14 research outputs found
Solving robotic kinematic problems : singularities and inverse kinematics
Kinematics is a branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the forces that cause such motion. For serial robot manipulators, kinematics consists of describing the open chain geometry as well as the position, velocity and/or acceleration of each one of its components. Rigid serial robot manipulators
are designed as a sequence of rigid bodies, called links, connected by motor-actuated pairs, called joints, that provide relative motion between consecutive links. Two kinematic problems of special relevance for serial robots are:
- Singularities: are the configurations where the robot loses at least one degree of freedom (DOF). This is equivalent to:
(a) The robot cannot translate or rotate its end-effector in at least one direction.
(b) Unbounded joint velocities are required to generate finite linear and angular velocities.
Either if it is real-time teleoperation or off-line path planning, singularities must be addressed to make the robot exhibit a good performance for a given task. The objective is not only to identify the singularities and their associated singular directions but to design strategies to avoid or handle them.
- Inverse kinematic problem: Given a particular position and orientation of the end-effector, also known as the end-effector pose, the inverse kinematics consists of finding the configurations that provide such desired pose. The importance of the inverse kinematics relies on its role in the programming and control of serial robots. Besides, since for each given pose the inverse kinematics has up to sixteen different solutions, the objective is to find a closed-form method for solving this problem, since closed-form methods allow to obtain all the solutions in a compact form.
The main goal of the Ph.D. dissertation is to contribute to the solution of both problems. In particular, with respect to the singularity problem, a novel scheme for the identification of the singularities and their associated singular directions is introduced. Moreover, geometric algebra is used to simplify such identification and to provide a distance function in the configuration space of the robot that allows the definition of algorithms for avoiding them.
With respect to the inverse kinematics, redundant robots are reduced to non-redundant ones by selecting a set of joints, denoted redundant joints, and by parameterizing their joint variables. This selection is made through a workspace analysis which also provides an upper bound for the number of different closed-form solutions. Once these joints have been identified, several
closed-form methods developed for non-redundant manipulators can be applied to obtain the analytical expressions of all the solutions. One of these methods is a novel strategy developed using again the conformal model of the spatial geometric algebra.
To sum up, the Ph.D dissertation provides a rigorous analysis of the two above-mentioned kinematic problems as well as novel strategies for solving them. To illustrate the different results introduced in the Ph.D. memory, examples are given at the end of each of its chapters.La cinemática es una rama de la mecánica clásica que describe el movimiento de puntos, cuerpos y sistemas de cuerpos sin considerar las fuerzas que causan dicho movimiento. Para un robot manipulador serie, la cinemática consiste en la descripción de su geometrÃa, su posición, velocidad y/o aceleración. Los robots manipuladores serie están diseñados como una secuencia de elementos estructurales rÃgidos, llamados eslabones, conectados entres si por articulaciones actuadas, que permiten el movimiento relativo entre pares de eslabones consecutivos. Dos problemas cinemáticos de especial relevancia para robots serie son: - Singularidades: son aquellas configuraciones donde el robot pierde al menos un grado de libertad (GDL). Esto equivale a: (a) El robot no puede trasladar ni rotar su elemento terminal en al menos una dirección. (b) Se requieren velocidades articulares no acotadas para generar velocidades lineales y angulares finitas. Ya sea en un sistema teleoperado en tiempo real o planificando una trayectoria, las singularidades deben manejarse para que el robot muestre un rendimiento óptimo mientras realiza una tarea. El objetivo no es solo identificar las singularidades y sus direcciones singulares asociadas, sino diseñar estrategias para evitarlas o manejarlas. - Problema de la cinemática inversa: dada una posición y orientación del elemento terminal (también conocida como la pose del elemento terminal), la cinemática inversa consiste en obtener las configuraciones asociadas a dicha pose. La importancia de la cinemática inversa se basa en el papel que juega en la programación y el control de robots serie. Además, dado que para cada pose la cinemática inversa tiene hasta dieciséis soluciones diferentes, el objetivo es encontrar un método cerrado para resolver este problema, ya que los métodos cerrados permiten obtener todas las soluciones en una forma compacta. El objetivo