An ontology-based approach towards coupling task and path planning for the simulation of manipulation tasks

This work deals with the simulation and the validation of complex manipulation tasks under strong geometric constraints in virtual environments. The targeted applications relate to the industry 4.0 framework; as up-to-date products are more and more integrated and the economic competition increases, industrial companies express the need to validate, from design stage on, not only the static CAD models of their products but also the tasks (e.g., assembly or maintenance) related to their Product Lifecycle Management (PLM). The scientific community looked at this issue from two points of view: - Task planning decomposes a manipulation task to be realized into a sequence of primitive actions (i.e., a task plan) - Path planning computes collision-free trajectories, notably for the manipulated objects. It traditionally uses purely geometric data, which leads to classical limitations (possible high computational processing times, low relevance of the proposed trajectory concerning the task to be performed, or failure); recent works have shown the interest of using higher abstraction level data. Joint task and path planning approaches found in the literature usually perform a classical task planning step, and then check out the feasibility of path planning requests associated with the primitive actions of this task plan. The link between task and path planning has to be improved, notably because of the lack of loopback between the path planning level and the task planning level: - The path planning information used to question the task plan is usually limited to the motion feasibility where richer information such as the relevance or the complexity of the proposed path would be needed; - path planning queries traditionally use purely geometric data and/or “blind” path planning methods (e.g., RRT), and no task-related information is used at the path planning level Our work focuses on using task level information at the path planning level. The path planning algorithm considered is RRT; we chose such a probabilistic algorithm because we consider path planning for the simulation and the validation of complex tasks under strong geometric constraints. We propose an ontology-based approach to use task level information to specify path planning queries for the primitive actions of a task plan. First, we propose an ontology to conceptualize the knowledge about the 3D environment in which the simulated task takes place. The environment where the simulated task takes place is considered as a closed part of 3D Cartesian space cluttered with mobile/fixed obstacles (considered as rigid bodies). It is represented by a digital model relying on a multilayer architecture involving semantic, topologic and geometric data. The originality of the proposed ontology lies in the fact that it conceptualizes heterogeneous knowledge about both the obstacles and the free space models. Second, we exploit this ontology to automatically generate a path planning query associated to each given primitive action of a task plan. Through a reasoning process involving the primitive actions instantiated in the ontology, we are able to infer the start and the goal configurations, as well as task-related geometric constraints. Finally, a multi-level path planner is called to generate the corresponding trajectory. The contributions of this work have been validated by full simulation of several manipulation tasks under strong geometric constraints. The results obtained demonstrate that using task-related information allows better control on the RRT path planning algorithm involved to check the motion feasibility for the primitive actions of a task plan, leading to lower computational time and more relevant trajectories for primitive actions

HERMESH : a geometrical domain composition method in computational mechanics

With this thesis we present the HERMESH method which has been classified by us as a a composition domain method. This term comes from the idea that HERMESH obtains a global solution of the problem from two independent meshes as a result of the mesh coupling. The global mesh maintains the same number of degrees of freedom as the sum of the independent meshes, which are coupled in the interfaces via new elements referred to by us as extension elements. For this reason we enunciate that the domain composition method is geometrical. The result of the global mesh is a non-conforming mesh in the interfaces between independent meshes due to these new connectivities formed with existing nodes and represented by the new extension elements. The first requirements were that the method be implicit, be valid for any partial differential equation and not imply any additional effort or loss in efficiency in the parallel performance of the code in which the method has been implemented. In our opinion, these properties constitute the main contribution in mesh coupling for the computational mechanics framework. From these requirements, we have been able to develop an automatic and topology-independent tool to compose independent meshes. The method can couple overlapping meshes with minimal intervention on the user's part. The overlapping can be partial or complete in the sense of overset meshes. The meshes can be disjoint with or without a gap between them. And we have demonstrated the flexibility of the method in the relative mesh size. In this work we present a detailed description of HERMESH which has been implemented in a high-performance computing computational mechanics code within the framework of the finite element methods. This code is called Alya. The numerical properties will be proved with different benchmark-type problems and the manufactured solution technique. Finally, the results in complex problems solved with HERMESH will be presented, clearly showing the versatility of the method.En este trabajo presentamos el metodo HERMESH al que hemos catalogado como un método de composición de dominios puesto que a partir de mallas independientes se obtiene una solución global del problema como la unión de los subproblemas que forman las mallas independientes. Como resultado, la malla global mantiene el mismo número de grados de libertad que la suma de los grados de libertad de las mallas independientes, las cuales se acoplan en las interfases internas a través de nuevos elementos a los que nos referimos como elementos de extensión. Por este motivo decimos que el método de composición de dominio es geométrico. El resultado de la malla global es una malla que no es conforme en las interfases entre las distintas mallas debido a las nuevas conectividades generadas sobre los nodos existentes. Los requerimientos de partida fueron que el método se implemente de forma implícita, sea válido para cualquier PDE y no implique ningún esfuerzo adicional ni perdida de eficiencia para el funcionamiento paralelo del código de altas prestaciones en el que ha sido implementado. Creemos que estas propiedades son las principales aportaciones de esta tesis dentro del marco de acoplamiento de mallas en mecánica computacional. A partir de estas premisas, hemos conseguido una herramienta automática e independiente de la topología para componer mallas. Es capaz de acoplar sin necesidad de intervención del usuario, mallas con solapamiento parcial o total así como mallas disjuntas con o sin "gap" entre ellas. También hemos visto que ofrece cierta flexibilidad en relación al tamaños relativos entre las mallas siendo un método válido como técnica de remallado local. Presentamos una descripción detallada de la implementación de esta técnica, llevada a cabo en un código de altas prestaciones de mecánica computacional en el contexto de elementos finitos, Alya. Se demostrarán todas las propiedades numéricas que ofrece el métodos a través de distintos problemas tipo benchmark y el método de la solución manufacturada. Finalmente se mostrarán los resultados en problemas complejos resueltos con el método HERMESH, que a su vez es una prueba de la gran flexibilidad que nos brinda

