Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot configuration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the final configuration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex field, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efficient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to find a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed.

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.

Dimensional synthesis of a spherical parallel manipulator based on the evaluation of global performance indexes

In this work, the dimensional synthesis of a spherical Parallel Manipulator (PM) with a -1S kinematic chain is presented. The goal of the synthesis is to find a set of parameters that defines the PM with the best performance in terms of workspace capabilities, dexterity and isotropy. The PM is parametrized in terms of a reference element, and a non-directed search of these parameters is carried out. First, the inverse kinematics and instantaneous kinematics of the mechanism are presented. The latter is found using the screw theory formulation. An algorithm that explores a bounded set of parameters and determines the corresponding value of global indexes is presented. The concepts of a novel global performance index and a compound index are introduced. Simulation results are shown and discussed. The best PMs found in terms of each performance index evaluated are locally analyzed in terms of its workspace and local dexterity. The relationship between the performance of the PM and its parameters is discussed, and a prototype with the best performance in terms of the compound index is presented and analyzed.

Force sensor of a climbing robot derived from its own flexible structure

One of the most important design constraints of a climbing robot is its own weight. When links or legs are used as a locomotion system they tend to be composed of special lightweight materials, or four-bars-linkage mechanisms are designed to reduce the weight with small rigidity looses. In these cases, flexibility appears and undesirable effects, such as dynamics vibrations, must be avoided at least when the robot moves at low speeds. The knowledge of the real tip position requires the computation of its compliance or stiffness matrix and the external forces applied to the structure. Gravitational forces can be estimated, but external tip forces need to be measured. This paper proposes a strain gauge system which achieves the following tasks: (i) measurement of the external tip forces, and (ii) estimation of the real tip position (including flexibility effects). The main advantages of the proposed system are: (a) the use of external force sensors is avoided, and (b) a substantial reduction of the robot weight is achieved in comparison with other external force measurement systems. The proposed method is applied to a real symmetric climbing robot and experimental results are presented.

Design, development and control of a new generation high performance linear actuator for parallel robots and other applications

The main focus of this research is to design and develop a high performance linear actuator based on a four bar mechanism. The present work includes the detailed analysis (kinematics and dynamics), design, implementation and experimental validation of the newly designed actuator. High performance is characterized by the acceleration of the actuator end effector. The principle of the newly designed actuator is to network the four bar rhombus configuration (where some bars are extended to form an X shape) to attain high acceleration. Firstly, a detailed kinematic analysis of the actuator is presented and kinematic performance is evaluated through MATLAB simulations. A dynamic equation of the actuator is achieved by using the Lagrangian dynamic formulation. A SIMULINK control model of the actuator is developed using the dynamic equation. In addition, Bond Graph methodology is presented for the dynamic simulation. The Bond Graph model comprises individual component modeling of the actuator along with control. Required torque was simulated using the Bond Graph model. Results indicate that, high acceleration (around 20g) can be achieved with modest (3 N-m or less) torque input. A practical prototype of the actuator is designed using SOLIDWORKS and then produced to verify the proof of concept. The design goal was to achieve the peak acceleration of more than 10g at the middle point of the travel length, when the end effector travels the stroke length (around 1 m). The actuator is primarily designed to operate in standalone condition and later to use it in the 3RPR parallel robot. A DC motor is used to operate the actuator. A quadrature encoder is attached with the DC motor to control the end effector. The associated control scheme of the actuator is analyzed and integrated with the physical prototype. From standalone experimentation of the actuator, around 17g acceleration was achieved by the end effector (stroke length was 0.2m to 0.78m). Results indicate that the developed dynamic model results are in good agreement. Finally, a Design of Experiment (DOE) based statistical approach is also introduced to identify the parametric combination that yields the greatest performance. Data are collected by using the Bond Graph model. This approach is helpful in designing the actuator without much complexity.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

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.

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.

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.

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.

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Some factors complicate comparisons between linkage maps from different studies. This problem can be resolved if measures of precision, such as confidence intervals and frequency distributions, are associated with markers. We examined the precision of distances and ordering of microsatellite markers in the consensus linkage maps of chromosomes 1, 3 and 4 from two F 2 reciprocal Brazilian chicken populations, using bootstrap sampling. Single and consensus maps were constructed. The consensus map was compared with the International Consensus Linkage Map and with the whole genome sequence. Some loci showed segregation distortion and missing data, but this did not affect the analyses negatively. Several inversions and position shifts were detected, based on 95% confidence intervals and frequency distributions of loci. Some discrepancies in distances between loci and in ordering were due to chance, whereas others could be attributed to other effects, including reciprocal crosses, sampling error of the founder animals from the two populations, F(2) population structure, number of and distance between microsatellite markers, number of informative meioses, loci segregation patterns, and sex. In the Brazilian consensus GGA1, locus LEI1038 was in a position closer to the true genome sequence than in the International Consensus Map, whereas for GGA3 and GGA4, no such differences were found. Extending these analyses to the remaining chromosomes should facilitate comparisons and the integration of several available genetic maps, allowing meta-analyses for map construction and quantitative trait loci (QTL) mapping. The precision of the estimates of QTL positions and their effects would be increased with such information.

