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

Constrained-Differential-Kinematics-Decomposition-Based NMPC for Online Manipulator Control with Low Computational Costs

Flexibility combined with the ability to consider external constraints comprises the main advantages of nonlinear model predictive control (NMPC). Applied as a motion controller, NMPC enables applications in varying and disturbed environments, but requires time-consuming computations. Hence, given the full nonlinear multi-DOF robot model, a delay-free execution providing short control horizons at appropriate prediction horizons for accurate motions is not applicable in common use. This contribution introduces an approach that analyzes and decomposes the differential kinematics similar to the inverse kinematics method to assign Cartesian boundary conditions to specific systems of equations during the model building, reducing the online computational costs. The resulting fully constrained NMPC realizes the translational obstacle avoidance during trajectory tracking using a reduced model considering both joint and Cartesian constraints coupled with a Jacobian transposed controller performing the end-effector’s orientation correction. Apart from a safe distance from the obstacles, the presented approach does not lead to any limitations of the reachable workspace, and all degrees of freedom (DOFs) of the robot are used. The simulative evaluation in Gazebo using the Stäubli TX2-90 commanded of ROS on a standard computer emphasizes the significantly lower online computational costs, accuracy analysis, and extended adaptability in obstacle avoidance, providing additional flexibility. An interpretation of the new concept is discussed for further use and extensions

Postprocesamiento CAM-ROBOTICA orientado al prototipado y mecanizado en células robotizadas complejas

The main interest of this thesis consists of the study and implementation of postprocessors to adapt the toolpath generated by a Computer Aided Manufacturing (CAM) system to a complex robotic workcell of eight joints, devoted to the rapid prototyping of 3D CAD-defined products. It consists of a 6R industrial manipulator mounted on a linear track and synchronized with a rotary table. To accomplish this main objective, previous work is required. Each task carried out entails a methodology, objective and partial results that complement each other, namely: - It is described the architecture of the workcell in depth, at both displacement and joint-rate levels, for both direct and inverse resolutions. The conditioning of the Jacobian matrix is described as kinetostatic performance index to evaluate the vicinity to singular postures. These ones are analysed from a geometric point of view. - Prior to any machining, the additional external joints require a calibration done in situ, usually in an industrial environment. A novel Non-contact Planar Constraint Calibration method is developed to estimate the external joints configuration parameters by means of a laser displacement sensor. - A first control is originally done by means of a fuzzy inference engine at the displacement level, which is integrated within the postprocessor of the CAM software. - Several Redundancy Resolution Schemes (RRS) at the joint-rate level are compared for the configuration of the postprocessor, dealing not only with the additional joints (intrinsic redundancy) but also with the redundancy due to the symmetry on the milling tool (functional redundancy). - The use of these schemes is optimized by adjusting two performance criterion vectors related to both singularity avoidance and maintenance of a preferred reference posture, as secondary tasks to be done during the path tracking. Two innovative fuzzy inference engines actively adjust the weight of each joint in these tasks.Andrés De La Esperanza, FJ. (2011). Postprocesamiento CAM-ROBOTICA orientado al prototipado y mecanizado en células robotizadas complejas [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10627Palanci

Master-Slave Coordination Using Virtual Constraints for a Redundant Dual-Arm Haptic Interface

Programming robots for tasks involving force interaction is difficult, since both the knowledge of the task and the dynamics of the robots are necessary. An immersive haptic interface for task demonstration is proposed, where theoperator can sense and act through the robot. This is achieved by coupling two robotic systems with virtual constraints such that they have the same coordinates in the operational space disregarding a fixed offset. Limitations caused by the singular configurations or the reach of the robots are naturally reflected to either side as haptic feedback

Kinematics and Robot Design II (KaRD2019) and III (KaRD2020)

