Deep Neural Network Based Subspace Learning of Robotic Manipulator Workspace Mapping

The manipulator workspace mapping is an important problem in robotics and has attracted significant attention in the community. However, most of the pre-existing algorithms have expensive time complexity due to the reliance on sophisticated kinematic equations. To solve this problem, this paper introduces subspace learning (SL), a variant of subspace embedding, where a set of robot and scope parameters is mapped to the corresponding workspace by a deep neural network (DNN). Trained on a large dataset of around $\mathbf{6\times 10^4}$ samples obtained from a MATLAB$^\circledR$ implementation of a classical method and sampling of designed uniform distributions, the experiments demonstrate that the embedding significantly reduces run-time from $\mathbf{5.23 \times 10^3}$ s of traditional discretization method to $\mathbf{0.224}$ s, with high accuracies (average F-measure is $\mathbf{0.9665}$ with batch gradient descent and resilient backpropagation).Comment: 12 pages, 12 figures, accepted for presentation at ICCAIRO 201

Reachability-based Trajectory Design

Autonomous mobile robots have the potential to increase the availability and accessibility of goods and services throughout society. However, to enable public trust in such systems, it is critical to certify that they are safe. This requires formally specifying safety, and designing motion planning methods that can guarantee safe operation (note, this work is only concerned with planning, not perception). The typical paradigm to attempt to ensure safety is receding-horizon planning, wherein a robot creates a short plan, then executes it while creating its next short plan in an iterative fashion, allowing a robot to incorporate new sensor information over time. However, this requires a robot to plan in real time. Therefore, the key challenge in making safety guarantees lies in balancing performance (how quickly a robot can plan) and conservatism (how cautiously a robot behaves). Existing methods suffer from a tradeoff between performance and conservatism, which is rooted in the choice of model used describe a robot; accuracy typically comes at the price of computation speed. To address this challenge, this dissertation proposes Reachability-based Trajectory Design (RTD), which performs real-time, receding-horizon planning with a simplified planning model, and ensures safety by describing the model error using a reachable set of the robot. RTD begins with the offline design of a continuum of parameterized trajectories for the plan- ning model; each trajectory ends with a fail-safe maneuver such as braking to a stop. RTD then computes the robot’s Forward Reachable Set (FRS), which contains all points in workspace reach- able by the robot for each parameterized trajectory. Importantly, the FRS also contains the error model, since a robot can typically never track planned trajectories perfectly. Online (at runtime), the robot intersects the FRS with sensed obstacles to provably determine which trajectory plans could cause collisions. Then, the robot performs trajectory optimization over the remaining safe trajectories. If no new safe plan can be found, the robot can execute its previously-found fail-safe maneuver, enabling perpetual safety. This dissertation begins by presenting RTD as a theoretical framework, then presents three representations of a robot’s FRS, using (1) sums-of-squares (SOS) polynomial programming, (2) zonotopes (a special type of convex polytope), and (3) rotatotopes (a generalization of zonotopes that enable representing a robot’s swept volume). To enable real-time planning, this work also de- velops an obstacle representation that enables provable safety while treating obstacles as discrete, finite sets of points. The practicality of RTD is demonstrated on four different wheeled robots (using the SOS FRS), two quadrotor aerial robots (using the zonotope FRS), and one manipulator robot (using the rotatotope FRS). Over thousands of simulations and dozens of hardware trials, RTD performs safe, real-time planning in arbitrary and challenging environments. In summary, this dissertation proposes RTD as a general purpose, practical framework for provably safe, real-time robot motion planning.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162884/1/skousik_1.pd

Manipulator Performance Measures - A Comprehensive Literature Survey

Due to copyright restrictions of the publisher this item is embargoed and access to the file is restricted until a year after the publishing date.The final publication is available at www.springerlink.comPerformance measures are quintessential to the design, synthesis, study and application of robotic manipulators. Numerous performance measures have been defined to study the performance and behavior of manipulators since the early days of robotics; some more widely accepted than others, but their real significance and limitations have not always been well understood. The aim of this survey is to review the definition, classification, scope, and limitations of some of the widely used performance measures. This work provides an extensive bibliography that can be of help to researchers interested in studying and evaluating the performance and behavior of robotic manipulators. Finally, a few recommendations are proposed based on the review so that the most commonly noticed limitations can be avoided when new performance measures are proposed.http://link.springer.com/article/10.1007/s10846-014-0024-y

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications

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 geometría, su posición, velocidad y/o aceleración. Los robots manipuladores serie están diseñados como una secuencia de elementos estructurales rígidos, 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 límite 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 analíticas 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, así 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 capítulos

Solving robotic kinematic problems : singularities and inverse kinematics

Aplicat embargament des de la data de defensa fins al 30/6/2019Kinematics 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 geometría, su posición, velocidad y/o aceleración. Los robots manipuladores serie están diseñados como una secuencia de elementos estructurales rígidos, 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 límite 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 analíticas 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, así 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 capítulos.Postprint (published version

Collision avoidance and dynamic modeling for wheeled mobile robots and industrial manipulators

Collision Avoidance and Dynamic Modeling are key topics for researchers dealing with mobile and industrial robotics. A wide variety of algorithms, approaches and methodologies have been exploited, designed or adapted to tackle the problems of finding safe trajectories for mobile robots and industrial manipulators, and of calculating reliable dynamics models able to capture expected and possible also unexpected behaviors of robots. The knowledge of these two aspects and their potential is important to ensure the efficient and correct functioning of Industry 4.0 plants such as automated warehouses, autonomous surveillance systems and assembly lines. Collision avoidance is a crucial aspect to improve automation and safety, and to solve the problem of planning collision-free trajectories in systems composed of multiple autonomous agents such as unmanned mobile robots and manipulators with several degrees of freedom. A rigorous and accurate model explaining the dynamics of robots, is necessary to tackle tasks such as simulation, torque estimation, reduction of mechanical vibrations and design of control law

Robot Manipulators

Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world