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 that it is possible to link several solutions to the forward kinematic problem without meeting a singularity, thus meaning that the aspects are not uniqueness domains. An additional set of surfaces, namely the characteristic surfaces, are characterized which divide the workspace into basic regions and yield new uniqueness domains. This study is illustrated all along the paper with a 3-RPR planar parallel manipulator. An octree model of spaces is used to compute the joint space, the workspace and all other newly defined sets.
This paper analyses the workspace of the three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. These manipulators are classified into different groups with similar kinematic properties. The classification criteria are based on the topology of the workspace. Each group is evaluated according to interesting kinematic properties such as the size of the workspace subregion reachable with four inverse kinematic solutions, the existence and the size of voids, and the size of the regions of feasible paths in the workspace.
IRCCyN, Institut de Recherche en Communications et Cybernetique de Nantes（南特通信与控制研究所（IRCCyN））；McGill University（麦吉尔大学）
This paper proposes a classification of three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The manipulators are classified into different types with similar kinematic properties. Each type is evaluated according to interesting kinematic properties such as, whether the workspace is fully reachable with…
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…
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…
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…
It was shown recently that parallel manipulators with several inverse kinematic solutions have the ability to avoid parallel singularities [Chablat 1998a] and self-collisions [Chablat 1998b] by choosing appropriate joint configurations for the legs. In effect, depending on the joint configurations of the legs, a given configuration of the end-effector may or may not be free of singularity and collision. Characterization of the collision/singularity-free workspace is useful but may be insufficient since two configurations can be accessible without collisions nor singularities but it may not exi…
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 …
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）
A family of 3R orthogonal manipulators without offset on the third body can be divided into exactly nine workspace topologies. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. Based on this classification, we evaluate theses manipulators by the condition number related to the joint space and the proportion of the region with four inverse kinematic solutions compared to a sphere containing all the workspace. This second performance number is in relation with the…
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 proposes a method to calculate the largest Regular Dextrous Workspace (RDW) of some types of three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. Then a new performance index based on the RDW is introduced, the isocontours of this index are plotted in the parameter space of the interesting types of manipulators and finally an inspection of the domains of the parameter spaces is conducted in order to identify the better manipulator architectures. The RDW is a part of the workspace whose shape is regular (cube, cylinder) and the performan…
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…
Changzhou University（常州大学）；Nanjing Vocational Institute of Mechatronic Technology（南京机电职业技术学院）；Dalian University of Technology（大连理工大学）；Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）
This paper presents a novel three-degree-of-freedom (3-DOF) translational parallel manipulator (TPM) by using a topological design method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations. The proposed PM is only composed of lower-mobility joints and actuated prismatic joints, together with the investigations on three kinematic issues of importance. The first aspect pertains to geometric modeling of the TPM in connection with its topological characteristics, such as the POC, degree of freedom and coupling degree, from which its symbolic direct kinemati…
This paper addresses the problem of cooperative object transportation for multiple Underwater Vehicle Manipulator Systems (UVMSs) in a constrained workspace involving static obstacles. We propose a Nonlinear Model Predictive Control (NMPC) approach for a team of UVMSs in order to transport an object while avoiding significant constraints and limitations such as: kinematic and representation singularities, obstacles within the workspace, joint limits and control input saturations. More precisely, by exploiting the coupled dynamics between the robots and the object, and using certain load sharin…
Laboratoire des Sciences du Numérique de Nantes（南特数字科学实验室）；École Polytéchnique de Montréal（蒙特利尔理工学院）
This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equilateral mobile platform and a U-shape base. The proposed design and appropriate selection of parameters allow to formulate simpler direct and inverse kinematics for the manipulator under study. The parallel singularities associated with the manipulator depend only on the orientation of the end-effector, and thus depend only on the orientation of the end effector. The quaternion parameters are used to represent the aspects, i.e. the singularity free regions of the workspace. A cylindrical algebraic decomposition…
IIIT Hyderabad（国际信息技术研究所海得拉巴分校）；University of Genoa（热那亚大学）；University of Tübingen（图宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；IIT Jodhpur（焦特布尔印度理工学院）
In this paper, a kinematic motion planning algorithm for cooperative spatial payload manipulation is presented. A hierarchical approach is introduced to compute real-time collision-free motion plans for a formation of mobile manipulator robots. Initially, collision-free configurations of a deformable 2-D virtual bounding box are identified, over a planning horizon, to define a convex workspace for the entire system. Then, 3-D payload configurations whose projections lie within the defined convex workspace are computed. Finally, a convex decentralized model-predictive controller is formulated t…
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.
