Computing cross-sections of the workspace of cable-driven parallel robots with 6 sagging cables

International audienceFinding the workspace of cable driven parallel robots (CDPR) with sagging cables (i.e. elastic and deformable cables) is a problem that has never been fully addressed in the literature as this is a complex issue: the inverse kinematics may have multiple solutions and the equations that describe the problem are non-linear and non algebraic. We address here the problem of determining an approximation of the border of horizontal cross-sections of the workspace for CDPR with 6 cables. We present an algorithm that give an outline of this border but also rises several theoretical issues. We then propose another algorithm that allow to determine a polygonal approximation of the workspace border induced by a specific constraint. All these algorithms are illustrated on a very large CDPR

Singularity of cable-driven parallel robot with sagging cables: preliminary investigation

International audienceThis paper addresses for the first time the singu-larity analysis of cable-driven parallel robot (CDPR) with sagging cables using the Irvine model. We present the mathematical framework of singularity analysis of CDPR using this cable model. We then show that, besides a cable model representation singularity, both the inverse and forward kinematics (IK and FK) have a singularity type, called parallel robot singularity, which correspond to the singularity of an equivalent parallel robot with rigid legs. We then show that both the IK and FK have also full singularities, that are not parallel robot singularity and are obtained when two of the IK or FK solution branches intersect. IK singularity will usually lie on the border of the CDPR workspace. We then exhibit an algorithm that allow one to prove that a singularity exist in the neighborhood of a given pose and to estimate its location with an arbitrary accuracy. Examples are provided for parallel robot, IK and FK singularities. However we have not been able to determine examples of combined singularity where both the IK and FK are singular (besides parallel robot singularity)

Efficient kinematics of a 2-1 and 3-1 CDPR with non-elastic sagging cables

International audienceSolving the kinematics of CDPR is complex as soon as cable sagging is taken into account. We are considering here CDPRs having 2 cables whose extremities are attached at the same point on the platform (i.e. CDPRs allowing only translational motion). Regarding the cables we assume that they are nonelastic but have a mass so that they will exhibit sagging. We first show that the inverse and direct kinematics (IK and DK) amount to solve a square system of equations. We then show that these systems of equations may be reduced to solving an equation in a single variable that cannot be solved analytically but can easily be solved numerically. Using this result we show that the sagging will play a role on the result of the IK/FK only if the load mass is lower than a threshold. We then present some preliminary results regarding the case of 3 cables which is much more complex: the IK may be reduced to solving an equation in a single variable but this solving is numerically difficult. Here again it seems that sagging may be neglected if the load mass is high enough. We also present a preliminary analysis of the 3-1 case

Computing cross-sections of the workspace of suspended cable-driven parallel robot with sagging cables having tension limitations

International audienceAlthough workspace is essential for the design and control of cable-driven parallel robots (CDPR) very few works have been devoted to this topic when sagging cables are considered , most probably because of the complexity of the cable model. In this paper we consider suspended CDPR with sagging cables that can support only a limited tension. We propose an algorithm to compute the border of horizontal cross-sections of the workspace for a given altitude and orientation of the platform. We show that singularities of the kinematics equations have to be taken into account for a proper determination of the border and that the workspace can be separated in several components according to the branch of the inverse kinematics on which the robot is evolving. We also compare the workspace obtained for ideal and sagging cables

Mixing neural networks and the Newton method for the kinematics of simple cable-driven parallel robots with sagging cables

International audienceCable-driven parallel robots (CDPR) use cables to move a platform. These cables can be coiled/uncoiled by winches and are all attached to the platform. We are considering here a specific class of CDPR, called N-1 which has N cables that are all attached to the platform at the same point B. With 2 cables we get a planar 2-dof robot while with N ≥ 3 we get a robot with 3 translational dof. We assume that the cables have elasticity and a mass so that sagging exists. In that case the inverse and direct kinematics (IK, DK) are difficult to solve. As kinematics plays an important role for the robot analysis it is necessary to design fast but exact kinematics procedures. In this paper we consider the 2-1 and 3-1 cases which have a single solution for the kinematic and addresses the use of neural network (NN) to solve the IK and DK. We show that NN provide very approximate results but also that it is possible to design a solving strategy mixing NN and the Newton method to get the exact result in a low computation time. We cannot formally prove that this approach will always work but extensive numerical tests have shown no failure

