Cuspidal robots can travel from one inverse kinematic solution to another without meeting a singularity. The name cuspidal was coined based on the existence of a cusp point in the workspace of 3R serial robots. The existence of a cusp point was proved to be a necessary and sufficient condition for orthogonal robots to be cuspidal, but it was not possible to extend this condition to non-orthogonal robots. The goal of this paper is to prove that this condition stands for any generic 3R robot. This result would give the designer more flexibility. In the presented work, the geometrical interpretation of the inverse kinematics of 3R robots is revisited and important observations on the nonsingular change of posture are noted. The paper presents a theorem regarding the existence of reduced aspects in any generic 3R serial robot. Based on these observations and on this theorem, we prove that the existence of a cusp point is a necessary and sufficient condition for any 3R generic robot to be cuspidal.
IMT Atlantique Bretagne Pays de la Loire（大西洋布列塔尼卢瓦尔河国家高等矿业电信学校）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The paper focuses on the redundancy resolution in kinematic control of a new type of serial manipulator composed of multiple tensegrity segments, which are moving in a multi-obstacle environment. The general problem is decomposed into two sub-problems, which deal with collision-free path planning for the robot end-effector and collision-free motion planning for the robot body. The first of them is solved via discrete dynamic programming, the second one is worked out using quadratic programming with mixed linear equality/nonequality constraints. Efficiency of the proposed technique is confirmed…
Kent Artificial Intelligence Laboratory（肯特人工智能实验室）
Apart from solving complicated problems that require a certain level of intelligence, fine-tuned deep neural networks can also create fast algorithms for slow, numerical tasks. In this paper, we introduce an improved version of [1]'s work, a fast, deep-learning framework capable of generating the full workspace of serial-link manipulators. The architecture consists of two neural networks: an estimation net that approximates the manipulator Jacobian, and a confidence net that measures the confidence of the approximation. We also introduce M3 (Manipulability Maps of Manipulators), a MATLAB robot…
This paper presents a kinematic definition of a serialized Stewart platform designed for autonomous in-space assembly called an Assembler. The Assemblers architecture describes problems inherent to the inverse kinematics of over-actuated mixed kinematic systems. This paper also presents a methodology for optimizing poses. In order to accomplish this with the Assembler system, an algorithm for finding a feasible solution to its inverse kinematics was developed with a wrapper for a nonlinear optimization algorithm designed to minimize the magnitude of forces incurred by each actuator. A simulate…
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…
Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；Queensland University of Technology（昆士兰科技大学）
The elementary transform sequence (ETS) provides a universal method of describing the kinematics of any serial-link manipulator. The ETS notation is intuitive and easy to understand, while avoiding the complexity and limitations of Denvit-Hartenberg frame assignment. In this paper, we describe a systematic method for computing the manipulator Jacobian and Hessian (differential kinematics) using the ETS notation. Differential kinematics have many applications including numerical inverse kinematics, resolved-rate motion control and manipulability motion control. Furthermore, we provide an open-s…
Singularity Avoidance with Application to Online Trajectory Optimization for Serial Manipulators
Automation and Control Institute (ACIN), TU Wien（维也纳工业大学自动化与控制研究所（ACIN））；Center for Vision, Automation and Control, AIT Austrian Institute of Technology（奥地利技术研究所（AIT）视觉、自动化与控制中心）
Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to six-degree-of-freedom robots can be a challenging problem. Many robots can be modeled as a polynomial map together with a real algebraic set so that the notion of cuspidality can be extended to these data. In this paper we design an algorithm that, on input a polynomial map in $n$ indeterminates, and $s$ polynomials in the same indeterminates describing a real algebraic s…
