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 makes it possible to display all possible non-singular assembly-mode changing trajectories.
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.
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.
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）
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 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…
This paper investigates the existence conditions of cusp points in the design parameter space of the R\underline{P}R-2P\underline{R}R parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which can possibly increase the size of the aspect, i.e. the maximum singularity free workspace. The method used is based on the notion of discriminant varieties and Cylindrical Algebraic Decomposition, and resorts to Gröbner bases for the solutions of systems of equations.
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…
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…
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 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 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…
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…
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.
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…
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…
Institut de Recherche en Cybernétique de Nantes（南特控制论研究所）
The goal of this paper is to explain, using a typical example, the distribution of the different assembly modes in the workspace and their effective role in the execution of trajectories. The singular and non-singular changes of assembly mode are described and compared to each other. The non-singular change of assembly mode is more deeply analysed and discussed in the context of trajectory planning. In particular, it is shown that, according to the location of the initial and final configurations with respect to the uniqueness domains in the workspace, there are three different cases to consid…
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…
University of Oulu（奥卢大学）；Aalto University（阿尔托大学）；Idiap Research Institute（Idiap研究所）
In this paper we show how different choices regarding compliance affect a dual-arm assembly task. In addition, we present how the compliance parameters can be learned from a human demonstration. Compliant motions can be used in assembly tasks to mitigate pose errors originating from, for example, inaccurate grasping. We present analytical background and accompanying experimental results on how to choose the center of compliance to enhance the convergence region of an alignment task. Then we present the possible ways of choosing the compliant axes for accomplishing alignment in a scenario where…
Enhancing Autonomous Manipulator Control with Human-in-loop for Uncertain Assembly Environments
Space Robotics Lab. (SRL) in Department of Aerospace Engineering, Graduate School of Engineering, Tohoku University（太空机器人实验室（SRL）位于航空航天工程系，工学研究生院，东北大学）
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…
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…
In the modern days, manipulators are found in the automated assembly lines of industries that produce products in masses. These manipulators can be used only in one configuration, that is either serial or parallel. In this paper, a new module which has two degrees of freedom is introduced. By connecting the two and three modules in series, 4 and 6 DoF hybrid manipulators can be formed respectively. By erecting 3 modules in parallel and with some minor modifications, a 6 DoF parallel manipulator can be formed. Hence the manipulator is reconfigurable and can be used as hybrid or parallel manipul…
Osaka University（大阪大学）；National Institute of Advanced Industrial Science and Technology (AIST)（日本产业技术综合研究所）
Industrial robot manipulators are playing a more significant role in modern manufacturing industries. Though peg-in-hole assembly is a common industrial task which has been extensively researched, safely solving complex high precision assembly in an unstructured environment remains an open problem. Reinforcement Learning (RL) methods have been proven successful in solving manipulation tasks autonomously. However, RL is still not widely adopted on real robotic systems because working with real hardware entails additional challenges, especially when using position-controlled manipulators. The ma…
IRMAR, Université de Rennes 1 – CNRS（法国国家科学研究中心、雷恩第一大学数学研究所（IRMAR））；IRCCyN, CNRS – École Centrale de Nantes（法国国家科学研究中心、南特中央理工学院南特通信与控制研究所（IRCCyN））
This paper investigates a situation pointed out in a recent paper, in which a non-singular change of assembly mode of a planar 2-RPR-PR parallel manipulator was realized by encircling a point of multiplicity 4. It is shown that this situation is, in fact, a non-generic one and gives rise to cusps under a small perturbation. Furthermore , we show that, for a large class of singularities of multiplicity 4, there are only two types of stable singularities occurring in a small perturbation: these two types are given by the complex square mapping and the quarto mapping. Incidentally , this paper co…
Graduate School of Engineering Science, Osaka University（大阪大学工程科学研究生院）；Intelligent Systems Research Institute, National Inst. of Advanced Industrial Science and Technology（日本产业技术综合研究所智能系统研究所）
This paper proposes a novel assembly planner for a manipulator which can simultaneously plan assembly sequence, robot motion, grasping configuration, and exchange of grippers. Our assembly planner assumes multiple grippers and can automatically selects a feasible one to assemble a part. For a given AND/OR graph of an assembly task, we consider generating the assembly graph from which assembly motion of a robot can be planned. The edges of the assembly graph are composed of three kinds of paths, i.e., transfer/assembly paths, transit paths and tool exchange paths. In this paper, we first explai…
Deploying large, complex space structures is of great interest to the modern scientific world as it can provide new capabilities in obtaining scientific, communicative, and observational information. However, many theoretical mission designs contain complexities that must be constrained by the requirements of the launch vehicle, such as volume and mass. To mitigate such constraints, the use of on-orbit additive manufacturing and robotic assembly allows for the flexibility of building large complex structures including telescopes, space stations, and communication satellites. The contribution o…
Robot assembly discovery is a challenging problem that lives at the intersection of resource allocation and motion planning. The goal is to combine a predefined set of objects to form something new while considering task execution with the robot-in-the-loop. In this work, we tackle the problem of building arbitrary, predefined target structures entirely from scratch using a set of Tetris-like building blocks and a robotic manipulator. Our novel hierarchical approach aims at efficiently decomposing the overall task into three feasible levels that benefit mutually from each other. On the high le…
Massachusetts Institute of Technology（麻省理工学院）；Princeton University（普林斯顿大学）
Additive robotic construction of building-scale discrete bar structures, such as trusses and space frames, is increasingly attractive due to the potential improvements in efficiency, safety, and design possibilities. However, programming complex robots, such as manipulators with seven degrees of freedom, to successfully complete construction tasks can be tedious, challenging, or impossible for a human to do manually. Namely, the structure must be constructed in a sequence that preserves structural properties, such as stiffness, at each step. At the same time, this sequence must allow for the r…
Morphogenetic Assembly and Adaptive Control for Heterogeneous Modular Robots
Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai, China（上海智能自主系统研究院，同济大学，上海，中国）；Department of Mechanical and Automation Engineering and T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong（机械与自动化工程系和T Stone机器人研究院，香港中文大学，香港）
Sparse Compositional Flow Matching by geometric assembly from motion primitives
Tsinghua Shenzhen Graduate School, Tsinghua University, Shenzhen, China（清华大学深圳研究生院，清华大学，深圳，中国）；School of AI, Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）人工智能学院）
