Presented in this paper is the kinematic analysis of a symmetrical three-degree-of-freedom planar parallel manipulator. In opposite to serial manipulators, parallel manipulators can admit not only multiple inverse kinematic solutions, but also multiple direct kinematic solutions. This property produces more complicated kinematic models but allows more flexibility in trajectory planning. To take into account this property, the notion of aspects, i.e. the maximal singularity-free domains, was introduced, based on the notion of working modes, which makes it possible to separate the inverse kinematic solutions. The aim of this paper is to show that a non-singular assembly-mode changing trajectory exist for a symmetrical planar parallel manipulator, with equilateral base and platform triangle.
A class of analytic planar 3-RPR manipulators is analyzed in this paper. These manipulators have congruent base and moving platforms and the moving platform is rotated of 180 deg about an axis in the plane. The forward kinematics is reduced to the solution of a 3rd-degree polynomial and a quadratic equation in sequence. The singularities are calculated and plotted in the joint space. The second-order singularities (cups points), which play an important role in non-singular change of assembly-mode motions, are also analyzed.
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）；McGill University（麦吉尔大学）
The subject of this paper is a special class of parallel manipulators. First, we analyze a family of three-degree-of-freedom manipulators. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. The singular configurations of these matrices are studied. The isotropic configurations are then studied based on the characteristic length of this manipulator. The isoconditioning loci of all Jacobian matrices are computed to define a global performance index to co…
This paper investigates two situations in which the forward kinematics of planar 3-RPR parallel manipulators degenerates. These situations have not been addressed before. The first degeneracy arises when the three input joint variables r1, r2 and r3 satisfy a certain relationship. This degeneracy yields a double root of the characteristic polynomial in t, which could be erroneously interpreted as two coalesce assembly modes. But, unlike what arises in non-degenerate cases, this double root yields two sets of solutions for the position coordinates (x, y) of the platform. In the second situation…
Institut de Recherche Mathématique de Rennes（雷恩数学研究所）；Université de Rennes I（雷恩第一大学）；Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
We study in this paper a class of 3-RPR manipulators for which the direct kinematic problem (DKP) is split into a cubic problem followed by a quadratic one. These manipulators are geometrically characterized by the fact that the moving triangle is the image of the base triangle by an indirect isometry. We introduce a specific coordinate system adapted to this geometric feature and which is also well adapted to the splitting of the DKP. This allows us to obtain easily precise descriptions of the singularities and of the cusp edges. These latter second order singularities are important for nonsi…
Optimal point-to-point trajectory planning for planar redundant manipulator is considered in this study. The main objective is to minimize the sum of the position error of the end-effector at each intermediate point along the trajectory so that the end-effector can track the prescribed trajectory accurately. An algorithm combining Genetic Algorithm and Pattern Search as a Generalized Pattern Search GPS is introduced to design the optimal trajectory. To verify the proposed algorithm, simulations for a 3-D-O-F planar manipulator with different end-effector trajectories have been carried out. A c…
The aim of this paper is the kinematic study of a 3-RPR planar parallel manipulator where the three fixed revolute joints are actuated. The direct and inverse kinematic problem as well as the singular configuration is characterized. On parallel singular configurations, the motion produce by the mobile platform can be compared to the Reuleaux straight-line mechanism.