principal de la tesis doctoral es contribuir a la solución de ambos problemas. En particular, con respecto al problema de las singularidades, se presenta un nuevo método para su identificación basado en el álgebra geométrica. Además, el álgebra geométrica permite definir una distancia en el espacio de configuraciones del robot que permite la definición de distintos algoritmos para evitar las configuraciones singulares. Con respecto a la cinemática inversa, los robots redundantes se reducen a robots no-redundantes mediante la selección de un conjunto de articulaciones, las articulaciones redundantes, para después parametrizar sus variables articulares. Esta selección se realiza a través de un análisis de espacio de trabajo que también proporciona un lÃmite superior para el número de diferentes soluciones en forma cerrada. Una vez las articulaciones redundantes han sido identificadas, varios métodos en forma cerrada desarrollados para robots no-redundantes pueden aplicarse a fin de obtener las expresiones analÃticas de todas las soluciones. Uno de dichos métodos es una nueva estrategia desarrollada usando el modelo conforme del álgebra geométrica tridimensional. En resumen, la tesis doctoral proporciona un análisis riguroso de los dos problemas cinemáticos mencionados anteriormente, asà como nuevas estrategias para resolverlos. Para ilustrar los diferentes resultados presentados en la tesis, la memoria contiene varios ejemplos al final de cada uno de sus capÃtulos
Hierarchical Manipulation for Constructing Free Standing Structures
abstract: In order for a robot to solve complex tasks in real world, it needs to compute discrete, high-level strategies that can be translated into continuous movement trajectories. These problems become increasingly difficult with increasing numbers of objects and domain constraints, as well as with the increasing degrees of freedom of robotic manipulator arms.
The first part of this thesis develops and investigates new methods for addressing these problems through hierarchical task and motion planning for manipulation with a focus on autonomous construction of free-standing structures using precision-cut planks. These planks can be arranged in various orientations to design complex structures; reliably and autonomously building such structures from scratch is computationally intractable due to the long planning horizon and the infinite branching factor of possible grasps and placements that the robot could make.
An abstract representation is developed for this class of problems and show how pose generators can be used to autonomously compute feasible robot motion plans for constructing a given structure. The approach was evaluated through simulation and on a real ABB YuMi robot. Results show that hierarchical algorithms for planning can effectively overcome the computational barriers to solving such problems.
The second part of this thesis proposes a deep learning-based algorithm to identify critical regions for motion planning. Further investigation is done whether these learned critical regions can be translated to learn high-level landmark actions for automated planning.Dissertation/ThesisMasters Thesis Computer Science 201
Navigation and Grasping with a Mobile Manipulator: from Simulation to Experimental Results
Cobot is the name for collaborative robots. This kind of robot is intended to work in close contact with the human being and to collaborate, by increasing the production rate and by reducing the human onerous tasks, in terms of repetitiveness and precision. At the state
of the art, Cobots are often fixed on a support platform, static in their workstation. The aim of this thesis is, hence, to explore, test and validate navigation algorithms for a holonomic mobile robot and in a second moment, to study its behavior with a Cobot mounted on it, in a pick-move-place application. To this purpose, the first part of the thesis addresses the mobile navigation, while the second part the mobile manipulation. Concerning mobile robotics, in the first place, a theoretical background is given and the kinematic model of a holonomic robot is derived. Then, the problem of simultaneous localization and mapping (SLAM) is addressed, i.e. how the robot is able to build a map while localizing itself. Finally, a dedicated chapter will explain the algorithms responsible for exploration and navigation: planners, exploration of frontiers and Monte Carlo localization. Once the necessary theoretical background has been given, these algorithms will be tested both in simulation and in practice on a real robot. In the second part, some theoretical knowledge about manipulators is given and also the kinematic model of the Cobot is derived, together with the algorithm used for a collision free trajectory planning. To conclude, the results of the complete task are shown, first of all in simulation and then on the real robotic system
Development of a methodology for the human-robot interaction based on vision systems for collaborative robotics
L'abstract è presente nell'allegato / the abstract is in the attachmen