Topological analysis of singularity loci for serial and parallel manipulators

Singularities of robot manipulators have been intensely studied in the last decades by researchers of many fields. Serial singularities produce some local loss of dexterity of the manipulator, therefore it might be desirable to search for singularityfree trajectories in the jointspace. On the other hand, parallel singularities are very dangerous for parallel manipulators, for they may provoke the local loss of platform control, and jeopardize the structural integrity of links or actuators. It is therefore utterly important to avoid parallel singularities, while operating a parallel machine. Furthermore, there might be some configurations of a parallel manipulators that are allowed by the constraints, but nevertheless are unreachable by any feasible path. The present work proposes a numerical procedure based upon Morse theory, an important branch of differential topology. Such procedure counts and identify the singularity-free regions that are cut by the singularity locus out of the configuration space, and the disjoint regions composing the configuration space of a parallel manipulator. Moreover, given any two configurations of a manipulator, a feasible or a singularity-free path connecting them can always be found, or it can be proved that none exists. Examples of applications to 3R and 6R serial manipulators, to 3UPS and 3UPU parallel wrists, to 3UPU parallel translational manipulators, and to 3RRR planar manipulators are reported in the work.

Coordinated Control of Robotic Swarms in Unknown Environments

This thesis gathers the work carried out by the author in the last three years of research and it concerns the study and implementation of algorithms to coordinate and control a swarm of mobile robots moving in unknown environments. In particular, the author's attention is focused on two different approaches in order to solve two different problems. The first algorithm considered in this work deals with the possibility of decomposing a main complex task in many simple subtasks by exploiting the decentralized implementation of the so called \emph{Null Space Behavioral} paradigm. This approach to the problem of merging different subtasks with assigned priority is slightly modified in order to handle critical situations that can be detected when robots are moving through an unknown environment. In fact, issues can occur when one or more robots got stuck in local minima: a smart strategy to avoid deadlock situations is provided by the author and the algorithm is validated by simulative analysis. The second problem deals with the use of concepts borrowed from \emph{graph theory} to control a group differential wheel robots by exploiting the Laplacian solution of the consensus problem. Constraints on the swarm communication topology have been introduced by the use of a range and bearing platform developed at the Distributed Intelligent Systems and Algorithms Laboratory (DISAL), EPFL (Lausanne, CH) where part of author's work has been carried out. The control algorithm is validated by demonstration and simulation analysis and, later, is performed by a team of four robots engaged in a formation mission. To conclude, the capabilities of the algorithm based on the local solution of the consensus problem for differential wheel robots are demonstrated with an application scenario, where nine robots are engaged in a hunting task.

Singularity-Free Fully-Isotropic Translational Parallel Manipulators

Parallel mechanisms show desirable characteristics such as a large payload to robot weight ratio, considerable stiffness, low inertia and high dynamic performances. In particular, parallel manipulators with fewer than six degrees of freedom have recently attracted researchers’ attention, as their employ may prove valuable in those applications in which a higher mobility is uncalled-for. The attention of this dissertation is focused on translational parallel manipulators (TPMs), that is on parallel manipulators whose output link (platform) is provided with a pure translational motion with respect to the frame. The first part deals with the general problem of the topological synthesis and classification of TPMs, that is it identifies the architectures that TPM legs must possess for the platform to be able to freely translate in space without altering its orientation. The second part studies both constraint and direct singularities of TPMs. In particular, special families of fully-isotropic mechanisms are identified. Such manipulators exhibit outstanding properties, as they are free from singularities and show a constant orthogonal Jacobian matrix throughout their workspace. As a consequence, both the direct and the inverse position problems are linear and the kinematic analysis proves straightforward.

