Planning singularity-free force-feasible paths on the Stewart platform

This paper provides a method for computing force-feasible paths on the Stewart platform. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the platform to counteract any external wrench lying inside a predefined six-dimensional region. In particular, the Jacobian matrix of the manipulator will be full rank along such path, so that the path will not traverse the forward singularity locus at any point. The path is computed by first characterizing the force-feasible C-space of the manipulator as the solution set of a system of equations, and then using a higher-dimensional continuation technique to explore this set systematically from one configuration, until the second configuration is found. Examples are included that demonstrate the performance of the method on illustrative situations.Preprin

Planning wrench-feasible motions for cable-driven hexapods

Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack-to keep the control of the robot-nor excessively tightto prevent cable breakage-even in the presence of bounded perturbations of the wrench. This paper proposes a path-planning method that accommodates such constraints simultaneously. Given two configurations of the robot, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying in a predefined uncertainty region. The configuration space, or C-space for short, is placed in correspondence with a smooth manifold, which facilitates the definition of a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path nonexistence is proved by exhaustion of the search. The force Jacobian is full rank everywhere on the C-space, which implies that the computed paths will naturally avoid crossing the forward singularity locus of the robot. The adjustment of tension limits, moreover, allows to maintain a meaningful clearance relative to such locus. The approach is applicable to compute paths subject to geometric constraints on the platform pose or to synthesize free-flying motions in the full 6-D C-space. Experiments illustrate the performance of the method in a real prototype.Postprint (author's final draft

Numerical computation and avoidance of manipulator singularities

This thesis develops general solutions to two open problems of robot kinematics: the exhaustive computation of the singularity set of a manipulator, and the synthesis of singularity-free paths between given configurations. Obtaining proper solutions to these problems is crucial, because singularities generally pose problems to the normal operation of a robot and, thus, they should be taken into account before the actual construction of a prototype. The ability to compute the whole singularity set also provides rich information on the global motion capabilities of a manipulator. The projections onto the task and joint spaces delimit the working regions in such spaces, may inform on the various assembly modes of the manipulator, and highlight areas where control or dexterity losses can arise, among other anomalous behaviour. These projections also supply a fair view of the feasible movements of the system, but do not reveal all possible singularity-free motions. Automatic motion planners allowing to circumvent problematic singularities should thus be devised to assist the design and programming stages of a manipulator. The key role played by singular configurations has been thoroughly known for several years, but existing methods for singularity computation or avoidance still concentrate on specific classes of manipulators. The absence of methods able to tackle these problems on a sufficiently large class of manipulators is problematic because it hinders the analysis of more complex manipulators or the development of new robot topologies. A main reason for this absence has been the lack of computational tools suitable to the underlying mathematics that such problems conceal. However, recent advances in the field of numerical methods for polynomial system solving now permit to confront these issues with a very general intention in mind. The purpose of this thesis is to take advantage of this progress and to propose general robust methods for the computation and avoidance of singularities on non-redundant manipulators of arbitrary architecture. Overall, the work seeks to contribute to the general understanding on how the motions of complex multibody systems can be predicted, planned, or controlled in an efficient and reliable way.Aquesta tesi desenvolupa solucions generals per dos problemes oberts de la cinemàtica de robots: el càlcul exhaustiu del conjunt singular d'un manipulador, i la síntesi de camins lliures de singularitats entre configuracions donades. Obtenir solucions adequades per aquests problemes és crucial, ja que les singularitats plantegen problemes al funcionament normal del robot i, per tant, haurien de ser completament identificades abans de la construcció d'un prototipus. La habilitat de computar tot el conjunt singular també proporciona informació rica sobre les capacitats globals de moviment d'un manipulador. Les projeccions cap a l'espai de tasques o d'articulacions delimiten les regions de treball en aquests espais, poden informar sobre les diferents maneres de muntar el manipulador, i remarquen les àrees on poden sorgir pèrdues de control o destresa, entre d'altres comportaments anòmals. Aquestes projeccions també proporcionen una imatge fidel dels moviments factibles del sistema, però no revelen tots els possibles moviments lliures de singularitats. Planificadors de moviment automàtics que permetin evitar les singularitats problemàtiques haurien de ser ideats per tal d'assistir les etapes de disseny i programació d'un manipulador. El paper clau que juguen les configuracions singulars ha estat àmpliament conegut durant anys, però els mètodes existents pel càlcul o evitació de singularitats encara es concentren en classes específiques de manipuladors. L'absència de mètodes capaços de tractar aquests problemes en una classe suficientment gran de manipuladors és problemàtica, ja que dificulta l'anàlisi de manipuladors més complexes o el desenvolupament de noves topologies de robots. Una raó principal d'aquesta absència ha estat la manca d'eines computacionals adequades a les matemàtiques subjacents que aquests problemes amaguen. No obstant, avenços recents en el camp de mètodes numèrics per la solució de sistemes polinòmics permeten ara enfrontar-se a aquests temes amb una intenció molt general en ment. El propòsit d'aquesta tesi és aprofitar aquest progrés i proposar mètodes robustos i generals pel càlcul i evitació de singularitats per manipuladors no redundants d'arquitectura arbitrària. En global, el treball busca contribuir a la comprensió general sobre com els moviments de sistemes multicos complexos es poden predir, planificar o controlar d'una manera eficient i segur