Harbin Institute of Technology（哈尔滨工业大学）；University of Maryland at College Park（马里兰大学帕克分校）
We present a novel algorithm for collision-free kinematics of multiple manipulators in a shared workspace with moving obstacles. Our optimization-based approach simultaneously handles collision-free constraints based on reciprocal velocity obstacles and inverse kinematics constraints for high-DOF manipulators. We present an efficient method based on particle swarm optimization that can generate collision-free configurations for each redundant manipulator. Furthermore, our approach can be used to compute safe and oscillation-free trajectories in a few milli-seconds. We highlight the real-time p…
Fast and Safe Trajectory Optimization for Mobile Manipulators With Neural Configuration Space Distance Field
Robotics and Autonomous Systems Thrust, The Hong Kong University of Science and Technology (Guangzhou)（香港科学与技术大学机器人与自主系统研究组）；Department of Electrical and Computer Engineering, National University of Singapore（新加坡国立大学电子与计算机工程系）；Idiap Research Institute（Idiap研究所）；Institute of Data Science, The University of Hong Kong（香港大学数据科学研究所）
RINGO: Real-time Navigation with a Guiding Trajectory for Aerial Manipulators in Unknown Environments
Institute of Robotics and Automatic Information System（机器人与自动信息系统研究所）；College of Artificial Intelligence（人工智能学院）；Tianjin Key Laboratory of Intelligent Robotics（天津市智能机器人重点实验室）；Nankai University（南开大学）；Institute of Intelligence Technology and Robotic Systems（智能技术与机器人系统研究所）；Shenzhen Research Institute of Nankai University（南开大学深圳研究院）
Zhejiang University（浙江大学）；Shenzhen Sensetime Technology CO.,LTD（深圳商汤科技有限公司）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）
Autonomous Underwater Vehicle-Manipulator systems (AUVMS) is a new tool for ocean exploration, the AUVMS path planning problem is addressed in this paper. AUVMS is a high dimension system with a large difference in inertia distribution, also it works in a complex environment with obstacles. By integrating the rapidly-exploring random tree(RRT) algorithm with the AUVMS kinematics model, the proposed RRTAUVMS algorithm could randomly sample in the configuration space(C-Space), and also grow the tree directly towards the workspace goal in the task space. The RRTAUVMS can also deal with the redund…
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…
QuadHand: A Compact Quadrotor Aerial Manipulator with MRC-SDF-Based Whole-Body Motion Planning
Nanyang Technological University（南洋理工大学）；NTU–VinUni Joint Research Laboratory for Embodied AI and Robotics（南洋理工大学-维纳大学具身智能与机器人联合研究实验室）；VinUniversity（维纳大学）
In this paper, based on Dynamical Systems (DS), we present an obstacle avoidance method that take into account workspace constraint for serial manipulators. Two modulation matrices that consider the effect of an obstacle and the workspace of a manipulator are determined when the obstacle does not intersect the workspace boundary and when the obstacle intersects the workspace boundary respectively. Using the modulation matrices, an original DS is deformed. The proposed approach can ensure that the trajectory of the manipulator computed according to the deformed DS neither penetrate the obstacle…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
A classification of a family of 3-revolute (3R) positioning manipulators is established. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves of the manipulator. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The design parameters space is shown to be partitioned into nine subspaces of distinct workspace topologies. Each separating surface is given as an explicit expression in the DH-parameters.
