Dynamics of undeactuated cable-driven parallel robots

This thesis focuses on the dynamics of underactuated cable-driven parallel robots (UACDPRs), including various aspects of robotic theory and practice, such as workspace computation, parameter identification, and trajectory planning. After a brief introduction to CDPRs, UACDPR kinematic and dynamic models are analyzed, under the relevant assumption of inextensible cables. The free oscillatory motion of the end-effector (EE), which is a unique feature of underactuated mechanisms, is studied in detail, from both a kinematic and a dynamic perspective. The free (small) oscillations of the EE around equilibria are proved to be harmonic and the corresponding natural oscillation frequencies are analytically computed. UACDPR workspace computation and analysis are then performed. A new performance index is proposed for the analysis of the influence of actuator errors on cable tensions around equilibrium configurations, and a new type of workspace, called tension-error-insensitive, is defined as the set of poses that a UACDPR EE can statically attain even in presence of actuation errors, while preserving tensions between assigned (positive) bounds. EE free oscillations are then employed to conceive a novel procedure aimed at identifying the EE inertial parameters. This approach does not require the use of force or torque measurements. Moreover, a self-calibration procedure for the experimental determination of UACDPR initial cable lengths is developed, which consequently enables the robot to automatically infer the EE initial pose at machine start-up. Lastly, trajectory planning of UACDPRs is investigated. Two alternative methods are proposed, which aim at (i) reducing EE oscillations even when model parameters are uncertain or (ii) eliminate EE oscillations in case model parameters are perfectly known. EE oscillations are reduced in real-time by dynamically scaling a nominal trajectory and filtering it with an input shaper, whereas they can be eliminated if an off-line trajectory is computed that accounts for the system internal dynamics.

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.

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.

High performance and energy-efficient instruction cache design and optimisation for ultra-low-power multi-core clusters

High Energy efficiency and high performance are the key regiments for Internet of Things (IoT) end-nodes. Exploiting cluster of multiple programmable processors has recently emerged as a suitable solution to address this challenge. However, one of the main bottlenecks for multi-core architectures is the instruction cache. While private caches fall into data replication and wasting area, fully shared caches lack scalability and form a bottleneck for the operating frequency. Hence we propose a hybrid solution where a larger shared cache (L1.5) is shared by multiple cores connected through a low-latency interconnect to small private caches (L1). However, it is still limited by large capacity miss with a small L1. Thus, we propose a sequential prefetch from L1 to L1.5 to improve the performance with little area overhead. Moreover, to cut the critical path for better timing, we optimized the core instruction fetch stage with non-blocking transfer by adopting a 4 x 32-bit ring buffer FIFO and adding a pipeline for the conditional branch. We present a detailed comparison of different instruction cache architectures' performance and energy efficiency recently proposed for Parallel Ultra-Low-Power clusters. On average, when executing a set of real-life IoT applications, our two-level cache improves the performance by up to 20% and loses 7% energy efficiency with respect to the private cache. Compared to a shared cache system, it improves performance by up to 17% and keeps the same energy efficiency. In the end, up to 20% timing (maximum frequency) improvement and software control enable the two-level instruction cache with prefetch adapt to various battery-powered usage cases to balance high performance and energy efficiency.

Mechanical design and hybrid control strategies for overconstrained cable-driven parallel robots

Cable-driven parallel robots offer significant advantages in terms of workspace dimensions and payload capability. They are attractive for many industrial tasks to be performed on a large scale, such as handling and manufacturing, without a substantial increase in costs and mechanical complexity with respect to a small-scale application. However, since cables can only sustain tensile stresses, cable tensions must be kept within positive limits during the end-effector motion. This problem can be managed by overconstraining the end-effector and controlling cable tensions. Tension control is typically achieved by mounting a load sensor on all cables, and using specific control algorithms to avoid cable slackness or breakage while the end-effector is controlled in a desired position. These algorithms require multiple cascade control loops and they can be complex and computationally demanding. To simplify the control of overconstrained cable-driven parallel robots, this Thesis proposes suitable mechanical design and hybrid control strategies. It is shown how a convenient design of the cable guidance system allows kinematic modeling to be simplified, without introducing geometric approximations. This guidance system employs swiveling pulleys equipped with position and tension sensors and provides a parallelogram arrangement of cables. Furthermore, a hybrid force/position control in the robot joint space is adopted. According to this strategy, a particular set of cables is chosen to be tension-controlled, whereas the other cables are length-controlled. The force-controlled cables are selected based on the computation of a novel index called force-distribution sensitivity to cable-tension errors. This index aims to evaluate the maximum expected cable-tension error in the length-controlled cables if a unit tension error is committed in the force-controlled cables. In practice, the computation of the force-distribution sensitivity allows determining which cables are best to be force-controlled, to ensure the lowest error in the overall force distribution when a hybrid force/position joint-space strategy is used.