Path planning and assembly mode-changes of 6-DOF Stewart-Gough-type parallel manipulators

© 2016 International Federation for the Promotion of Mechanism and Machine Science The Stewart-Gough platform (SGP) is a six degree-of-freedom (DOF) parallel manipulator whose reachable workspace is complex due to its closed-loop configuration and six DOF outputs. As such, methods of path planning that involve storing the entire reachable workspace in memory at high resolutions are not feasible due to this six-dimensional workspace. In addition, complete path planning algorithms struggle in higher dimensional applications without significant customisations. As a result, many workspace analysis algorithms and path planning schemes use iterative techniques, particularly when tracking the manipulator's many direct kinematic solutions. The aim of this paper is to present the viability of singularity-free path planning in the Stewart-Gough platform's 6-dimensional workspace on modern-day computing systems by demonstrating its assembly mode-changing capability. The entire workspace volume is found using flood-fill algorithms with smooth and singularity-free trajectories generated within this known workspace. Workspace volume analysis was also performed with results comparable to other works

Computing wrench-feasible paths for cable-driven hexapods

Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack -to keep the control of the robot- nor excessively tight -to prevent cable breakage- even in the presence of bounded perturbations of the wrench. This paper proposes a path planning method that accommodates such constraints simultaneously. Given two configurations of the robot, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying in a predefined uncertainty region. The feasible C-space is placed in correspondence with a smooth manifold, which facilitates the definition of a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path non-existence is proved at the resolution of the search. The force Jacobian is full rank everywhere on the C-space, which implies that the computed paths will naturally avoid crossing the forward singularity locus of the robot. The adjustment of tension limits, moreover, allows to maintain a meaningful clearance relative to such locus. The approach is applicable to compute paths subject to geometric constraints on the platform pose, or to synthesize free-flying motions in the full six-dimensional C-space. Experiments are included that illustrate the performance of the method in a real prototype.Postprint (published version

Parallel robots with unconventional joints to achieve under-actuation and reconfigurability