To continuously generate trajectories for serial manipulators with high dimensional degrees of freedom (DOF) in the dynamic environment, a real-time optimal trajectory generation method based on machine learning aiming at high dimensional inputs is presented in this paper. First, a learning optimization (LO) framework is established, and implementations with different sub-methods are discussed. Additionally, multiple criteria are defined to evaluate the performance of LO models. Furthermore, aiming at high dimensional inputs, a database generation method based on input space dimension-reducing…
CIIRC CTU in Prague（布拉格捷克理工大学信息、机器人与控制研究所）；Sorbonne Université, LIP6 CNRS（索邦大学，法国国家科学研究中心LIP6实验室）；LAAS-CNRS, FEE CTU in Prague（法国国家科学研究中心系统分析与架构实验室，布拉格捷克理工大学电气工程学院）
The Inverse Kinematics (IK) problem is to nd robot control parameters to bring it into the desired position under the kinematics and collision constraints. We present a global solution to the optimal IK problem for a general serial 7DOF manipulator with revolute joints and a quadratic polynomial objective function. We show that the kinematic constraints due to rotations can all be generated by second-degree polynomials. This is important since it signicantly simplies further step where we nd the optimal solution by Lasserre relaxations of non-convex polynomial systems. We demonstrate that the …
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 kinema…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
This article synthezises the most important results on the kinematics of cuspidal manipulators i.e. nonredundant manipulators that can change posture without meeting a singularity. The characteristic surfaces, the uniqueness domains and the regions of feasible paths in the workspace are defined. Then, several sufficient geometric conditions for a manipulator to be noncuspidal are enumerated and a general necessary and sufficient condition for a manipulator to be cuspidal is provided. An explicit DH-parameter-based condition for an orthogonal manipulator to be cuspidal is derived. The full clas…
Institut de Recherche en Cybernétique de Nantes（南特控制论研究所）
The aim of this paper is to characterize the moveability of fully-parallel manipulators in the presence of obstacles. Fully parallel manipulators are used in applications where accuracy, stiffness or high speeds and accelerations are required \cite{Merlet:97}. However, one of its main drawbacks is a relatively small workspace compared to the one of serial manipulators. This is due mainly to the existence of potential internal collisions, and the existence of singularities. In this paper, the notion of free aspect is defined which permits to exhibit domains of the workspace and the joint space …
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…
KU Leuven – University of Leuven（鲁汶大学）；University of Cambridge（剑桥大学）
This work addresses the inverse kinematics of serial robots using conformal geometric algebra. Classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time or the development of particular geometric strategies that cannot be generalized to arbitrary serial robots. In this work, we present a compact, elegant and intuitive formulation of robot kinematics based on conformal geometric algebra that provides a suitable framework for the closed-form resolution of the inverse kinematic problem for manipulators with a spherical wrist. For…
A polynomial solution to the inverse kinematic problem of the Kinova Gen3 Lite robot is proposed in this paper. This serial robot is based on a 6R kinematic chain and is not wrist-partitioned. We first start from the forward kinematics equation providing the position and orientation of the end-effector, finally, the univariate polynomial equation is given as a function of the first joint variable $θ_{1}$. The remaining joint variables are computed by back substitution. Thus, an unique set of joint position is obtain for each root of the univariate equation. Numerical examples, simulated in ROS…
Research Institute for Symbolic Computation, Johannes Kepler University（约翰内斯·开普勒大学符号计算研究所）；University of the Philippines Diliman（菲律宾大学迪里曼分校）
We develop an algorithm that solves the inverse kinematics of general serial 2RP3R, 2R2P2R, 3RP2R and 6R manipulators based on the HuPf algorithm. We identify the workspaces of the 3-subchains of the manipulator with a quasi-projective variety in $\mathbb{P}^7$ via dual quaternions. This allows us to compute linear forms that describe linear spaces containing the workspaces of these 3-subchains. We present numerical examples that illustrate the algorithm and show the real solutions.
