das equações do movimento para prever a trajetória, é refinado. Finalmente, simulações com estradas com obstáculos são geradas. Por fim, os resultados dessas simulações são discutidos, percebendo-se que apresentam um valor inesperado. Ao atravessar um obstáculo, as rodas perdem o contacto com a superfície, provocando a descolagem do carro. No entanto, é concluído que a análise de sistemas multicorpo é de extrema relevância para a simulação de realidades complexas, produzindo resultados precisos.This work, hereby presented, has a primary target of studying the behaviour of a road vehicle’s suspension system, while it is traversing roads with big obstacles, such as potholes or speed bumps/humps. To accomplish this task, a broad literature review was made. Since this is an extensive topic, three types of review were made. Firstly, an overview of the state-of-the-art technology used in tires and suspension systems nowadays is compiled. A brief mention to vehicle kinematics is also made. Then, the dynamics of the contact tire/road are systematically explained, in order to understand the diverse tire force models that exist. Lastly, a rundown of the fundamental concepts of multibody dynamics analysis is exposed to substantiate the modelling of a vehicle as a multibody system later on. With the theory behind, all concepts previously abridged are put to practice, into the formulation of a method to estimate the trajectory of a vehicle crossing a certain road. The first step to execute this is to choose the tire force model to use. It is seen that, in this case, the mathematical models are the best choice, which culminates in the selection of the Magic Formula model. The following steps consist of introducing the contact estimation methodology created to simulate the tire/road dynamics of a vehicle. Two different methods are exposed: the first for fully flat roads, with no obstacles; the second, for road that possess obstacles, like bumps for example. This model is then inserted into a multibody dynamics analysis program, MUBODYNA3D, and some forward dynamic simulations are performed. These simulations start with the definition of the vehicle as a multibody system, with bodies connected by kinematic joints. The first simulations are performed in flat roads to validate the models and methodologies created. The solver, that integrates the results of the equations of motion to predict the trajectory, are then refined. Finally, simulations using roads with obstacles are conducted and the results analysed. In the end, the simulations result in some unexpected behaviour from the vehicle. While crossing an obstacle, it tends to lose contact with the surface and, thus, lift off the road, which is unrealistic. Nonetheless, it is concluded that multibody systems analysis is extremely important to simulate and analyse complex realities, with precise results

DYNAMICAL SIMULATION OF A VALVETRAIN MECHANISM: AN ENGINEERING EDUCATION APPROACH

The present work aims to present a valvetrain model considering the dynamics functioning aspects of an Otto’s engine. The model will be constructed using Adams/View® software, which is a powerful modeling and simulating environment of dynamic systems. It allows building, simulating, refining and optimizing any mechanical system. In fact, the model will help engineering students to understand how the mechanism works, in terms of displacement, velocity and acceleration of the valve as a function of the time. It is also possible to know the behavior of the force in the spring as a function of the time and, finally, the torque applied in the cam due to a angular velocity input. Relative to spring force, during the Otto engine cycle, the cam lobe must be able to open and close the valve as fast and as smoothly as possible. The force responsible to close the valve is applied by the valve spring, which is also responsible for keeping contact between the cam lobe and the valve. Dynamic forces impose limits on cam and valve lift. Thus, the simulation model allows determining these forces and displacements through the cam rotation. As main objectives the authors wish to make available a model which is capable to show in 3D the animation of a valvetrain mechanism of an Otto engine, obtaining the main curves for analysis and evaluation of this mechanism performance

A Dynamics and Stability Framework for Avian Jumping Take-off

Jumping take-off in birds is an explosive behaviour with the goal of providing a rapid transition from ground to airborne locomotion. An effective jump is predicated on the need to maintain dynamic stability through the acceleration phase. The present study concerns understanding how birds retain control of body attitude and trajectory during take-off. Cursory observation suggests that stability is achieved with relatively little cost. However, analysis of the problem shows that the stability margins during jumping are actually very small and that stability considerations play a significant role in selection of appropriate jumping kinematics. We use theoretical models to understand stability in prehensile take-off (from a perch) and also in non-prehensile take-off (from the ground). The primary instability is tipping, defined as rotation of the centre of gravity about the ground contact point. Tipping occurs when the centre of pressure falls outside the functional foot. A contribution of the paper is the development of graphical tipping stability margins for both centre of gravity location and acceleration angle. We show that the nose-up angular acceleration extends stability bounds forward and is hence helpful in achieving shallow take-offs. The stability margins are used to interrogate simulated take-offs of real birds using published experimental kinematic data from a guinea fowl (ground take-off) and a diamond dove (perch take-off). For the guinea fowl the initial part of the jump is stable, however simulations exhibit a stuttering instability not observed experimentally that is probably due to absence of compliance in the idealised joints. The diamond dove model confirms that the foot provides an active torque reaction during take-off, extending the range of stable jump angles by around 45{\deg}.Comment: 21 pages, 11 figures; supplementary material: https://figshare.com/s/86b12868d64828db0d5d; DOI: 10.6084/m9.figshare.721056

MUSME 2011 4 th International Symposium on Multibody Systems and Mechatronics

El libro de actas recoge las aportaciones de los autores a través de los correspondientes artículos a la Dinámica de Sistemas Multicuerpo y la Mecatrónica (Musme). Estas disciplinas se han convertido en una importante herramienta para diseñar máquinas, analizar prototipos virtuales y realizar análisis CAD sobre complejos sistemas mecánicos articulados multicuerpo. La dinámica de sistemas multicuerpo comprende un gran número de aspectos que incluyen la mecánica, dinámica estructural, matemáticas aplicadas, métodos de control, ciencia de los ordenadores y mecatrónica. Los artículos recogidos en el libro de actas están relacionados con alguno de los siguientes tópicos del congreso: Análisis y síntesis de mecanismos ; Diseño de algoritmos para sistemas mecatrónicos ; Procedimientos de simulación y resultados ; Prototipos y rendimiento ; Robots y micromáquinas ; Validaciones experimentales ; Teoría de simulación mecatrónica ; Sistemas mecatrónicos ; Control de sistemas mecatrónicosUniversitat Politècnica de València (2011). MUSME 2011 4 th International Symposium on Multibody Systems and Mechatronics. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/13224Archivo delegad