Finite element methods with local Trefftz trial functions

In the development of numerical methods for boundary value problems, the requirement of flexible mesh handling gains more and more importance. The available work deals with a new kind of conforming finite element methods on polygonal/polyhedral meshes. The idea is to use basis functions which are defined implicitly as local solutions of the underlying homogeneous problem with constant coefficients. They are referred to local Trefftz functions. These local problems are treated by means of boundary integral equations and are approximated by the use of the boundary element method in the numerics. The method is applied to the stationary diffusion equation, where lower as well as higher order basis functions are introduced in two space dimensions. The convergence is analysed with respect to the H^1- as well as the L_2-norm and rates of convergence are proven. In case of non-constant diffusion coefficients, a special approximation is proposed. Beside the uniform refinement, an adaptive strategy is given which makes use of the residual error estimator and an introduced refinement procedure. The reliability of the residual error estimate is proven on polygonal meshes. Finally, the generalization to arbitrary polyhedral meshes with polygonal faces is discussed. All theoretical results and considerations are confirmed by numerical experiments.In der Entwicklung numerischer Verfahren zur Approximation von Randwertaufgaben werden flexible Vernetzungen der zugrunde liegenden Gebiete immer wichtiger. Die vorliegende Arbeit beschäftigt sich mit neuartigen Finiten Element Methoden, die zu konformen Approximationen auf polygonalen und polyhedralen Gittern führen. Der Gedanke dieser Vorgehensweise liegt darin, die Ansatzfunktionen implizit als Lösungen von lokalen Randwertaufgaben zu definieren, wie dies auch schon E. Trefftz vorgeschlagen hat. Hierbei wird die Differentialgleichung des Ursprungsproblems mit konstanten Koeffizienten und homogener rechter Seite verwendet. Die lokalen Probleme werden mit Randintegralgleichungen und in der Realisierung mit Randelementmethoden behandelt. Das Verfahren wird auf die stationäre Diffusionsgleichung angewendet, wofür Ansatzfunktionen niedriger als auch höherer Ordnung eingeführt werden. Konvergenzraten bezüglich der H^1- sowie der L_2-Norm werden untersucht und bewiesen. Im Falle eines nicht konstanten Diffusionskoeffizienten wird eine spezielle Vorgehensweise vorgeschlagen. Neben der gleichmäßigen Verfeinerung der Netze wird ebenso eine adaptive Strategie angegeben, die von dem residualen Fehlerschätzer und einer eingeführten Verfeinerung Gebrauch macht. Die Zuverlässigkeit des Fehlerschätzers auf polygonalen Netzen wird bewiesen und schließlich wird das Verfahren erweitert, so dass es auf polyhedralen Gittern mit polygonalen Elementflächen angewendet werden kann. Alle theoretischen Resultate und Überlegungen werden durch numerische Experimente bestätigt