Design and Control of Robotic Hands

The application of dexterous robotic hands out of research laboratories has been limited by the intrinsic complexity that these devices present. This is directly reflected as an economically unreasonable cost and a low overall reliability. Within the research reported in this thesis it is shown how the problem of complexity in the design of robotic hands can be tackled, taking advantage of modern technologies (i.e. rapid prototyping), leading to innovative concepts for the design of the mechanical structure, the actuation and sensory systems. The solutions adopted drastically reduce the prototyping and production costs and increase the reliability, reducing the number of parts required and averaging their single reliability factors. In order to get guidelines for the design process, the problem of robotic grasp and manipulation by a dual arm/hand system has been reviewed. In this way, the requirements that should be fulfilled at hardware level to guarantee successful execution of the task has been highlighted. The contribution of this research from the manipulation planning side focuses on the redundancy resolution that arise in the execution of the task in a dexterous arm/hand system. In literature the problem of coordination of arm and hand during manipulation of an object has been widely analyzed in theory but often experimentally demonstrated in simplified robotic setup. Our aim is to cover the lack in the study of this topic and experimentally evaluate it in a complex system as a anthropomorphic arm hand system.

Model and control of tendon actuated robots

The use of tendons for the transmission of the forces and the movements in robotic devices has been investigated from several researchers all over the world. The interest in this kind of actuation modality is based on the possibility of optimizing the position of the actuators with respect to the moving part of the robot, in the reduced weight, high reliability, simplicity in the mechanic design and, finally, in the reduced cost of the resulting kinematic chain. After a brief discussion about the benefits that the use of tendons can introduce in the motion control of a robotic device, the design and control aspects of the UB Hand 3 anthropomorphic robotic hand are presented. In particular, the tendon-sheaths transmission system adopted in the UB Hand 3 is analyzed and the problem of force control and friction compensation is taken into account. The implementation of a tendon based antagonistic actuated robotic arm is then investigated. With this kind of actuation modality, and by using transmission elements with nonlinear force/compression characteristic, it is possible to achieve simultaneous stiffness and position control, improving in this way the safety of the device during the operation in unknown environments and in the case of interaction with other robots or with humans. The problem of modeling and control of this type of robotic devices is then considered and the stability analysis of proposed controller is reported. At the end, some tools for the realtime simulation of dynamic systems are presented. This realtime simulation environment has been developed with the aim of improving the reliability of the realtime control applications both for rapid prototyping of controllers and as teaching tools for the automatic control courses.

Path planning for image based visual servoing

This thesis deals with Visual Servoing and its strictly connected disciplines like projective geometry, image processing, robotics and non-linear control. More specifically the work addresses the problem to control a robotic manipulator through one of the largely used Visual Servoing techniques: the Image Based Visual Servoing (IBVS). In Image Based Visual Servoing the robot is driven by on-line performing a feedback control loop that is closed directly in the 2D space of the camera sensor. The work considers the case of a monocular system with the only camera mounted on the robot end effector (eye in hand configuration). Through IBVS the system can be positioned with respect to a 3D fixed target by minimizing the differences between its initial view and its goal view, corresponding respectively to the initial and the goal system configurations: the robot Cartesian Motion is thus generated only by means of visual informations. However, the execution of a positioning control task by IBVS is not straightforward because singularity problems may occur and local minima may be reached where the reached image is very close to the target one but the 3D positioning task is far from being fulfilled: this happens in particular for large camera displacements, when the the initial and the goal target views are noticeably different. To overcame singularity and local minima drawbacks, maintaining the good properties of IBVS robustness with respect to modeling and camera calibration errors, an opportune image path planning can be exploited. This work deals with the problem of generating opportune image plane trajectories for tracked points of the servoing control scheme (a trajectory is made of a path plus a time law). The generated image plane paths must be feasible i.e. they must be compliant with rigid body motion of the camera with respect to the object so as to avoid image jacobian singularities and local minima problems. In addition, the image planned trajectories must generate camera velocity screws which are smooth and within the allowed bounds of the robot. We will show that a scaled 3D motion planning algorithm can be devised in order to generate feasible image plane trajectories. Since the paths in the image are off-line generated it is also possible to tune the planning parameters so as to maintain the target inside the camera field of view even if, in some unfortunate cases, the feature target points would leave the camera images due to 3D robot motions. To test the validity of the proposed approach some both experiments and simulations results have been reported taking also into account the influence of noise in the path planning strategy. The experiments have been realized with a 6DOF anthropomorphic manipulator with a fire-wire camera installed on its end effector: the results demonstrate the good performances and the feasibility of the proposed approach.