University of Toronto（多伦多大学）；University of Zagreb（萨格勒布大学）；Vector Institute（向量研究所）
Inverse kinematics is a fundamental problem for articulated robots: fast and accurate algorithms are needed for translating task-related workspace constraints and goals into feasible joint configurations. In general, inverse kinematics for serial kinematic chains is a difficult nonlinear problem, for which closed form solutions cannot be easily obtained. Therefore, computationally efficient numerical methods that can be adapted to a general class of manipulators are of great importance. % to motion planning and workspace generation tasks. In this paper, we use convex optimization techniques to…
Nantes Université（南特大学）；École Centrale Nantes（南特中央理工学院）；CNRS（法国国家科学研究中心）
Cuspidal robots can move from one inverse or direct kinematic solution to another without ever passing through a singularity. These robots have remained unknown because almost all industrial robots do not have this feature. However, in fact, industrial robots are the exceptions. Some robots appeared recently in the industrial market can be shown to be cuspidal but, surprisingly, almost nobody knows it and robot users meet difficulties in planning trajectories with these robots. This paper proposes a review on the fundamental and application aspects of cuspidal robots. It addresses the importan…
Parallel Transmission Aware Co-Design: Enhancing Manipulator Performance Through Actuation-Space Optimization
Robotics Innovation Center, DFKI GmbH（DFKI机器人创新中心）；Dynamics Division, Department of Mechanics & Maritime Sciences, Chalmers University of Technology（楚基姆斯理工大学机械与航海科学系动力分部）；AG Robotik, University of Bremen（不莱梅大学机器人技术研究所）
The present project deals with the elastostatic modeling and calibration experiment of spacial industrial manipulators using an optimal selection of measurements pose, for the calibration procedure, the optimal pose selection aims to the efficiency improvement of identification procedure for serial manipulators which reduces noise impact on the parameters identification precision, it is usually used for planar manipulators, our work is mainly to extend the approach for a more complicated manipulator in 3D space using a wise decomposition of the spacial manipulator into a set of serial sub-chai…
Co-optimizing Physical Reconfiguration Parameters and Controllers for an Origami-inspired Reconfigurable Manipulator
Colorado State University（科罗拉多州立大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Manning College of Information and Computer Sciences（曼宁信息与计算机科学学院）
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…
Laboratoire des Sciences du Numérique de Nantes（南特数字科学实验室）；Ecole Centrale Nantes（南特中央理工学院）；IMT Atlantique（IMT大西洋）；Innopolis University（因诺波利斯大学）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The paper focuses on the kinematics control of a compliant serial manipulator composed of a new type of dualtriangle elastic segments. Some useful optimization techniques were applied to solve the geometric redundancy problem, ensure the stability of the manipulator configurations with respect to the external forces/torques applied to the endeffector. The efficiency of the developed control algorisms is confirmed by simulation.
Laboratoire des Sciences du Numérique de Nantes (LS2N), UMR CNRS 6004（南特数字科学实验室（法国国家科学研究中心UMR 6004））；Ecole Centrale Nantes（南特中央理工学院）；IMT Atlantique（大西洋电信学院）；Innopolis University（因诺波利斯大学）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The paper focuses on the mechanics of a compliant serial manipulator composed of new type of dual-triangle elastic segments. Both the analytical and numerical methods were used to find the manipulator stable and unstable equilibrium configurations, as well as to predict corresponding manipulator shapes. The stiffness analysis was carried on for both loaded and unloaded modes, the stiffness matrices were computed using the Virtual Joint Method (VJM). The results demonstrate that either buckling or quasi-buckling phenomenon may occur under the loading, if the manipulator corresponding initial co…
Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）；IMT Atlantique（大西洋国立高等矿业电信学校）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The paper focuses on the stiffness modeling of a new type of compliant manipulator and its non-linear behavior while interacting with the environment. The manipulator under study is a serial mechanical structure composed of dualtriangle segments. The main attention is paid to the initial straight configuration which may suddenly change its shape under the loading. It was discovered that under the external loading such manipulator may have six equilibrium configurations but only two of them are stable. In the neighborhood of these configurations, the manipulator behavior was analyzed using the …
Innopolis University（因诺波利斯大学）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）；Le Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）；IMT Atlantique（大西洋国立高等工业技术与矿业学校）
The paper presents advancement of the matrix structural analysis technique (MSA) for stiffness modeling of robotic manipulators. In contrast to the classical MSA, it can be applied to both parallel and serial manipulators composed of flexible and rigid links connected by rigid, passive or elastic joints with multiple external loadings. The manipulator stiffness model is presented as a set of basic equations describing the link elasticities that are supplemented by a set of constraints describing connections between links. These equations are aggregated straightforwardly in a common linear syst…