This volume collects papers published in two Special Issues “Kinematics and Robot Design II, KaRD2019” (https://www.mdpi.com/journal/robotics/special_issues/KRD2019) and “Kinematics and Robot Design III, KaRD2020” (https://www.mdpi.com/journal/robotics/special_issues/KaRD2020), which are the second and third issues of the KaRD Special Issue series hosted by the open access journal robotics.The KaRD series is an open environment where researchers present their works and discuss all topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. It aims at being an established reference for researchers in the field as other serial international conferences/publications are. Even though the KaRD series publishes one Special Issue per year, all the received papers are peer-reviewed as soon as they are submitted and, if accepted, they are immediately published in MDPI Robotics. Kinematics is so intimately related to the design of robotic/automatic systems that the admitted topics of the KaRD series practically cover all the subjects normally present in well-established international conferences on “mechanisms and robotics”.KaRD2019 together with KaRD2020 received 22 papers and, after the peer-review process, accepted only 17 papers. The accepted papers cover problems related to theoretical/computational kinematics, to biomedical engineering and to other design/applicative aspects

Dynamic whole-body motion generation under rigid contacts and other unilateral constraints

The most widely used technique for generating wholebody motions on a humanoid robot accounting for various tasks and constraints is inverse kinematics. Based on the task-function approach, this class of methods enables the coordination of robot movements to execute several tasks in parallel and account for the sensor feedback in real time, thanks to the low computation cost. To some extent, it also enables us to deal with some of the robot constraints (e.g., joint limits or visibility) and manage the quasi-static balance of the robot. In order to fully use the whole range of possible motions, this paper proposes extending the task-function approach to handle the full dynamics of the robot multibody along with any constraint written as equality or inequality of the state and control variables. The definition of multiple objectives is made possible by ordering them inside a strict hierarchy. Several models of contact with the environment can be implemented in the framework. We propose a reduced formulation of the multiple rigid planar contact that keeps a low computation cost. The efficiency of this approach is illustrated by presenting several multicontact dynamic motions in simulation and on the real HRP-2 robot

Design, implementation, control, and user evaluations of assiston-arm self-aligning upper-extremity exoskeleton

Physical rehabilitation therapy is indispensable for treating neurological disabilities. The use of robotic devices for rehabilitation holds high promise, since these devices can bear the physical burden of rehabilitation exercises during intense therapy sessions, while therapists are employed as decision makers. Robot-assisted rehabilitation devices are advantageous as they can be applied to patients with all levels of impairment, allow for easy tuning of the duration and intensity of therapies and enable customized, interactive treatment protocols. Moreover, since robotic devices are particularly good at repetitive tasks, rehabilitation robots can decrease the physical burden on therapists and enable a single therapist to supervise multiple patients simultaneously; hence, help to lower cost of therapies. While the intensity and quality of manually delivered therapies depend on the skill and fatigue level of therapists, high-intensity robotic therapies can always be delivered with high accuracy. Thanks to their integrated sensors, robotic devices can gather measurements throughout therapies, enable quantitative tracking of patient progress and development of evidence-based personalized rehabilitation programs. In this dissertation, we present the design, control, characterization and user evaluations of AssistOn-Arm, a powered, self-aligning exoskeleton for robotassisted upper-extremity rehabilitation. AssistOn-Arm is designed as a passive back-driveable impedance-type robot such that patients/therapists can move the device transparently, without much interference of the device dynamics on natural movements. Thanks to its novel kinematics and mechanically transparent design, AssistOn-Arm can passively self-align its joint axes to provide an ideal match between human joint axes and the exoskeleton axes, guaranteeing ergonomic movements and comfort throughout physical therapies. The self-aligning property of AssistOn-Arm not only increases the usable range of motion for robot-assisted upper-extremity exercises to cover almost the whole human arm workspace, but also enables the delivery of glenohumeral mobilization (scapular elevation/depression and protraction/retraction) and scapular stabilization exercises, extending the type of therapies that can be administered using upper-extremity exoskeletons. Furthermore, the self-alignment property of AssistOn-Arm signi cantly shortens the setup time required to attach a patient to the exoskeleton. As an impedance-type device with high passive back-driveability, AssistOn- Arm can be force controlled without the need of force sensors; hence, high delity interaction control performance can be achieved with open-loop impedance control. This control architecture not only simpli es implementation, but also enhances safety (coupled stability robustness), since open-loop force control does not su er from the fundamental bandwidth and stability limitations of force-feedback. Experimental characterizations and user studies with healthy volunteers con- rm the transparency, range of motion, and control performance of AssistOn- Ar