A Fibonacci control system with application to hyper-redundant manipulators

We study a robot snake model based on a discrete linear control system involving Fibonacci sequence and closely related to the theory of expansions in non-integer bases. The present paper includes an investigation of the reachable workspace, a more general analysis of the control system underlying the model, its reachability and local controllability properties and the relation with expansions in non-integer bases and with iterated function systems

Control of Redundant Robots Under Hard Joint Constraints: Saturation in the Null Space

We present an efficient method for addressing online the inversion of differential task kinematics for redundant manipulators, in the presence of hard limits on joint space motion that can never be violated. The proposed SNS (Saturation in the Null Space) algorithm proceeds by successively discarding the use of joints that would exceed their motion bounds when using the minimum norm solution. When processing multiple tasks with priority, the SNS method realizes a preemptive strategy by preserving the correct order of priority in spite of the presence of saturations. In the single- and multi-task case, the algorithm automatically integrates a least possible task scaling procedure, when an original task is found to be unfeasible. The optimality properties of the SNS algorithm are analyzed by considering an associated Quadratic Programming problem. Its solution leads to a variant of the algorithm, which guarantees optimality also when the basic SNS algorithm does not. Numerically efficient versions of these algorithms are proposed. Their performance allows real-time control of robots executing many prioritized tasks with a large number of hard bounds. Experimental results are reported

Continuous-time recurrent neural networks for quadratic programming: theory and engineering applications.

Liu Shubao.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 90-98).Abstracts in English and Chinese.Abstract --- p.i摘要 --- p.iiiAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Time-Varying Quadratic Optimization --- p.1Chapter 1.2 --- Recurrent Neural Networks --- p.3Chapter 1.2.1 --- From Feedforward to Recurrent Networks --- p.3Chapter 1.2.2 --- Computational Power and Complexity --- p.6Chapter 1.2.3 --- Implementation Issues --- p.7Chapter 1.3 --- Thesis Organization --- p.9Chapter I --- Theory and Models --- p.11Chapter 2 --- Linearly Constrained QP --- p.13Chapter 2.1 --- Model Description --- p.14Chapter 2.2 --- Convergence Analysis --- p.17Chapter 3 --- Quadratically Constrained QP --- p.26Chapter 3.1 --- Problem Formulation --- p.26Chapter 3.2 --- Model Description --- p.27Chapter 3.2.1 --- Model 1 (Dual Model) --- p.28Chapter 3.2.2 --- Model 2 (Improved Dual Model) --- p.28Chapter II --- Engineering Applications --- p.29Chapter 4 --- KWTA Network Circuit Design --- p.31Chapter 4.1 --- Introduction --- p.31Chapter 4.2 --- Equivalent Reformulation --- p.32Chapter 4.3 --- KWTA Network Model --- p.36Chapter 4.4 --- Simulation Results --- p.40Chapter 4.5 --- Conclusions --- p.40Chapter 5 --- Dynamic Control of Manipulators --- p.43Chapter 5.1 --- Introduction --- p.43Chapter 5.2 --- Problem Formulation --- p.44Chapter 5.3 --- Simplified Dual Neural Network --- p.47Chapter 5.4 --- Simulation Results --- p.51Chapter 5.5 --- Concluding Remarks --- p.55Chapter 6 --- Robot Arm Obstacle Avoidance --- p.56Chapter 6.1 --- Introduction --- p.56Chapter 6.2 --- Obstacle Avoidance Scheme --- p.58Chapter 6.2.1 --- Equality Constrained Formulation --- p.58Chapter 6.2.2 --- Inequality Constrained Formulation --- p.60Chapter 6.3 --- Simplified Dual Neural Network Model --- p.64Chapter 6.3.1 --- Existing Approaches --- p.64Chapter 6.3.2 --- Model Derivation --- p.65Chapter 6.3.3 --- Convergence Analysis --- p.67Chapter 6.3.4 --- Model Comparision --- p.69Chapter 6.4 --- Simulation Results --- p.70Chapter 6.5 --- Concluding Remarks --- p.71Chapter 7 --- Multiuser Detection --- p.77Chapter 7.1 --- Introduction --- p.77Chapter 7.2 --- Problem Formulation --- p.78Chapter 7.3 --- Neural Network Architecture --- p.82Chapter 7.4 --- Simulation Results --- p.84Chapter 8 --- Conclusions and Future Works --- p.88Chapter 8.1 --- Concluding Remarks --- p.88Chapter 8.2 --- Future Prospects --- p.88Bibliography --- p.8