Status of Early 19th-Century Names Authored in Parallel by Wied and Schinz for South American Reptiles and Amphibians, with Designations of Three Nomina Protecta

Prince Maximilian zu Wied's great exploration of coastal Brazil in 1815-1817 resulted in important collections of reptiles, amphibians, birds, and mammals, many of which were new species later described by Wied himself The bulk of his collection was purchased for the American Museum of Natural History in 1869, although many ""type specimens"" had disappeared earlier. Wied carefully identified his localities but did not designate type specimens or type localities, which are taxonomic concepts that were not yet established. Information and manuscript names on a fraction (17 species) of his Brazilian reptiles and amphibians were transmitted by Wied to Prof. Heinrich Rudolf Schinz at the University of Zurich. Schinz included these species (credited to their discoverer ""Princ. Max."") in the second volume of Das Thierreich ... (1822). Most are junior objective synonyms of names published by Wied. However, six of the 17 names used by Schinz predate Wied's own publications. Three were manuscript names never published by Wied because he determined the species to be previously known. (1) Lacerta vittata Schinz, 1822 (a nomen oblitum) = Lacerta striata sensu Wied (a misidentification, non Linnaeus nec sensu Merrem) = Kentropyx calcarata Spix, 1825, herein qualified as a nomen protectum. (2) Polychrus virescens Schinz, 1822 = Lacerta marmorata Linnaeus, 1758 (now Polychrus marmoratus). (3) Scincus cyanurus Schinz, 1822 (a nomen oblitum) = Gymnophthalmus quadrilineatus sensu Wied (a misidentification, non Linnaeus nec sensu Merrem) = Micrablepharus maximiliani (Reinhardt and Lutken, ""1861"" [1862]), herein qualified as a nomen protectum. Qualifying Scincus cyanurus Schinz, 1822, as a nomen oblitum also removes the problem of homonymy with the later-named Pacific skink Scincus cyanurus Lesson (= Emoia cyanura). The remaining three names used by Schinz are senior objective synonyms that take priority over Wied's names. (4) Bufo cinctus Schinz, 1822, is senior to Bufo cinctus Wied, 1823; both, however, are junior synonyms of Bufo crucifer Wied, 1821 = Chaunus crucifer (Wied). (5) Agama picta Schinz, 1822, is senior to Agama picta Wied, 1823, requiring a change of authorship for this poorly known species, to be known as Enyalius pictus (Schinz). (6) Lacerta cyanomelas Schinz, 1822, predates Teius cyanomelas Wied, 1824 (1822-1831) both nomina oblita. Wied's illustration and description shows cyanomelas as apparently conspecific with the recently described but already well-known Cnemidophorus nativo Rocha et al., 1997, which is the valid name because of its qualification herein as a nomen protectum. The preceding specific name cyanomelas (as corrected in an errata section) is misspelled several ways in different copies of Schinz's original description (""cyanom las,"" ""cyanomlas,"" and cyanom""). Loosening, separation, and final loss of the last three letters of movable type in the printing chase probably accounts for the variant misspellings.

Single-nucleotide polymorphism, linkage disequilibrium and geographic structure in the malaria parasite Plasmodium vivax: prospects for genome-wide association studies

Background: The ideal malaria parasite populations for initial mapping of genomic regions contributing to phenotypes such as drug resistance and virulence, through genome-wide association studies, are those with high genetic diversity, allowing for numerous informative markers, and rare meiotic recombination, allowing for strong linkage disequilibrium (LD) between markers and phenotype-determining loci. However, levels of genetic diversity and LD in field populations of the major human malaria parasite P. vivax remain little characterized. Results: We examined single-nucleotide polymorphisms (SNPs) and LD patterns across a 100-kb chromosome segment of P. vivax in 238 field isolates from areas of low to moderate malaria endemicity in South America and Asia, where LD tends to be more extensive than in holoendemic populations, and in two monkey-adapted strains (Salvador-I, from El Salvador, and Belem, from Brazil). We found varying levels of SNP diversity and LD across populations, with the highest diversity and strongest LD in the area of lowest malaria transmission. We found several clusters of contiguous markers with rare meiotic recombination and characterized a relatively conserved haplotype structure among populations, suggesting the existence of recombination hotspots in the genome region analyzed. Both silent and nonsynonymous SNPs revealed substantial between-population differentiation, which accounted for similar to 40% of the overall genetic diversity observed. Although parasites clustered according to their continental origin, we found evidence for substructure within the Brazilian population of P. vivax. We also explored between-population differentiation patterns revealed by loci putatively affected by natural selection and found marked geographic variation in frequencies of nucleotide substitutions at the pvmdr-1 locus, putatively associated with drug resistance. Conclusion: These findings support the feasibility of genome-wide association studies in carefully selected populations of P. vivax, using relatively low densities of markers, but underscore the risk of false positives caused by population structure at both local and regional levels.

Harmonic identification using parallel neural networks in single-phase systems

In this paper, artificial neural networks are employed in a novel approach to identify harmonic components of single-phase nonlinear load currents, whose amplitude and phase angle are subject to unpredictable changes, even in steady-state. The first six harmonic current components are identified through the variation analysis of waveform characteristics. The effectiveness of this method is tested by applying it to the model of a single-phase active power filter, dedicated to the selective compensation of harmonic current drained by an AC controller. Simulation and experimental results are presented to validate the proposed approach. (C) 2010 Elsevier B. V. All rights reserved.