Workspace Of Manipulator Research Articles

Analytical derivation of singularity-free tubes in the constant-orientation workspace of 6-6 Stewart platform manipulators

Abstract This paper presents the novel concept of a singularity-free tube (SFT) in the constant orientation workspace of a spatial parallel manipulator. The concept is developed and demonstrated in the context of a $6$ - $6$ spatial parallel manipulator, namely, the semi-regular Stewart platform manipulator. Given two points in the said workspace, the SFT is a tubular volume which contains these points and is free of gain-type or forward-kinematic singularities. The purpose of identifying such regions in space is to allow abundant freedom to the path-planner to connect the said points by a path, which can be free of gain-type singularities simply by remaining inside the SFT at all times. To demonstrate the concept, two smooth paths obtained by formulating two different optimisation problems have been presented as examples. The SFT can be of great help in singularity-free path-planning in many similar manipulators.

An analytical study of Euler angle and Rodrigues parameter representations of $\mathbb{SO}(3)$ towards describing subsets of ${\mathbb{SO}}(3)$ geometrically and establishing the relations between these

Abstract Descriptions of various subsets of $\mathbb{SO}(3)$ are encountered frequently in robotics, for example, in the context of specifying the orientation workspaces of manipulators. Often, the Cartesian concept of a cuboid is extended into the domain of Euler angles, notwithstanding the fact that the physical implications of this practice are not documented. Motivated by this lacuna in the existing literature, this article focuses on studying sets of rotations described by such cuboids by mapping them to the space of Rodrigues parameters, where a physically meaningful measure of distance from the origin is available and the spherical geometry is intrinsically pertinent. It is established that the planar faces of the said cuboid transform into hyperboloids of one sheet and hence, the cuboid itself maps into a solid of complicated non-convex shape. To quantify the extents of these solids, the largest spheres contained within them are computed analytically. It is expected that this study would help in the process of design and path planning of spatial robots, especially those of parallel architecture, due to a better and quantitative understanding of their orientation workspaces.

Task-Dependent Comfort Zone, a Base Placement Strategy for Mobile Manipulators Based on Manipulability Measures

The present contribution introduces the task-dependent comfort zone as a base placement strategy for mobile manipulators using different manipulability measures. Four different manipulability measures depending on end-effector velocities, forces, stiffness, and accelerations are considered. By evaluating a discrete subspace of the manipulator workspace with these manipulability measures and using image-processing algorithms, a suitable goal position for the autonomous mobile manipulator was defined within the comfort zone. This always ensures a certain manipulator manipulablity value with a lower limit with respect to the maximum possible manipulability in the discrete subspace. Results are shown for three different mobile manipulators using the velocity-dependent manipulability measure in a simulation.

A versatile door opening system with mobile manipulator through adaptive position-force control and reinforcement learning

The ability of robots to navigate through doors is crucial for their effective operation in indoor environments. Consequently, extensive research has been conducted to develop robots capable of opening specific doors. However, the diverse combinations of door handles and opening directions necessitate a more versatile door opening system for robots to successfully operate in real-world environments. In this paper, we propose a mobile manipulator system that can autonomously open various doors without prior knowledge. By using convolutional neural networks, point cloud extraction techniques, and external force measurements during exploratory motion, we obtained information regarding handle types, poses, and door characteristics. Through two different approaches, adaptive position-force control and deep reinforcement learning, we successfully opened doors without precise trajectory or excessive external force. The adaptive position-force control method involves moving the end-effector in the direction of the door opening while responding compliantly to external forces, ensuring safety and manipulator workspace. Meanwhile, the deep reinforcement learning policy minimizes applied forces and eliminates unnecessary movements, enabling stable operation across doors with different poses and widths. The RL-based approach outperforms the adaptive position-force control method in terms of compensating for external forces, ensuring smooth motion, and achieving efficient speed. It reduces the maximum force required by 3.27 times and improves motion smoothness by 1.82 times. However, the non-learning-based adaptive position-force control method demonstrates more versatility in opening a wider range of doors, encompassing revolute doors with four distinct opening directions and varying widths.

EXPLORATION OF THE INVERSE AND FORWARD KINEMATICS OF A TWO-LINK ROBOT ARM USING MATLAB

This contribution focuses on solving the inverse and forward kinematics in the kinematic analysis of a two-link manipulator model. It involves determining the trajectory of the end effector through fifth-degree polynomial interpolation. Furthermore, given initial and final arm angle values, it computes not only the end effector trajectory but also the angular parameters of individual actuators in both arms. Additionally, it calculates the variations of angular parameters such as rotation angle, angular velocity, and angular acceleration in each kinematic pair. The direct kinematics task is utilized to define the manipulator's workspace. The task is carried out using Matlab software, and the results are presented in the form of graphs and tables.

