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Program event for Monday 16, May
|8:00||Welcome of participants|
|8:40||Introduction to the workshop
|8:45||Keynote lecture 1 – Geometric analysis of parallel robots and its extension to other research fields||Abstract|
|Confirmed speaker: Prof. Manfred HUSTY (Innsbrück University, Austria)|
|9:30||Keynote lecture 2 – Screw theory and its extension to other research fields||Abstract|
|Confirmed speaker: Dr. Marco CARRICATO (Bologna University, Italy)|
|10:45||Keynote lecture 3 – Grassmann geometry and Grassmann-Cayley algebra and their extension to other research fields||Abstract|
|Confirmed speaker: Dr. Stéphane CARO (IRCCyN Nantes, France)|
|11:30||Keynote lecture 4 – Dynamic modeling of parallel robots and its extension to other research fields||Abstract|
|Confirmed speaker: Prof. Clément GOSSELIN (Laval University, Québec, Canada)|
|13:45||Keynote lecture 5 – Applications of parallel robots: Famous, unnoticed and potential applications of PKMs||Abstract|
|Confirmed speaker: Dr. Olivier COMPANY (LIRMM Montpellier, France)|
|14:30||Keynote lecture 6 – Cable-driven parallel robots and their extension to teaching activities and other research fields||Abstract|
|Confirmed speaker: Dr. Jean-Pierre MERLET (INRIA Sophia-Antipolis, France)|
|15:45||Keynote lecture 7 – Advanced control of parallel robots and its extension to other research fields||Abstract|
|Confirmed speaker: Prof. Philippe MARTINET and Dr. Sébastien BRIOT (IRCCyN Nantes, France)|
|16:15||Round table with all speakers||
|17:30||End of the workshop|
Abstract: Various mathematical formulations are used to describe mechanism and robot kinematics. The mathematical formulation is the basis for kinematic analysis and synthesis, i.e., determining displacements, velocities and accelerations, on the one hand, and obtaining design parameters on the other. Vector/matrix formulation containing trigonometric functions is arguably the most favoured approach used in the engineering research community. A less well known but nevertheless very successful approach relies on algebraic formulation. This involves describing mechanism constraints with algebraic (polynomial) equations and solving these equation sets, that pertain to some given mechanism or robot, with the powerful tools of algebraic and numerical algebraic geometry.
For 15 years, now, the author and his collaborators have been applying algebraic formulation to kinematics in particular instances but wide range of analysis and synthesis problems. These instances include direct and inverse pose determination in general parallel (e.g., Stuart-Gough platform) and serial (e.g., 6R) robots, singularity distribution and workspace mapping. This has also been carried out in cases of lower degree of mobility parallel robots as well as for planar and spherical mechanisms. Fundamental to such formulations is the algebraic parametrization of the various displacement groups (planar, spherical, spatial). These parameters are usually elements of the group's quaternion algebra. We contend that this approach provides a most effective insight into the structure of the equation and what it reveals about the corresponding mechanical systems under investigation.
Topics to be addressed are:
- Methods to establish the sets of equations -- the canonical equations,
- Solution methods for sets of polynomial equations,
- Adapting the algebraic formulation to the mechanism's degree of freedom,
- Jacobian and singularities,
- Some examples.
In this session, the theory of screws will be introduced and it will be shown how they can find application in several fields of robotics, including singularity analysis, type synthesis, constraint design, etc.
Screws are geometrical entities that represent both the instantaneous motion of a rigid body (in the form of a twist) and the set of generalized forces acting upon it (in the form of a wrench). Thus, screw theory naturally provides the geometrical and algebraic concepts and tools underlying the first-order kinematics and statics of rigid bodies. The importance of screw theory in robotics is widely recognized. Methods and formalisms based on the geometry and algebra of screws have been shown to be particularly effective and have led to significant advances in a variety of areas of robotics, including mobility analysis, singularities, constraint design, and type synthesis of parallel manipulators. The main reason for this success is the strong geometrical insight that screw theory sheds on many complex physical phenomena that roboticists have to deal with. This lecture will deliver an overview of the basic concepts and some of the main applications of screw-theory, with emphasis being given on geometrical interpretation and understanding, rather than on computational issues.