The potential of the 3-UPU translational parallel manipulator and a procedure to select the best architecture

The 3-UPU three degrees of freedom fully parallel manipulator, where U and P are for universal and prismatic pair respectively, is a very well known manipulator that can provide the platform with three degrees of freedom of pure translation, pure rotation or mixed translation and rotation with respect to the base, according to the relative directions of the revolute pair axes (each universal pair comprises two revolute pairs with intersecting and perpendicular axes). In particular, pure translational parallel 3-UPU manipulators (3-UPU TPMs) received great attention. Many studies have been reported in the literature on singularities, workspace, and joint clearance influence on the platform accuracy of this manipulator. However, much work has still to be done to reveal all the features this topology can offer to the designer when different architecture, i.e. different geometry are considered. Therefore, this dissertation will focus on this type of the 3-UPU manipulators. The first part of the dissertation presents six new architectures of the 3-UPU TPMs which offer interesting features to the designer. In the second part, a procedure is presented which is based on some indexes, in order to allows the designer to select the best architecture of the 3-UPU TPMs for a given task. Four indexes are proposed as stiffness, clearance, singularity and size of the manipulator in order to apply the procedure.

Comportamento elastodinamico di meccanismi in catena chiusa bilanciati: analisi numerica e sperimentale di un quadrilatero articolato

The study presented in this work deals with the investigation of the effects produced by two common techniques of static balancing on the dynamic performances of closed-chain linkages, taking into account the compliance of the mechanism components. The long-term goal of the research consists in determining an optimal balancing strategy for parallel spatial manipulators. The present contribution is a starting point and it focuses on the planar four-bar linkage, intended as the simplest example of closed-chain mechanism. The elastodynamic behaviour of an unbalanced four-bar linkage and two balanced ones, respectively obtained by mass and elastic balancing, is investigated by means of both numerical simulations and experimental tests. The purpose of this work is to obtain preliminary results, to be refined and broadened in future developments

Design and Characterization of Curved and Spherical Flexure Hinges for Planar and Spatial Compliant Mechanisms

A flexure hinge is a flexible connector that can provide a limited rotational motion between two rigid parts by means of material deformation. These connectors can be used to substitute traditional kinematic pairs (like bearing couplings) in rigid-body mechanisms. When compared to their rigid-body counterpart, flexure hinges are characterized by reduced weight, absence of backlash and friction, part-count reduction, but restricted range of motion. There are several types of flexure hinges in the literature that have been studied and characterized for different applications. In our study, we have introduced new types of flexures with curved structures i.e. circularly curved-beam flexures and spherical flexures. These flexures have been utilized for both planar applications (e.g. articulated robotic fingers) and spatial applications (e.g. spherical compliant mechanisms). We have derived closed-form compliance equations for both circularly curved-beam flexures and spherical flexures. Each element of the spatial compliance matrix is analytically computed as a function of hinge dimensions and employed material. The theoretical model is then validated by comparing analytical data with the results obtained through Finite Element Analysis. A case study is also presented for each class of flexures, concerning the potential applications in the optimal design of planar and spatial compliant mechanisms. Each case study is followed by comparing the performance of these novel flexures with the performance of commonly used geometries in terms of principle compliance factors, parasitic motions and maximum stress demands. Furthermore, we have extended our study to the design and analysis of serial and parallel compliant mechanisms, where the proposed flexures have been employed to achieve spatial motions e.g. compliant spherical joints.

Kinematics and statics of cable-driven parallel robots by interval-analysis-based methods

In the past two decades the work of a growing portion of researchers in robotics focused on a particular group of machines, belonging to the family of parallel manipulators: the cable robots. Although these robots share several theoretical elements with the better known parallel robots, they still present completely (or partly) unsolved issues. In particular, the study of their kinematic, already a difficult subject for conventional parallel manipulators, is further complicated by the non-linear nature of cables, which can exert only efforts of pure traction. The work presented in this thesis therefore focuses on the study of the kinematics of these robots and on the development of numerical techniques able to address some of the problems related to it. Most of the work is focused on the development of an interval-analysis based procedure for the solution of the direct geometric problem of a generic cable manipulator. This technique, as well as allowing for a rapid solution of the problem, also guarantees the results obtained against rounding and elimination errors and can take into account any uncertainties in the model of the problem. The developed code has been tested with the help of a small manipulator whose realization is described in this dissertation together with the auxiliary work done during its design and simulation phases.