Guaranteed manipulator precision via interval analysis of inverse kinematics.

International audienceThe paper presents a new methodology for solving the inverse problem of manipulator precision design. Such design problems are often encountered when the end-effector uncertainty bounds are given, but it is not clear how to allocate precision bounds on individual robot axes. The approach presented in this paper uses interval analysis as a tool for uncertainty modeling and computational analysis. In prior work, the exponential formulation of the forward kinematics map was extended to intervals. Here, we use this result as an inclusion function in the computation of solutions to set-valued inverse kinematic problems. Simulation results are presented in two case studies to illustrate how we can go from an uncertainty interval at the end-effector to a design domain of allowable uncertainties at individual joints and links. The proposed method can be used to determine the level of precision needed in the design of a manipulator such that a predefined end-effector precision can be guaranteed. Also, the approach is general as such it can be easily extended to any degree-of-freedom and kinematic configuration

Robust Mechanism synthesis with random and interval variables

Robust mechanism synthesis ensures that the performance of a mechanism is not sensitive to uncertainties in the mechanism and its environment. The uncertainties include the dimension variations, installation errors, random input motion, and various external forces. Robust mechanism synthesis is used to minimize the impact of these uncertainties on the mechanism performance. Robust mechanism synthesis has been performed by either a probabilistic approach or a worst case approach. The former approach describes uncertain parameters as random variables while the latter approach treats uncertain parameters as interval variables. In this work, methods are developed for robustness assessment and robust mechanism synthesis when both random and interval variables exists --Abstract, page iii

Planificación automática y supervisión de operaciones de montaje mediante robots

One of the main topics to be solved in order to fully automate a robotized assembly task is the automatic determination of the movements to be done by the robot to properly perform the tasks when the existing uncertainty is not negligible. This problem is of particular theoretical and practical interest when rotational degrees of freedom and friction forces are taken into account. In this thesis, an automatic movement planner that considers these aspects is proposed, including the description of how to execute the plan and supervise the evolution of the task. In order to generate the plan, the task is represented by a finite number of states, which are associated to the nodes of a graph with the links connecting contiguous states. Then, using uncertainty models developed in the thesis, the domains of the possible configurations and reaction forces that can be measured by the corresponding sensors in each task state are determined. From the existing initial conditions of the task and the desired final conditions, an initial and a goal state are determined, and, using the state graph, a sequence of contiguous states joining them is searched. At the same time, state transition operators (movement directions of the robot) that may allow the transition from one state to the next in the sequence are also determined.The execution of the task according to the plan basically consist in the estimation of the current state by matching the sensorial information obtained on-line with the domains of configuration and force of each state, and then, the application of the proper state transition operator to proceed in the state sequence towards the goal state.The main contributions of the thesis are the following: on one side, as a general contribution, the proposed planning procedure that allows the simultaneous consideration of friction forces, rotational degrees of freedom, and the different uncertainty sources that affect a robotized task; on the other side, as more specific contributions, the proposal of task states as the occurrence of a set of basic contacts, and, for movements on a plane, the fusion of the uncertainty models and the determination of the reaction forces possible in any contact situation by using the dual representation of the force lines. The thesis includes the application of the developed concepts to a simple assembly task (the block in the corner problem) considering movements on a plane. Although the implementation is not a general application prototype, it contributes to the validation of the theoretical results of the work.Uno de los principales problemas a resolver en la automatización total de una tarea de montaje robotizada, es la determinación automática de los movimientos que debe realizar el robot para llevar a cabo la tarea cuando la incertidumbre que le afecta es significativa. Este problema es de especial interés teórico y práctico cuando se consideran grados de libertad de rotación y fuerzas de fricción. En la tesis se propone un planificador automático de movimientos que tiene en cuenta estos aspectos. Se describe también cómo llevar a cabo la ejecución del plan y supervisar la evolución de la tarea.Para llevar a cabo la planificación, la tarea se representa mediante un conjunto finito de estados. Considerando la incertidumbre mediante modelos desarrollados en la tesis, se determinan los dominios de observación de configuraciones y de fuerzas de reacción que pueden ser indicadas por los sensores cuando tiene lugar cada estado de la tarea. Los estados de la tarea se representan como nodos de un grafo en el que los arcos unen los estados contiguos.A partir de las condiciones iniciales de la tarea y condiciones finales deseadas se establecen sendos estados inicial y final, y, utilizando el grafo de estados, se determina una secuencia de estados contiguos que los ligue. Paralelamente, se determinan operadores de cambio de estado (direcciones de movimiento del robot) que pueden permitir la transición de un estado a otro de la secuencia.La ejecución de la tarea acorde al plan consiste básicamente en estimar el estado en curso contrastando la información sensorial obtenida en-línea con los dominios de observación de configuración y fuerza, para aplicar entonces el operador de cambio de estado que corresponda, y así sucesivamente hasta alcanzar el estado final.Las principales aportaciones de la tesis son las siguientes. Por un lado, desde un punto de vista general, cabe destacar el procedimiento de planificación propuesto, que permite considerar simultáneamente fuerzas de fricción, grados de libertad de rotación y las incertidumbres que afectan a una tarea de montaje robotizada. Por otra parte, pueden mencionarse como aportaciones particulares, la introducción del concepto de estados de la tarea como ocurrencia de un determinado conjunto de contactos básicos y, para el caso de movimientos en un plano, el modelado y fusión de incertidumbre de una forma más precisa que las descritas en trabajos previos, así como la determinación de las fuerzas de reacción que pueden tener lugar en cualquier contacto mediante el uso de la representación dual de sus rectas de acción. La tesis incluye la aplicación de los conceptos teóricos desarrollados a una tarea de montaje (bloque en la esquina) considerando movimientos de los objetos en un plano. Aunque la implementación no pretende ser un prototipo de aplicación general, contribuye a la validación de los resultados del trabajo

Advancement in robot programming with specific reference to graphical methods

This research study is concerned with the derivation of advanced robot programming methods. The methods include the use of proprietary simulation modelling and design software tools for the off-line programming of industrial robots. The study has involved the generation of integration software to facilitate the co-operative operation of these software tools. The three major researcli'themes7of "ease of usage", calibration and the integration of product design data have been followed to advance robot programming. The "ease of usage" is concerned with enhancements in the man-machine interface for robo t simulation systems in terms of computer assisted solid modelling and computer assisted task generation. Robot simulation models represent an idealised situation, and any off-line robot programs generated from'them may contain'discrepancies which could seriously effect thq programs' performance; Calibration techniques have therefore been investigated as 'a method of overcoming discrepancies between the simulation model and the real world. At the present time, most computer aided design systems operate as isolated islands of computer technology, whereas their product databases should be used to support decision making processes and ultimately facilitate the generation of machine programs. Thus the integration of product design data has been studied as an important step towards truly computer integrated manufacturing. The functionality of the three areas of study have been generalised and form the basis for recommended enhancements to future robot programming systems