Practical use of robotic manipulators made from soft materials requires generating and executing complex motions. We present the first approach for generating trajectories of a thermally-actuated soft robotic manipulator. Based on simplified approximations of the soft arm and its antagonistic shape-memory alloy actuator coils, we justify a dynamics model of a discretized rigid manipulator with joint torques proportional to wire temperature. Then, we propose a method to calibrate this model from experimental data and demonstrate that the simulation aligns well with a hardware test. Finally, we …
INRIA（法国国家信息与自动化研究所）；Institut de Recherche en Cybernétique de Nantes（南特控制论研究所）
The goal of this paper is to define the n-connected regions in the Cartesian workspace of fully-parallel manipulators, i.e. the maximal regions where it is possible to execute point-to-point motions. The manipulators considered in this study may have multiple direct and inverse kinematic solutions. The N-connected regions are characterized by projection, onto the Cartesian workspace, of the connected components of the reachable configuration space defined in the Cartesian product of the Cartesian space by the joint space. Generalized octree models are used for the construction of all spaces. T…
École Centrale de Nantes（南特中央理工学院）；Université de Nantes（南特大学）
This work investigates new kinematic features of parallel manipulators. It is well known that parallel manipulators admit generally several direct kinematic solutions for a given set of input joint values. The aim of this paper is to characterize the uniqueness domains in the workspace of parallel manipulators, as well as their image in the joint space. The study focuses on the most usual case of parallel manipulators with only one inverse kinematic solution. The notion of aspect introduced for serial manipulators in [Borrel 86] is redefined for such parallel manipulators. Then, it is shown th…
Institut de Recherche en Cybernétique de Nantes（南特控制论研究所）；École Centrale de Nantes（南特中央理工学院）
The aim of this paper is to characterize the notion of aspect in the workspace and in the joint space for parallel manipulators. In opposite to the serial manipulators, the parallel manipulators can admit not only multiple inverse kinematic solutions, but also multiple direct kinematic solutions. The notion of aspect introduced for serial manipulators in [Borrel 86], and redefined for parallel manipulators with only one inverse kinematic solution in [Wenger 1997], is redefined for general fully parallel manipulators. Two Jacobian matrices appear in the kinematic relations between the joint-rat…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
This paper investigates the singular curves in two-dimensional slices of the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it reviews an important previous work, which, to the authors' knowledge, has never been exploited yet. Second, it determines the cusp points in any two-dimensional slice of the jo…
Institut de Recherche en Cybernétique de Nantes（南特控制论研究所）；École Centrale de Nantes（南特中央理工学院）；McGill University（麦吉尔大学）
The subject of this paper is a special class of closed-chain manipulators. First, we analyze a family of two-degree-of-freedom (dof) five-bar planar linkages. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the ``inverse kinematics" and the "direct kinematics" matrices. It is shown that the loci of points of the workspace where the condition number of the direct-kinematics matrix remains constant, i.e., the isoconditioning loci, are the coupler points of the four-bar linkage obtained upon locking the middle joi…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
Recursive modelling for the kinematics of a 3-PRP planar parallel robot is presented in this paper. Three planar chains connecting to the moving platform of the manipulator are located in a vertical plane. Knowing the motion of the platform, we develop the inverse kinematics and determine the positions, velocities and accelerations of the robot. Several matrix equations offer iterative expressions and graphs for the displacements, velocities and accelerations of three prismatic actuators.
Admittance-Based Motion Planning with Vision-Guided Initialization for Robotic Manipulators in Self-Driving Laboratories
Department of Electronics Systems, Aalborg University（电子系统系，奥尔堡大学）；Department of Information Technology and Electrical Engineering, Università degli Studi di Napoli Federico II（信息科技与电气工程系，那不勒斯费迪里奇二世大学）
We study parametric equations, which describe the position of an in-parallel planar manipulator. We discuss isometries in the Gauss plane, then we write the loop-closure equations in terms of the rotations as the parameters.
Ecole des Mines de Nantes（南特矿业学院）；Institut de Recherches en Communications et en Cybernetique de Nantes（南特通信与网络研究所）
The paper presents a novel technique for the design of optimal calibration experiments for a planar anthropomorphic manipulator with n degrees of freedom. Proposed approach for selection of manipulator configurations allows essentially improving calibration accuracy and reducing parameter identification errors. The results are illustrated by application examples that deal with typical anthropomorphic manipulators.