A Task-Driven, Planner-in-the-Loop Computational Design Framework for Modular Manipulators
Humanoids and Human Centered Mechatronics Research Line, Italian Institute of Technology (IIT) Genoa, Italy（意大利理工学院（IIT）热那亚人类与以人为中心的机电研究组）；Department of Industrial Engineering, University of Trento, Trento, Italy（特伦托大学工业工程系）
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与网络研究所）
A classification of a family of 3-revolute (3R) positining manipulators is established. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The design parameters space is shown to be divided into nine domains of distinct workspace topologies, in which all manipulators have similar global kinematic properties. Each separating surface is given as an explicit expression in the DH-parameters.
IIIT-Hyderabad（海得拉巴国际信息技术学院）；TCS Research（塔塔咨询服务研究院）；University of Michigan（密歇根大学）
This paper proposes a novel controller framework that provides trajectory tracking for an Aerial Manipulator (AM) while ensuring the safe operation of the system under unknown bounded disturbances. The AM considered here is a 2-DOF (degrees-of-freedom) manipulator rigidly attached to a UAV. Our proposed controller structure follows the conventional inner loop PID control for attitude dynamics and an outer loop controller for tracking a reference trajectory. The outer loop control is based on the Model Predictive Control (MPC) with constraints derived using the Barrier Lyapunov Function (BLF) f…
Zhejiang University（浙江大学）；University of Technology Sydney (UTS)（悉尼科技大学）
A mechanism to derive non-repetitive coverage path solutions with a proven minimal number of discontinuities is proposed in this work, with the aim to avoid unnecessary, costly end effector lift-offs for manipulators. The problem is motivated by the automatic polishing of an object. Due to the non-bijective mapping between the workspace and the joint-space, a continuous coverage path in the workspace may easily be truncated in the joint-space, incuring undesirable end effector lift-offs. Inversely, there may be multiple configuration choices to cover the same point of a coverage path through t…
Carnegie Mellon University（卡内基梅隆大学）；Mitsubishi Heavy Industries（三菱重工）
In this work we tackle the path planning problem for a 21-dimensional snake robot-like manipulator, navigating a cluttered gas turbine for the purposes of inspection. Heuristic search based approaches are effective planning strategies for common manipulation domains. However, their performance on high dimensional systems is heavily reliant on the effectiveness of the action space and the heuristics chosen. The complex nature of our system, reachability constraints, and highly cluttered turbine environment renders naive choices of action spaces and heuristics ineffective. To this extent we have…
Master control console is a place where robots collaborate with humans in a shared environment. To this end, ergonomics is an important aspect to be considered. With ergonomic design, the surgeons can feel more comfortable to conduct the surgical tasks with higher efficiency, and the quality of the teleoperated robotic surgery can be improved. In this paper, an Ergonomic Interaction Workspace Analysis method is proposed to optimize master manipulators and fulfil ergonomics consideration for designing a master manipulator for teleoperated robotic surgery.
This paper discusses modelling two 6 DOF arm robots. The first step of modelling a robot is establishing its Denavit-Hartenberg parameters. It requires assigning proper coordinates for each link and finding their exact dimensions. In this project we will develop the direct kinematics and workspace representations for two manipulators: the Smokie Robot and the Barrett WAM. After finding the D-H parameters and creating Transformation Matrices,MATLAB programming is used to represent their workspaces.