1. Twists, wrenches and screws. Plucker representation of a screw.
2. Twist and wrench vector spaces: linear dependance and independence.
3. Work and reciprocity. Constraints.
4. Screw-system classification. Invariant screw systems. Persistent screw systems.
5. Applications: mobility analysis; singularities of serial chains; singularities of closed chains and parallel manipulators; synthesis of parallel manipulators.
In the past decades, parallel manipulators have attracted the attention of academic and industrial communities. As compared with serial manipulators, properly designed parallel manipulators have higher stiffness and higher accuracy, although their workspace is smaller. When the manipulation task requires less than six dof, the use of lower-mobility parallel manipulators may bring some advantages in terms of complexity and dynamic performance. Planar motions, spherical motions, translational motions and Schönflies motions are some motion types that require less than six dof. The singular configurations of lower-mobility parallel manipulators are critical poses that lead either to a loss of control or to a change of the motion performed by the moving platform.
The first step towards the parallel singularity analysis of parallel manipulators is the formulation of a 6×6 Jacobian matrix and the parallel singularities are related to its rank deficiency. Classical methods consist in a direct analysis of this matrix by exploring the vanishing conditions of its determinant. These methods often fail to provide satisfactory results since the determinant of the Jacobian matrix is usually unwieldy to assess, even with a computer algebra system. Thus, alternative approaches using Grassmann-Cayley Algebra and Grassmann Geometry were proposed in the literature to deal with the vanishing conditions of this determinant.
This lecture will deal with the singularity analysis of lower-mobility parallel manipulators based on Grassmann-Cayley algebra and Grassmann geometry. The extension of the results to other areas will be addressed. In particular, applications in robot design, reconfigurable robots, compliant robots and multi-arm robots will be discussed.
In this lecture, the different techniques that can be used for the dynamic modelling of parallel robots will first be presented. The dynamic balancing of parallel mechanisms will also be introduced. Then, the extension of the results to other areas will be addressed. In particular, applications in cable-driven robots, physical human/robot interaction, assistive devices, haptic devices, humanoid/multi-pod robots will be discussed.
Cams and closed loop mechanisms have been studied in previous centuries mainly for motion transformation and synchronization in the industry before the emergence of controlled systems. In the past 50 years, complex spatial closed loop mechanisms have been designed and controlled for some applications in the industry. A lot of research has been devoted to these mechanisms about synthesis, kinematics, optimization, control… but very often, targeted applications were devoted to industrial tasks, metal harvesting, positioning, pick and place… The goal of this presentation will be to mention quickly well-known ones, but also to explore and focus various unnoticed applications in other domains. We will also try to imagine future applications for already developed tools, mechanisms and technologies.
Changing the actuation system of parallel robots to cables may seem to be innocutuous but has a high impact on the analysis and on potential applications of this kind of parallel robots. In this talk we will present the current state of the art of this field (in which remains several complex open issues) and existing applications in the field of assistance, rehabilitation, industrial maintenance of large installation and education (not only in robotics). We then review the applicability of the underlying theory of cable-driven parallel robots to other domains such as grasping, civil engineering and robot navigation
In order to get the best accuracy of a robot end-effector, it is preferable to use sensor-based controllers. As the end-effector pose is an external property of a parallel robot, it is natural to use exteroceptive sensors to measure it in order to suppress inaccuracies coming from modelling errors. Cameras offer this possibility. So, it is possible to obtain higher accuracy than in the case of classic control schemes (based on geometrical model).
In some cases, it is impossible to directly observe the end-effector, but the leg directions can instead be used. In this case, however, unusual results were recorded, namely: (i) the possibility of controlling the robot by observing a number of legs less than the total number of legs, and that (ii) in some cases, the robot does not converge to the desired end-effector pose, even if the observed leg directions did.
These results can be explained through the use of the hidden robot concept, which is a tangible visualisation of the mapping between the observed leg direction space (internal property) and Cartesian space (external property). This hidden robot has different assembly modes and singular configurations from the real robot, and it is a powerful tool to simplify the analysis of the aforementioned mapping.
In this talk, the concept of hidden robot model is generalised for any type of parallel robot controlled through visual servoing based on observation of the legs. It will be also shown how this concept of hidden robot can be extended to other classes of robots, such as, for instance, dual-arm robots manipulating an object