Contributions to the performance analysis of continuum parallel robots

Continuum parallel robots (CPRs) are manipulators employing multiple flexible beams arranged in parallel and connected to a rigid end-effector. CPRs promise higher payload and accuracy than serial CRs while keeping great flexibility. As the risk of injury during accidental contacts between a human and a CPR should be reduced, CPRs may be used in large-scale collaborative tasks or assisted robotic surgery. There exist various CPR designs, but the prototype conception is rarely based on performance considerations, and the CPRs realization in mainly based on intuitions or rigid-link parallel manipulators architectures. This thesis focuses on the performance analysis of CPRs, and the tools needed for such evaluation, such as workspace computation algorithms. In particular, workspace computation strategies for CPRs are essential for the performance assessment, since the CPRs workspace may be used as a performance index or it can serve for optimal-design tools. Two new workspace computation algorithms are proposed in this manuscript, the former focusing on the workspace volume computation and the certification of its numerical results, while the latter aims at computing the workspace boundary only. Due to the elastic nature of CPRs, a key performance indicator for these robots is the stability of their equilibrium configurations. This thesis proposes the experimental validation of the equilibrium stability assessment on a real prototype, demonstrating limitations of some commonly used assumptions. Additionally, a performance index measuring the distance to instability is originally proposed in this manuscript. Differently from the majority of the existing approaches, the clear advantage of the proposed index is a sound physical meaning; accordingly, the index can be used for a more straightforward performance quantification, and to derive robot specifications.

Grant-free protocols for massive multiple access

In next generation Internet-of-Things, the overhead introduced by grant-based multiple access protocols may engulf the access network as a consequence of the proliferation of connected devices. Grant-free access protocols are therefore gaining an increasing interest to support massive multiple access. In addition to scalability requirements, new demands have emerged for massive multiple access, including latency and reliability. The challenges envisaged for future wireless communication networks, particularly in the context of massive access, include: i) a very large population size of low power devices transmitting short packets; ii) an ever-increasing scalability requirement; iii) a mild fixed maximum latency requirement; iv) a non-trivial requirement on reliability. To this aim, we suggest the joint utilization of grant-free access protocols, massive MIMO at the base station side, framed schemes to let the contention start and end within a frame, and succesive interference cancellation techniques at the base station side. In essence, this approach is encapsulated in the concept of coded random access with massive MIMO processing. These schemes can be explored from various angles, spanning the protocol stack from the physical (PHY) to the medium access control (MAC) layer. In this thesis, we delve into both of these layers, examining topics ranging from symbol-level signal processing to succesive interference cancellation-based scheduling strategies. In parallel with proposing new schemes, our work includes a theoretical analysis aimed at providing valuable system design guidelines. As a main theoretical outcome, we propose a novel joint PHY and MAC layer design based on density evolution on sparse graphs.

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.

Energy consumption of parallel algorithms for solving linear systems on HPC architecture

Modern High-Performance Computing HPC systems are gradually increasing in size and complexity due to the correspondent demand of larger simulations requiring more complicated tasks and higher accuracy. However, as side effects of the Dennard’s scaling approaching its ultimate power limit, the efficiency of software plays also an important role in increasing the overall performance of a computation. Tools to measure application performance in these increasingly complex environments provide insights into the intricate ways in which software and hardware interact. The monitoring of the power consumption in order to save energy is possible through processors interfaces like Intel Running Average Power Limit RAPL. Given the low level of these interfaces, they are often paired with an application-level tool like Performance Application Programming Interface PAPI. Since several problems in many heterogeneous fields can be represented as a complex linear system, an optimized and scalable linear system solver algorithm can decrease significantly the time spent to compute its resolution. One of the most widely used algorithms deployed for the resolution of large simulation is the Gaussian Elimination, which has its most popular implementation for HPC systems in the Scalable Linear Algebra PACKage ScaLAPACK library. However, another relevant algorithm, which is increasing in popularity in the academic field, is the Inhibition Method. This thesis compares the energy consumption of the Inhibition Method and Gaussian Elimination from ScaLAPACK to profile their execution during the resolution of linear systems above the HPC architecture offered by CINECA. Moreover, it also collates the energy and power values for different ranks, nodes, and sockets configurations. The monitoring tools employed to track the energy consumption of these algorithms are PAPI and RAPL, that will be integrated with the parallel execution of the algorithms managed with the Message Passing Interface MPI.