On the regularity of the inverse jacobian of parallel robots

Checking the regularity of the inverse jacobian matrix of a parallel robot is an essential element for the safe use of this type of mechanism. Ideally such check should be made for all poses of the useful workspace of the robot or for any pose along a given trajectory and should take into account the uncertainties in the robot modeling and control. We propose various methods that facilitate this check. We exhibit especially a sufficient condition for the regularity that is directly related to the extreme poses that can be reached by the robot

On the regularity of the inverse jacobian of parallel robots

Checking the regularity of the inverse jacobian matrix of a parallel robot is an essential element for the safe use of this type of mechanism. Ideally such check should be made for all poses of the useful workspace of the robot or for any pose along a given trajectory and should take into account the uncertainties in the robot modeling and control. We propose various methods that facilitate this check. We exhibit especially a sufficient condition for the regularity that is directly related to the extreme poses that can be reached by the robot

Interval Analysis and Reliability in Robotics

A robot is typical of systems that are inherently submitted to uncertainties although they should be highly reliable (i.e. for a robot used in surgical applications). The sources of uncertainties are the manufacturing tolerances of the mechanical parts constituting the robot which make the real robot always different from its theoretical model and control errors. We exhibit properties of a robot that are sensitive to the uncertainties and we present methods, using mainly interval analysis, that allow one to manage these uncertainties to ensure the reliability of the robot

Optimization of the 2PRU-1PRS Parallel Manipulator Based on Workspace and Power Consumption Criteria

In the last few years, parallel manipulators are being increasingly studied and used for different applications. The performance of parallel manipulators is very sensitive to the geometric parameters, so it is essential to optimize them in order to obtain the desired function. We propose two optimization algorithms that consider the size and regularity of the workspace. The first one obtains the geometric parameters combination that results in the biggest and most regular workspace. The second method analyzes the geometric parameters combinations that result in an acceptable size of the workspace—even if it is not the biggest one—and finds out which ones result in the lowest power consumption. Even if the results vary depending on the application and trajectories studied, the proposed methodology can be followed to any type of parallel manipulator, application or trajectory. In this work we focus on the dimension optimization of the geometric parameters of the 2PRU-1PRS Multi-Axial Shaking Table (MAST) for automobile pieces testing purposes.This research was funded by the Regional Government of the Basque Country (IT949-16) and the Science and Innovation Ministry of the Spanish Government (PID2019-105262RB-I00)

A Branch and Prune Algorithm for the Computation of Generalized Aspects of Parallel Robots

International audienceParallel robots enjoy enhanced mechanical characteristics that have to be contrasted with a more complicated design. In particular, they often have parallel singularities at some poses, and the robots may become uncontrollable, and could even be damaged, in such configurations. The computation of the connected components in the set of nonsingular reachable configurations, called generalized aspects, is therefore a key issue in their design. This paper introduces a new method, based on numerical constraint programming, to compute a certified enclosure of the generalized aspects. Though this method does not allow counting their number rigorously, it constructs inner approximations of the nonsingular workspace that allow commanding parallel robots safely. It also provides a lower-bound on the exact number of generalized aspects. It is moreover the first general method able to handle any parallel robot in theory, though its computational complexity currently restricts its usage to robots with three degrees of freedom. Finally, the contraint programming paradigm it relies on makes it possible to consider various additional constraints (e.g., collision avoidance), making it suitable for practical considerations

Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

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