The singularities of serial robotic manipulators are those configurations in which the robot loses the ability to move in at least one direction. Hence, their identification is fundamental to enhance the performance of current control and motion planning strategies. While classical approaches entail the computation of the determinant of either a 6x n or nxn matrix for an n degrees of freedom serial robot, this work addresses a novel singularity identification method based on modelling the twists defined by the joint axes of the robot as vectors of the six-dimensional and three-dimensional geom…
This paper proposes a novel modelling approach for a heavy-duty manipulator with parallel$-$serial structures connected in series. Each considered parallel$-$serial structure contains a revolute segment with rigid links connected by a passive revolute joint and actuated by a linear hydraulic actuator, thus forming a closed kinematic loop. In addition, prismatic segments, consisting of prismatic joints driven by hydraulic linear actuators, also are considered. Expressions for actuator forces are derived using the Newton$-$Euler (N$-$E) dynamics formulation. The derivation process does not assum…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
The aim of this paper is to classify one family of 3R serial positioning manipulators. This categorization is based on the number of cusp points of quaternary, binary, generic and non-generic manipulators. It was found three subsets of manipulators with 0, 2 or 4 cusp points and one homotopy class for generic quaternary manipulators. This classification allows us to define the design parameters for which the manipulator is cuspidal or not, i.e., for which the manipulator can or cannot change posture without meeting a singularity, respectively.
This chapter is dedicated to the so-called cuspidal robots, i.e. those robots that can move from one inverse geometric solution to another without meeting a singular confuguration. This feature was discovered quite recently and has then been fascinating a lot of researchers. After a brief history of cuspidal robots, the chapter provides the main features of cuspidal robots: explanation of the non-singular change of posture, uniqueness domains, regions of feasible paths, identification and classification of cuspidal robots. The chapter focuses on 3-R orthogonal serial robots. The case of 6-dof …
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
The workspace topologies of a family of 3-revolute (3R) positioning manipulators are enumerated. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps that appear on these singular curves. The design parameters space is shown to be divided into five domains where all manipulators have the same number of cusps. Each separating surface is given as an explicit expression in the DH-parameters. As an application of this work, we provide a necessary and sufficient condition for a 3R orthogonal manipulator to be cuspida…
Ecole des Mines de Nantes（南特矿业学院）；Institut de Recherches en Communications et en Cybernétique de Nantes（南特通信与控制论研究所）；University of Agder（阿格德大学）
The paper presents the compliance errors compensation technique for over-constrained parallel manipulators under external and internal loadings. This technique is based on the non-linear stiffness modeling which is able to take into account the influence of non-perfect geometry of serial chains caused by manufacturing errors. Within the developed technique, the deviation compensation reduces to an adjustment of a target trajectory that is modified in the off-line mode. The advantages and practical significance of the proposed technique are illustrated by an example that deals with groove milli…
Laboratoire d’informatique de Paris（巴黎信息学实验室）；Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制论研究所）
This paper investigates the cuspidal configurations of 3-RPR parallel manipulators that may appear on their singular surfaces in the joint space. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a non-singular change of assembly mode. In previous works, the cusp points were calculated in sections of the joint space by solving a 24th-degree polynomial without any proof that this polynomial was the only one that gives all solutions. The purpose of this study is to propose a rigorous methodology to determine the cusp points of 3-R\unde…
Energy-Cautious Designation of Kinematic Parameters for a Sustainable Parallel-Serial Heavy-Duty Manipulator Driven by Electromechanical Linear Actuator
Faculty of Engineering and Natural Sciences, Tampere University（坦佩雷大学工程与自然科学学院）
Leg-Arm Coordinated Operation for Curtain Wall Installation
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；Shenzhen University of Advanced Technology and University of Chinese Academy of Sciences（深圳先进技术大学和中国科学院大学）
Modular robots can be tailored to achieve specific tasks and rearranged to achieve previously infeasible ones. The challenge is choosing an appropriate design from a large search space. In this work, we describe a framework that automatically synthesizes the design and controls for a serial chain modular manipulator given a task description. The task includes points to be reached in the 3D space, time constraints, a load to be sustained at the end-effector, and obstacles to be avoided in the environment. These specifications are encoded as a constrained optimization in the robot's kinematics a…
