Optimal pose selection for the calibration of an overconstrained Cable-Driven Parallel Robot

In this project an optimal pose selection method for the calibration of an overconstrained Cable-Driven Parallel robot is presented. This manipulator belongs to a subcategory of parallel robots, where the classic rigid "legs" are replaced by cables. Cables are flexible elements that bring advantages and disadvantages to the robot modeling. For this reason, there are many open research issues, and the calibration of geometric parameters is one of them. The identification of the geometry of a robot, in particular, is usually called Kinematic Calibration. Many methods have been proposed in the past years for the solution of the latter problem. Although these methods are based on calibration using different kinematic models, when the robot’s geometry becomes more complex, their robustness and reliability decrease. This fact makes the selection of the calibration poses more complicated. The position and the orientation of the endeffector in the workspace become important in terms of selection. Thus, in general, it is necessary to evaluate the robustness of the chosen calibration method, by means, for example, of a parameter such as the observability index. In fact, it is known from the theory, that the maximization of the above mentioned index identifies the best choice of calibration poses, and consequently, using this pose set may improve the calibration process. The objective of this thesis is to analyze optimization algorithms which aim to calculate an optimal choice of poses both in quantitative and qualitative terms. Quantitatively, because it is of fundamental importance to understand how many poses are needed. Not necessarily a greater number of poses leads to a better result. Qualitatively, because it is useful to understand if the selected combination of poses actually gives additional information in the process of the identification of the parameters.

Direct Kinematics of Underactuated Cable-Driven Parallel Robots: Sensitivity to Redundant Measurements

Underactuated cable-driven parallel robots (UACDPRs) shift a 6-degree-of-freedom end-effector (EE) with fewer than 6 cables. This thesis proposes a new automatic calibration technique that is applicable for under-actuated cable-driven parallel robots. The purpose of this work is to develop a method that uses free motion as an exciting trajectory for the acquisition of calibration data. The key point of this approach is to find a relationship between the unknown parameters to be calibrated (the lengths of the cables) and the parameters that could be measured by sensors (the swivel pulley angles measured by the encoders and roll-and-pitch angles measured by inclinometers on the platform). The equations involved are the geometrical-closure equations and the finite-difference velocity equations, solved using the least-squares algorithm. Simulations are performed on a parallel robot driven by 4 cables for validation. The final purpose of the calibration method is, still, the determination of the platform initial pose. As a consequence of underactuation, the EE is underconstrained and, for assigned cable lengths, the EE pose cannot be obtained by means of forward kinematics only. Hence, a direct-kinematics algorithm for a 4-cable UACDPR using redundant sensor measurements is proposed. The proposed method measures two orientation parameters of the EE besides cable lengths, in order to determine the other four pose variables, namely 3 position coordinates and one additional orientation parameter. Then, we study the performance of the direct-kinematics algorithm through the computation of the sensitivity of the direct-kinematics solution to measurement errors. Furthermore, position and orientation error upper limits are computed for bounded cable lengths errors resulting from the calibration procedure, and roll and pitch angles errors which are due to inclinometer inaccuracies.

Feedback control of underactuated cable-driven parallel robots

In this work an Underactuated Cable-Driven Parallel Robot (UACDPR) that operates in the three dimensional Euclidean space is considered. The End-Effector has 6 degrees of freedom and is actuated by 4 cables, therefore from a mechanical point of view the robot is defined underconstrained. However, considering only three controlled pose variables, the degree of redundancy for the control theory can be considered one. The aim of this thesis is to design a feedback controller for a point-to-point motion that satisfies the transient requirements, and is capable of reducing oscillations that derive from the reduced number of constraints. A force control is chosen for the positioning of the End-Effector, and error with respect to the reference is computed through data measure of several sensors (load cells, encoders and inclinometers) such as cable lengths, tension and orientation of the platform. In order to express the relation between pose and cable tension, the inverse model is derived from the kinematic and dynamic model of the parallel robot. The intrinsic non-linear nature of UACDPRs systems introduces an additional level of complexity in the development of the controller, as a result the control law is composed by a partial feedback linearization, and damping injection to reduce orientation instability. The fourth cable allows to satisfy a further tension distribution constraint, ensuring positive tension during all the instants of motion. Then simulations with different initial conditions are presented in order to optimize control parameters, and lastly an experimental validation of the model is carried out, the results are analysed and limits of the presented approach are defined.

Geometrico-static modelling of continuum parallel robots

In this thesis, we explore three methods for the geometrico-static modelling of continuum parallel robots. Inspired by biological trunks, tentacles and snakes, continuum robot designs can reach confined spaces, manipulate objects in complex environments and conform to curvilinear paths in space. In addition, parallel continuum manipulators have the potential to inherit some of the compactness and compliance of continuum robots while retaining some of the precision, stability and strength of rigid-links parallel robots. Subsequently, the foundation of our work is performed on slender beam by applying the Cosserat rod theory, appropriate to model continuum robots. After that, three different approaches are developed on a case study of a planar parallel continuum robot constituted of two connected flexible links. We solve the forward and inverse geometrico-static problem namely by using (a) shooting methods to obtain a numerical solution, (b) an elliptic method to find a quasi-analytical solution, and (c) the Corde model to perform further model analysis. The performances of each of the studied methods are evaluated and their limits are highlighted. This thesis is divided as follows. Chapter one gives the introduction on the field of the continuum robotics and introduce the parallel continuum robots that is studied in this work. Chapter two describe the geometrico-static problem and gives the mathematical description of this problem. Chapter three explains the numerical approach with the shooting method and chapter four introduce the quasi-analytical solution. Then, Chapter five introduce the analytic method inspired by the Corde model and chapter six gives the conclusions of this work.