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）；McGill University（麦吉尔大学）
Proposed in this paper is a kinetostatic performance index for the optimum dimensioning of planar manipulators of the serial type. The index is based on the concept of distance of the underlying Jacobian matrix to a given isotropic matrix that is used as a reference model for purposes of performance evaluation. Applications of the index fall in the realm of design, but control applications are outlined. The paper focuses on planar manipulators, the basic concepts being currently extended to their three-dimensional counterparts.
IRCCyN, Institut de recherche en communications et cybernéthique de Nantes（南特通信与控制研究所（IRCCyN））
In this paper, a method to compute joint space singularity surfaces of 3-RPR planar parallel manipulators is first presented. Then, a procedure to determine maximal joint space singularity-free boxes is introduced. Numerical examples are given in order to illustrate graphically the results. This study is of high interest for planning trajectories in the joint space of 3-RPR parallel manipulators and for manipulators design as it may constitute a tool for choosing appropriate joint limits and thus for sizing the link lengths of the manipulator.
McGill University（麦吉尔大学）；INRIA Rocquencourt（法国国家信息与自动化研究所罗克库尔分部）；Centre for Intelligent Machines（智能机器中心）
The paper discusses the kinematics of manipulators builts of planar closed kinematic chains. A special kinematic scheme is extracted from the array of these mechanisms that looks the most promising for the creation of different types of robotic manipulators. The structural features of this manipulator determine a number of its original properties that essentially simplify its control. These features allow the main control problems to be effectively overcome by application of the simple kinematic problems. The workspace and singular configurations of a basic planar manipulator are studied. By u…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）；CNRS（法国国家科学研究中心）
This paper deals with the comparison of planar parallel manipulator architectures based on a multi-objective design optimization approach. The manipulator architectures are compared with regard to their mass in motion and their regular workspace size, i.e., the objective functions. The optimization problem is subject to constraints on the manipulator dexterity and stiffness. For a given external wrench, the displacements of the moving platform have to be smaller than given values throughout the obtained maximum regular dexterous workspace. The contributions of the paper are highlighted with th…
Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）；Innopolis University（因诺波利斯大学）；IMT Atlantique Nantes（大西洋矿业电信学院南特校区）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The paper focuses on the stiffness analysis of multi-link serial planar manipulators, which may demonstrate nonlinear stiffness behavior under the compressive loading. Two important cases are considered, where the manipulator has either a straight or non-straight initial configuration. It was proved that in the first case the loading may cause the buckling if it exceeds some critical value, and the manipulator suddenly changes its straight shape and stiffness properties. For computing this critical force, a general eigenvalue-based technique was proposed that can be applied to any multi-link s…
L'Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), École Central de Nantes（南特通信与控制研究所，南特中央学院）
Cusps and nodes on plane sections of the singularity locus in the joint space of parallel manipulators play an important role in nonsingular assembly-mode changing motions. This paper analyses in detail such points, both in the joint space and in the workspace. It is shown that a cusp (resp. a node) defines a point of tangency (resp. a crossing point) in the workspace between the singular curves and the curves associated with the so-called characteristics surfaces. The study is conducted on a planar 3-RPR manipulator for illustrative purposes.
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）；McGill University（麦吉尔大学）
The subject of this paper is a special class of three-degree-of-freedom parallel manipulators. The singular configurations of the two Jacobian matrices are first studied. The isotropic configurations are then found based on the characteristic length of this manipulator. The isoconditioning loci for the Jacobian matrices are plotted to define a global performance index allowing the comparison of the different working modes. The index thus resulting is compared with the Cartesian workspace surface and the average of the condition number.