Influence of uncertainties on the positioning of cable-driven parallel robots

International audiencePositioning accuracy of cable-driven parallel robots is influenced by many factors such as geometry, actuator sensor accuracy and disturbances in the applied wrench. Another uncertainty source is the elasticity of the cables. While the influence of many factors may be decreased by calibration and/or sensor fusion, elasticity parameters are difficult to estimate and their effect on the positioning errors has yet to be determined. In this paper we consider a generic cable model that include cable elasticity and the effect of cable weight and we propose a generic algorithm that allows one to safely calculate the minimum and maximum of the positioning error at a given pose when the elasticity parameters are constrained to lie within some given bounds. The algorithm is designed for being able to manage the effect of different uncertainties sources and we compare the influence of elasticity versus the effect of uncertainties in the cable lengths

Advances in Robot Kinematics : Proceedings of the 15th international conference on Advances in Robot Kinematics

International audienceThe motion of mechanisms, kinematics, is one of the most fundamental aspect of robot design, analysis and control but is also relevant to other scientific domains such as biome- chanics, molecular biology, . . . . The series of books on Advances in Robot Kinematics (ARK) report the latest achievement in this field. ARK has a long history as the first book was published in 1991 and since then new issues have been published every 2 years. Each book is the follow-up of a single-track symposium in which the participants exchange their results and opinions in a meeting that bring together the best of world’s researchers and scientists together with young students. Since 1992 the ARK symposia have come under the patronage of the International Federation for the Promotion of Machine Science-IFToMM.This book is the 13th in the series and is the result of peer-review process intended to select the newest and most original achievements in this field. For the first time the articles of this symposium will be published in a green open-access archive to favor free dissemination of the results. However the book will also be o↵ered as a on-demand printed book.The papers proposed in this book show that robot kinematics is an exciting domain with an immense number of research challenges that go well beyond the field of robotics.The last symposium related with this book was organized by the French National Re- search Institute in Computer Science and Control Theory (INRIA) in Grasse, France

Design, implementation and control of a deformable manipulator robot based on a compliant spine

International audienceThis paper presents the conception, the numerical modeling and the control of a dexterous, deformable manipulator bio-inspired by the skeletal spine found in vertebrate animals. Through the implementation of this new manipulator, we show a methodology based on numerical models and simulations, that goes from design to control of continuum and soft robots. The manipulator is modeled using Finite Element Method (FEM), using a set of beam elements that reproduce the lattice structure of the robot. The model is computed and inverted in real-time using optimisation methods. A closed-loop control strategy is implemented to account for the disparities between the model and the robot. This control strategy allows for accurate positioning, not only of the tip of the manipulator, but also the positioning of selected middle points along its backbone. In a scenario where the robot is piloted by a human operator, the command of the robot is enhanced by a haptic loop that renders the boundaries of its task space as well as the contact with its environment. The experimental validation of the model and control strategies is also presented in the form of an inspection task use case

A panorama of methods for dealing with sagging cables in cable-driven parallel robots

International audienceWe are considering cable-driven parallel robot (CDPR), where the legs of the robot are constituted of cables that can be independently coiled/uncoiled. We show that whatever the size of the CDPR is we may have slack cables so that using a sagging cable model that takes into account both the mass and elasticity of the cables will improve the positioning accuracy.Being able to solve the inverse and direct kinematics (IK/DK) with sagging cables is crucial for kinematic analysis while being quite complex as both IK/DK may have multiple solutions. We present a panorama of solving methods for the IK/DK with their advantages and drawbacks

Fast, generic and reliable control and simulation of soft robots using model order reduction

International audienceObtaining an accurate mechanical model of a soft deformable robot compatible with the computation time imposed by robotic applications is often considered as an unattainable goal. This paper should invert this idea. The proposed methodology offers the possibility to dramatically reduce the size and the online computation time of a Finite Element Model (FEM) of a soft robot. After a set of expensive offline simulations based on the whole model, we apply snapshot-proper orthogonal decomposition to sharply reduce the number of state variables of the soft robot model. To keep the computational efficiency, hyperre-duction is used to perform the integration on a reduced domain. The method allows to tune the error during the two main steps of complexity reduction. The method handles external loads (contact, friction, gravity...) with precision as long as they are tested during the offline simulations. The method is validated on two very different examples of FE models of soft robots and on one real soft robot. It enables acceleration factors of more than 100, while saving accuracy, in particular compared to coarsely meshed FE models and provides a generic way to control soft robots