Mobile manipulation is usually achieved by sequentially executing base and manipulator movements. This simplification, however, leads to a loss in efficiency and in some cases a reduction of workspace size. Even though different methods have been proposed to solve Whole-Body Control (WBC) online, they are either limited by a kinematic model or do not allow for reactive, online obstacle avoidance. In order to overcome these drawbacks, in this work, we propose an end-to-end Reinforcement Learning (RL) approach to WBC. We compared our learned controller against a state-of-the-art sampling-based m…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
This article provides a formalism making it possible to manage the solutions of the direct and inverse kinematic models of the fully parallel manipulators. We introduce the concept of working modes to separate the solutions from the opposite geometrical model. Then, we define, for each working mode, the aspects of these manipulators. To separate the solutions from the direct kinematics model, we introduce the concept of characteristic surfaces. Then, we define the uniqueness domains, as being the greatest domains of the workspace in which there is unicity of solutions. The principal applicatio…
Mechanical Engineering, University of Michigan（密歇根大学机械工程学院）；Robotics Institute, University of Michigan（密歇根大学机器人研究所）；Mechanical and Industrial Engineering, Louisiana State University（路易斯安那州立大学机械与工业工程学院）；Naval Architecture and Marine Engineering, University of Michigan（密歇根大学船舶与海洋工程学院）；Ford Motor Company（福特汽车公司）；Office of Naval Research（美国海军研究办公室）
For robotic arms to operate in arbitrary environments, especially near people, it is critical to certify the safety of their motion planning algorithms. However, there is often a trade-off between safety and real-time performance; one can either carefully design safe plans, or rapidly generate potentially-unsafe plans. This work presents a receding-horizon, real-time trajectory planner with safety guarantees, called ARMTD (Autonomous Reachability-based Manipulator Trajectory Design). The method first computes (offline) a reachable set of parameterized trajectories for each joint of an arm. Eac…
Laboratoire des Sciences du Numérique de Nantes（南特数字科学实验室）；University of Innsbruck（因斯布鲁克大学）
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 interpretat…
University of Cassino and Southern Lazio（卡西诺和南拉齐奥大学）
In this paper we present a framework that allows the motion control of a robotic arm automatically handling different kinds of safety-related tasks. The developed controller is based on a Task-Priority Inverse Kinematics algorithm that allows the manipulator's motion while respecting constraints defined either in the joint or in the operational space in the form of equality-based or set-based tasks. This gives the possibility to define, among the others, tasks as joint-limits, obstacle avoidance or limiting the workspace in the operational space. Additionally, an algorithm for the real-time co…
Belarusian State University of Informatics and Radioelectronics（白俄罗斯信息与无线电电子大学）；Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
The paper addresses kinematic and geometrical aspects of the Orthoglide, a three-DOF parallel mechanism. This machine consists of three fixed linear joints, which are mounted orthogonally, three identical legs and a mobile platform, which moves in the Cartesian x-y-z space with fixed orientation. New solutions to solve inverse/direct kinematics are proposed and we perform a detailed workspace and singularity analysis, taking into account specific joint limit constraints.
TU Wien（维也纳工业大学）；University of Liverpool（利物浦大学）；Austrian Institute of Technology GmbH (AIT)（奥地利技术研究院有限公司）
Solving the analytical inverse kinematics (IK) of redundant manipulators in real time is a difficult problem in robotics since its solution for a given target pose is not unique. Moreover, choosing the optimal IK solution with respect to application-specific demands helps to improve the robustness and to increase the success rate when driving the manipulator from its current configuration towards a desired pose. This is necessary, especially in high-dynamic tasks like catching objects in mid-flights. To compute a suitable target configuration in the joint space for a given target pose in the t…
A study on a Real-Time VR-Based Teleoperation Framework for Manipulator in Dynamic Environment
Department of Robotics, Hanyang University（韩世大学机器人系）；Department of Smart Construction Engineering, Hanyang University（韩世大学智能建造工程系）；Department of Interdisciplinary Robot Engineering Systems, Hanyang University（韩世大学跨学科机器人工程系统系）；School of Smart Convergence Engineering, Hanyang University, Ansan（韩世大学智能融合工程学院，安山）
University of Oslo（奥斯陆大学）；Oslo University Hospital（奥斯陆大学医院）
With advancing technologies, robotic manipulators and visual environment sensors are becoming cheaper and more widespread. However, robot control can be still a limiting factor for better adaptation of these technologies. Robotic manipulators are performing very well in structured workspaces, but do not adapt well to unexpected changes, like people entering the workspace. We present a method combining 3D Camera based workspace mapping, and a predictive and reflexive robot manipulator trajectory estimation to allow more efficient and safer operation in dynamic workspaces. In experiments on a re…
This paper introduces a novel motion planner, incrementally stochastic and accelerated gradient information mixed optimization (iSAGO), for robotic manipulators in a narrow workspace. Primarily, we propose the overall scheme of iSAGO informed by the mixed momenta for an efficient constrained optimization based on the penalty method. In the stochastic part, we generate the adaptive stochastic momenta via the random selection of sub-functionals based on the adaptive momentum (Adam) method to solve the body-obstacle stuck case. Due to the slow convergence of the stochastic part, we integrate the …
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…
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…