Institut de Robòtica i Informàtica Industrial, CSIC - UPC（工业机器人与信息学研究所，西班牙国家研究委员会-加泰罗尼亚理工大学）；INRIA Nancy-Grand Est（法国国家信息与自动化研究所南锡-大东部研究中心）；Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制论研究所）；INRIA Paris-Rocquencourt（法国国家信息与自动化研究所巴黎-罗克库尔研究中心）；Université Pierre et Marie Curie Paris VI（巴黎第六大学皮埃尔和玛丽·居里大学）
This paper investigates the conditions in the design parameter space for the existence and distribution of the cusp locus for planar parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which increases the maximum singularity-free workspace. An accurate algorithm for the determination is proposed amending some imprecisions done by previous existing algorithms. This is combined with methods of Cylindric Algebraic Decomposition, Gröbner bases and Discriminant Varieties in order to partition the parameter space into cells with constant number of cusp points…
We study determining the posture of an in-parallel planar manipulator, which has three connectors composed of revolute, prismatic and revolute joints, from specified active joint variables. We construct an ideal in the field of complex numbers, and we introduce self inversive polynomials. We provide results for an in-parallel planar manipulator, which has a base and moving platform in right triangular shape. Using Sage computer algebra system, we compute its Groebner bases. We illustrate that the single variable polynomials obtained from the Groebner bases are self reciprocal.
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
This paper investigates the singular curves in the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it exposes a method to compute joint space singular curves of 3-RPR planar parallel manipulators. Second, it presents an algorithm for detecting and computing all cusp points in the joint space of these sa…
Socially-aware Object Transportation by a Mobile Manipulator in Static Planar Environments with Obstacles
Computer Vision and Robotics Laboratory (VeRLab), Department of Computer Science, Universidade Federal de Minas Gerais（计算机视觉与机器人实验室（VeRLab）、计算机科学系、巴西矿务大学）
This paper presents the accessibility and small-time local controllability (STLC) results for $N$-link horizontal planar manipulators with only one unactuated joint. STLC is important in controls, both for design considerations and because large and swinging maneuvers may be avoided for close reconfiguration if a system is STLC. Despite the fact that controllability of underactuated horizontal planar manipulators has been extensively studied, most work focused only on three-link and global controllability. This paper thus has two contributions: 1) using Lie brackets to study the accessibility …
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Halmstad University（哈尔姆斯塔德大学）
We release two artificial datasets, Simulated Flying Shapes and Simulated Planar Manipulator that allow to test the learning ability of video processing systems. In particular, the dataset is meant as a tool which allows to easily assess the sanity of deep neural network models that aim to encode, reconstruct or predict video frame sequences. The datasets each consist of 90000 videos. The Simulated Flying Shapes dataset comprises scenes showing two objects of equal shape (rectangle, triangle and circle) and size in which one object approaches its counterpart. The Simulated Planar Manipulator s…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
This paper presents an algorithm for detecting and computing the cusp points in the joint space of 3-RPR planar parallel manipulators. In manipulator kinematics, cusp points are special points, which appear on the singular curves of the manipulators. The nonsingular change of assembly mode of 3-RPR parallel manipulators was shown to be associated with the existence of cusp points. At each of these points, three direct kinematic solutions coincide. In the literature, a condition for the existence of three coincident direct kinematic solutions was established, but has never been exploited, becau…
Institut de Recherche en Cybernétique de Nantes（南特控制论研究所）；École Centrale de Nantes（南特中央理工学院）；Université de Nantes（南特大学）
The aim of this paper is to characterize the uniqueness domains in the workspace of parallel manipulators, as well as their image in the joint space. The notion of aspect introduced for serial manipulators in [Borrel 86] is redefined for such parallel manipulators. Then, it is shown that it is possible to link several solutions to the direct kinematic problem without meeting a singularity, thus meaning that the aspects are not uniqueness domains. Additional surfaces are characterized in the workspace which yield new uniqueness domains. An octree model of spaces is used to compute the joint spa…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制论研究所）