The aim of the thesis is to define, analyze, and verify through simulations and practical implementations, parallel robots with unconventional joints that allow them to be under-actuated and/or reconfigurable. The new designs will be derived from the: * 6SPS robot (alternatively 6UPS or 6SPU, depending on the implementation) when considering the spatial case (i.e., robots with 3 degrees of freedom of rotation and 3 degrees of freedom of translation). * S-3SPS robot (alternatively S-3UPS or S-3SPU, depending on the implementation) when considering spherical robots (i.e., robots with 3 degrees of freedom of rotation). In both cases, we will see how, through certain geometric transformations, some of the standard joints can be replaced by lockable or non-holonomic joints. These substitutions permit reducing the number of legs (and hence the number of actuators needed to control the robot), without losing the robot's ability to bring its mobile platform to any position and orientation (in case of a spatial robot), or to any orientation (in case of a spherical robot), within its workspace. The expected benefit of these new designs is to obtain parallel robots with: * larger working spaces because the possibility of collisions between legs is reduced, and the number of joints (with their intrinsic range limitations) is also reduced; * lower weight because the number of actuators and joints is reduced; and * lower cost because the number of actuators and controllers is also reduced. The elimination of an actuator and the introduction of a motion constraint reduces in one the dimension of the space of allowed velocities attainable from a given configuration. As a result, it will be necessary, in general, to plan maneuvers to reach the desired configuration for the moving platform. Therefore, the obtained robots will only be suitable for applications where accuracy is required in the final position and a certain margin of error is acceptable in the generated trajectories.El objetivo de esta tesis es definir, analizar y verificar, mediante simulaciones e implementaciones prácticas, robots paralelos con articulaciones no-convencionales con el fin de incorporarles propiedades de sub-actuación y reconfigurabilidad. Los nuevos diseños se basaran en robots paralelos tipo: * 6SPS (alternativamente 6UPS o 6SPU, dependiendo de la implementación) para el caso de robot espacial (es decir, robots con 3 grados de libertad de rotación y de 3 grados de libertad de la traducción). * S-3SPS (alternativamente S-3UPS o S-3SPU, dependiendo de la implementación) para el caso de robot esférico (es decir, robots con 3 grados de libertad de rotación). En ambos casos, veremos cómo, a través de ciertas transformaciones geométricas, algunas de la articulaciones convencionales pueden ser sustituidas por articulaciones bloqueables o no holonómicos. Estas sustituciones permiten la reducción de la número de patas (y por tanto el número de actuadores necesarios para controlar el robot), sin perder la capacidad del robot para llevar su plataforma móvil a cualquier posición y orientación (en el caso de un robot espacial), o para cualquier orientación (en el caso de un robot esférico), dentro de su espacio de trabajo. El beneficio esperado de estos nuevos diseños es la obtención de robots paralelos con: * Espacios de trabajo mayores debido a que la posibilidad de colisiones entre las patas se reduce, y el número de articulaciones (con sus limitaciones intrínsecas de rango) también se reduce; * Menor peso debido a que el número de actuadores y de articulaciones se reduce; y * Un menor coste debido a que el número de actuadores y controladores también se reduce. La eliminación de un actuador y la introducción de una restricción de movimiento reduce, en uno, la dimensión del espacio de velocidades alcanzables para una configuración dada. Como resultado, será necesario, en general, planificar maniobras para llegar a la configuración deseada de la plataforma móvil. Por lo tanto, los robots obtenidos sólo serán adecuados para aplicaciones donde la precisión se requiera en la posición final y exista un cierto margen de error aceptable en las trayectorias generadasPostprint (published version

Parallel robots with unconventional joints to achieve under-actuation and reconfigurability