DETC2004-57447 MANIPULATOR TASK-BASED PERFORMANCE OPTIMIZATION

ABSTRACT This research uses new developments in redundancy resolution and real-time capability analysis to improve the ability of an articulated arm to satisfy task constraints. Task constraints are specified using numerical values of position, velocity, force, and accuracy. Inherent in the definition of task constraints is the number of output constraints that the system needs to satisfy. The relationship of this with the input space (degrees of freedom) defines the ability to optimize manipulator performance. This is done through a Task-Based Redundancy Resolution (TBRR) scheme that uses the extra resources to find a solution that avoids system constraints (joint limits, singularities, etc.) and satisfies task constraints. To avoid system constraints, we use well-understood criteria associated with the constraints. For task requirements, the robot capabilities are estimated based on kinematic and dynamic manipulability analyses. We then compare the robot capabilities with the userspecified requirement values. This eliminates a confusing chore of selecting a proper set of performance criteria for a task at hand. The breakthrough of this approach lies in the fact that it continuously evaluates the relationship between task constraints and system resources, and when possible, improves system performance. This makes it equally applicable to redundant and non-redundant systems. The scheme is implemented using an object-oriented operational software framework and its effectiveness is demonstrated in computer simulations of a 10-DOF manipulator

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

Instantaneous Momentum-Based Control of Floating Base Systems

In the last two decades a growing number of robotic applications such as autonomous drones, wheeled robots and industrial manipulators started to be employed in several human environments. However, these machines often possess limited locomotion and/or manipulation capabilities, thus reducing the number of achievable tasks and increasing the complexity of robot-environment interaction. Augmenting robots locomotion and manipulation abilities is a fundamental research topic, with a view to enhance robots participation in complex tasks involving safe interaction and cooperation with humans. To this purpose, humanoid robots, aerial manipulators and the novel design of flying humanoid robots are among the most promising platforms researchers are studying in the attempt to remove the existing technological barriers. These robots are often modeled as floating base systems, and have lost the assumption -- typical of fixed base robots -- of having one link always attached to the ground. From the robot control side, contact forces regulation revealed to be fundamental for the execution of interaction tasks. Contact forces can be influenced by directly controlling the robot's momentum rate of change, and this fact gives rise to several momentum-based control strategies. Nevertheless, effective design of force and torque controllers still remains a complex challenge. The variability of sensor load during interaction, the inaccuracy of the force/torque sensing technology and the inherent nonlinearities of robot models are only a few complexities impairing efficient robot force control. This research project focuses on the design of balancing and flight controllers for floating base robots interacting with the surrounding environment. More specifically, the research is built upon the state-of-the-art of momentum-based controllers and applied to three robotic platforms: the humanoid robot iCub, the aerial manipulator OTHex and the jet-powered humanoid robot iRonCub. The project enforces the existing literature with both theoretical and experimental results, aimed at achieving high robot performances and improved stability and robustness, in presence of different physical robot-environment interactions

Synthesis of continuous whole-body motion in hexapod robot for humanitarian demining

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonIn the context of control, the motion of a legged robot is very challenging compared with traditional fixed manipulator. Recently, many researches have been conducted to control the motion of legged robot with different techniques. On the other hand, manipulation tasks have been addressed in many applications. These researches solved either the mobility or the manipulation problems, but integrating both properties in one system is still not available. In this thesis, a control algorithm is presented to control both locomotion and manipulation in a six legged robot. Landmines detection process is considered as a case study of this project to accelerate the mine detection operation by performing both walking and scanning simultaneously. In order to qualify the robot to perform more tasks in addition to the walking task, the joint redundancy of the robot is exploited optimally. The tasks are arranged according to their importance to high level of priority and low level of priority. A new task priority redundancy resolution technique is developed to overcome the effect of the algorithmic singularities and the kinematic singularity. The computational aspects of the solution are also considered in view of a real-time implementation. Due to the dynamic changes in the size of the robot motion space, the algorithm has the ability to make a trade-off between the number of achieved tasks and the imposed constraints. Furthermore, an appropriate hierarchy is imposed in order to ensure an accurate decoupling between the executed tasks. The dynamic effect of the arm on the overall performance of the robot is attenuated by reducing the optimisation variables. The effectiveness of the method is evaluated on a Computer Aided Design (CAD) model and the simulations of the whole operation are conducted using MATLAB and SimMechanics.Iraqi ministry of Higher Education and Scientific Researc

Ground Robotic Hand Applications for the Space Program study (GRASP)

This document reports on a NASA-STDP effort to address research interests of the NASA Kennedy Space Center (KSC) through a study entitled, Ground Robotic-Hand Applications for the Space Program (GRASP). The primary objective of the GRASP study was to identify beneficial applications of specialized end-effectors and robotic hand devices for automating any ground operations which are performed at the Kennedy Space Center. Thus, operations for expendable vehicles, the Space Shuttle and its components, and all payloads were included in the study. Typical benefits of automating operations, or augmenting human operators performing physical tasks, include: reduced costs; enhanced safety and reliability; and reduced processing turnaround time