The aim of this paper is to compute of the generalized aspects, i.e. the maximal singularity-free domains in the Cartesian product of the joint space and workspace, for a planar parallel mechanism in using quadtree model and interval analysis based method. The parallel mechanisms can admit several solutions to the inverses and the direct kinematic models. These singular configurations divide the joint space and the workspace in several not connected domains. To compute this domains, the quadtree model can be made by using a discretization of the space. Unfortunately, with this method, some sin…
Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague（布拉格捷克理工大学电气工程学院控制论系）；Czech Institute of Informatics, Robotics, and Cybernetics, Czech Technical University in Prague（布拉格捷克理工大学捷克信息学、机器人学与控制论研究所）
We present a robot kinematic calibration method that combines complementary calibration approaches: self-contact, planar constraints, and self-observation. We analyze the estimation of the end effector parameters, joint offsets of the manipulators, and calibration of the complete kinematic chain (DH parameters). The results are compared with ground truth measurements provided by a laser tracker. Our main findings are: (1) When applying the complementary calibration approaches in isolation, the self-contact approach yields the best and most stable results. (2) All combinations of more than one …
Institut de Recherche en Cybernétique de Nantes (IRCyN)（南特控制论研究所）；McGill University（麦吉尔大学）
This paper focuses on the kinematic properties of a new three-degree-of-freedom hybrid manipulator. This manipulator is obtained by adding in series to a five-bar planar mechanism (similar to the one studied by Bajpai and Roth) a third revolute passing through the line of centers of the two actuated revolute joints of the above linkage. The resulting architecture is hybrid in that it has both serial and parallel links. Fully-parallel manipulators are known for the existence of particularly undesirable singularities (referred to as parallel singularities) where control is lost [4] and [6]. On t…
A resolved acceleration control (RAC) and proportional-integral active force control (PIAFC) is proposed as an approach for the robust motion control of a mobile manipulator (MM) comprising a differentially driven wheeled mobile platform with a two-link planar arm mounted on top of the platform. The study emphasizes on the integrated kinematic and dynamic control strategy in which the RAC is used to manipulate the kinematic component while the PIAFC is implemented to compensate the dynamic effects including the bounded known/unknown disturbances and uncertainties. The effectivenss and robustne…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
When moving from one arbitrary location at another, a parallel manipulator may change its assembly-mode without crossing a singularity. Because the non-singular change of assembly-mode cannot be simply detected, the actual assembly-mode during motion is difficult to track. This paper proposes a global explanatory approach to help better understand non-singular assembly-mode changing motions for 3-RPR planar parallel manipulators. The approach consists in fixing one of the actuated joints and analyzing the configuration-space as a surface in a 3-dimensional space. Such a global description make…
MineRobot: An Actuator-Centered Kinematic Modeling and Solving Framework for Underground Mining Robots
College of Computer Science and Engineering, Shandong University of Science and Technology（山东科技大学计算机科学与工程学院）；Shandong Lionking Software Co., Ltd.（山东狮王软件有限公司）；College of Intelligent Equipment, Shandong University of Science and Technology（山东科技大学智能装备学院）
This paper presents modeling of a compliant 2D manipulator, a so called soft hydraulic/fluidic elastomer actuator. Our focus is on fiber-Reinforced Fluidic Elastomer Actuators (RFEA) driven by a constant pressure hydraulic supply and modulated on/off valves. We present a model that not only provides the dynamics behavior of the system but also the kinematics of the actuator. In addition to that, the relation between the applied hydraulic pressure and the bending angle of the soft actuator and thus, its tip position is formulated in a systematic way. We also present a steady state model that ca…
CNRS（法国国家科学研究中心）；University of the West of Scotland（西苏格兰大学）
This article presents a new variable actuation mechanism based on the 3-RPR parallel robot. This mechanismis an evolution of the NaVARo robot, a 3-RRR parallel robot, for which the second revolute joint of the threelegs is replaced by a scissor to obtain a larger working space and avoid the use of parallelograms to operate thesecond revolute joint. To obtain better spatial rigidity, the leg mechanism is constructed by placing the scissorsin an orthogonal plane to the plane of the manipulator displacement (3-RRR or even the 3-RPR). This geometricproperty brings the significant consequence of al…