The aim of the thesis is to define, analyze, and verify through simulations and practical implementations, parallel robots with unconventional joints that allow them to be under-actuated and/or reconfigurable. The new designs will be derived from the: * 6SPS robot (alternatively 6UPS or 6SPU, depending on the implementation) when considering the spatial case (i.e., robots with 3 degrees of freedom of rotation and 3 degrees of freedom of translation). * S-3SPS robot (alternatively S-3UPS or S-3SPU, depending on the implementation) when considering spherical robots (i.e., robots with 3 degrees of freedom of rotation). In both cases, we will see how, through certain geometric transformations, some of the standard joints can be replaced by lockable or non-holonomic joints. These substitutions permit reducing the number of legs (and hence the number of actuators needed to control the robot), without losing the robot's ability to bring its mobile platform to any position and orientation (in case of a spatial robot), or to any orientation (in case of a spherical robot), within its workspace. The expected benefit of these new designs is to obtain parallel robots with: * larger working spaces because the possibility of collisions between legs is reduced, and the number of joints (with their intrinsic range limitations) is also reduced; * lower weight because the number of actuators and joints is reduced; and * lower cost because the number of actuators and controllers is also reduced. The elimination of an actuator and the introduction of a motion constraint reduces in one the dimension of the space of allowed velocities attainable from a given configuration. As a result, it will be necessary, in general, to plan maneuvers to reach the desired configuration for the moving platform. Therefore, the obtained robots will only be suitable for applications where accuracy is required in the final position and a certain margin of error is acceptable in the generated trajectories.El objetivo de esta tesis es definir, analizar y verificar, mediante simulaciones e implementaciones prácticas, robots paralelos con articulaciones no-convencionales con el fin de incorporarles propiedades de sub-actuación y reconfigurabilidad. Los nuevos diseños se basaran en robots paralelos tipo: * 6SPS (alternativamente 6UPS o 6SPU, dependiendo de la implementación) para el caso de robot espacial (es decir, robots con 3 grados de libertad de rotación y de 3 grados de libertad de la traducción). * S-3SPS (alternativamente S-3UPS o S-3SPU, dependiendo de la implementación) para el caso de robot esférico (es decir, robots con 3 grados de libertad de rotación). En ambos casos, veremos cómo, a través de ciertas transformaciones geométricas, algunas de la articulaciones convencionales pueden ser sustituidas por articulaciones bloqueables o no holonómicos. Estas sustituciones permiten la reducción de la número de patas (y por tanto el número de actuadores necesarios para controlar el robot), sin perder la capacidad del robot para llevar su plataforma móvil a cualquier posición y orientación (en el caso de un robot espacial), o para cualquier orientación (en el caso de un robot esférico), dentro de su espacio de trabajo. El beneficio esperado de estos nuevos diseños es la obtención de robots paralelos con: * Espacios de trabajo mayores debido a que la posibilidad de colisiones entre las patas se reduce, y el número de articulaciones (con sus limitaciones intrínsecas de rango) también se reduce; * Menor peso debido a que el número de actuadores y de articulaciones se reduce; y * Un menor coste debido a que el número de actuadores y controladores también se reduce. La eliminación de un actuador y la introducción de una restricción de movimiento reduce, en uno, la dimensión del espacio de velocidades alcanzables para una configuración dada. Como resultado, será necesario, en general, planificar maniobras para llegar a la configuración deseada de la plataforma móvil. Por lo tanto, los robots obtenidos sólo serán adecuados para aplicaciones donde la precisión se requiera en la posición final y exista un cierto margen de error aceptable en las trayectorias generada

Reconfiguration and tool path planning of hexapod machine tools

Hexapod machine tools have the potential to achieve increased accuracy, speed, acceleration and rigidity over conventional machines, and are regarded by many researchers as the machine tools of the next generation. However, their small and complex workspace often limits the range of tasks they can perform, and their parallel structure raises many new issues preventing the direct use of conventional tool path planning methods. This dissertation presents an investigation of new reconfiguration and tool path planning methods for enhancing the ability of hexapods to adapt to workspace changes and assisting them in being integrated into the current manufacturing environments. A reconfiguration method which includes the consideration of foot-placement space (FPS) determination and placement parameter identification has been developed. Based on the desired workspace of a hexapod and the motion range of its leg modules, the FPS of a hexapod machine is defined and a construction method of the FPS is presented. An implementation algorithm for the construction method is developed. The equations for identifying the position and orientation of the base joints for the hexapod at a new location are formulated. For the position identification problem, an algorithm based on Dialytic Elimination is derived. Through examples, it is shown that the FPS determination method can provide feasible locations for the feet of the legs to realize the required workspace. It is also shown that these identification equations can be solved through a numerical approach or through Dialytic Elimination using symbolic manipulation. Three dissimilarities between hexapods and five-axis machines are identified and studied to enhance the basic understanding of tool path planning for hexapods. The first significant difference is the existence of an extra degree of freedom (γ angle). The second dissimilarity is that a hexapod has a widely varying inverse Jacobian over the workspace. This leads to the result that a hexapod usually has a nonlinear path when following a straight-line segment over two sampled poses. These factors indicate that the traditional path planning methods should not be used for hexapods without modification. A kinematics-based tool path planning method for hexapod machine tools is proposed to guide the part placement and the determination of γ angle. The algorithms to search for the feasible part locations and γ sets are presented. Three local planning methods for the γ angle are described. It is demonstrated that the method is feasible and is effective in enhancing the performance of the hexapod machine. As the nonlinear error is computationally expensive to evaluate in real time, the measurement of total leg length error is proposed. This measure is proved to be effective in controlling the nonlinear error