Expanding the wrench feasible workspace of quadrotor-based mobile cable-driven parallel manipulators using multi-objective optimization and machine learning

Quadrotor-based Reconfigurable Cable-Driven Parallel Manipulators (QRCDPMs) have previously been introduced as having significant potential in extending the feasible workspace of Cable-Driven Parallel Manipulators (CDPMs). However, such configurations have limitations in executing positive Z-direction trajectories resulting in non-optimal workspace and performance. This study proposes a novel Quadrotor-based Enhanced Reconfiguration Cable-Driven Parallel Manipulator (QERCDPM) that significantly enhances the Wrench Feasible Workspace (WFW). This allows for extended safe platform operation along all XYZ directions by adjusting the bottom cable exit point. Simulation results indicate that the proposed setup achieves a 96.39 % ratio of safe workspace to available workspace in various cable exit points configurations. Tension Distribution analysis for different trajectories demonstrates the proposed setup's superior cable tension management, increased flexibility and reachability. A Random Forest based Particle Swarm Optimization - Modified Frequency Bat Algorithm (RFPSOMFB) optimization algorithm is proposed, which outperforms existing methods in terms of run time and solution quality. The findings hold significance for applications requiring safe and efficient trajectory execution in dynamic and constrained environments, contributing to the evolution of multi-robot based intelligent and distributed systems.

An improved inverse kinematics solution method for the hyper‐redundant manipulator with end‐link pose constraint

AbstractHyper‐redundant manipulators have strong flexibility that benefits from their redundant limb structure. However, a large number of redundant degrees of freedom will also lead the solution of inverse kinematics much more difficult, which restricts their motion performance to some extent. Inspired by the FABRIK (Forward and Backward Reaching Inverse Kinematics) method, an improved inverse kinematics solution method for the hyper‐redundant manipulator is proposed. Based on the space vector method, the kinematic model of the manipulator is established to dynamically acquire its endpoint position, and the workspace is further obtained by using the Monte Carlo method. The original search method is optimized, the include angle decoupling mechanism between adjacent links is established to obtain the rotation angles of each joint, and the joint angle limitation is introduced to meet the actual manipulator structural restriction. On this basis, the pose constraint mechanism is established to realize the control of the end‐link pose, and the linear degree of freedom is introduced to realize the solution after the directional expansion of the manipulator's workspace. A series of simulation experiments are carried out. In the experiments, the position error of the manipulator's endpoint is always less than 10−6 mm. Meanwhile, the comparative experimental results show that compared with the original method, the proposed method exhibits higher position accuracy under the condition that the computation time is almost the same. In addition, in the end‐link pose constraint experiment and path motion experiments, the pose error of the end‐link is always less than 10−7°, indicating that the end‐link pose can also meet the high accuracy requirements under the premise of ensuring high position accuracy. Finally, the prototype experiment further verifies its performance.

Sensor-Based Identification of Singularities in Parallel Manipulators

Singularities are configurations where the number of degrees of freedom of a robot changes instantaneously. In parallel manipulators, a singularity could reduce the mobility of the end-effector or produce uncontrolled motions of the mobile platform. Thus, a singularity is a critical problem for mechanical design and model-based control. This paper presents a general sensor-based method to identify singularities in the workspace of parallel manipulators with low computational cost. The proposed experimental method identifies a singularity by measuring sudden changes in the end-effector movements and huge increments in the forces applied by the actuators. This paper uses an inertial measurement unit and a 3D tracking system for measuring the end-effector movements, and current sensors for the forces exerted by the actuators. The proposed sensor-based identification of singularities is adjusted and implemented in three different robots to validate its effectiveness and feasibility for identifying singularities. The case studies are two prototypes for educational purposes—a five-bar mechanism and an L-CaPaMan parallel robot—and a four-degree-of-freedom robot for rehabilitation purposes. The tests showcase its potential as a practical solution for singularity identification in educational and industrial robots.

Optimized Ray-Based Method for Workspace Determination of Kinematic Redundant Manipulators

Abstract Determining the workspace of a robotic manipulator is highly significant for knowing its abilities and planning the robot application. Several techniques exist for robot workspace determination. However, these methods are usually affected by computational redundancy, like in the Monte Carlo based method case, and their implementation can be complex. The workspace analysis of kinematic redundant manipulators is even more complex. This paper proposes a kinematically optimized ray-based workspace determination algorithm based on a simple idea and not affected by computational redundancy. The proposed method can be applied to any serial robot but is tested only on spatial kinematic redundant robots. The results show how the approach can correctly determine the robot workspace boundaries in a short time. Then, the correctness and computational time of the proposed optimized ray-based method are compared to pseudo-inverse Jacobian ray-based and Monte Carlo methods. The comparison demonstrates that the proposed method has better results in a shorter time. Finally, some limitations of the proposed algorithm are discussed.

Modeling the workspace of a three-link planar manipulator

A study of the working space of a three-link planar manipulator was carried out. The basis is taken from analytical dependencies that allow solving the direct problem of kinematics, i.e. determine the coordinates of the gripper center point using three generalized coordinates of the manipulator. The analysis performed made it possible to give a geometric interpretation of the dependencies. It has been established that the workspace of the manipulator is a three-parameter set of points. On a plane, this set of points is represented in the form of two disks consisting of ring cells, for which the corresponding analytical dependencies are obtained. The geometric image of this set is a three-dimensional torus. The resulting models are visualized, which facilitates the solution of this problem. To determine the values of the generalized coordinates of the gripper center points, a mapping was carried out by orthogonal projection of the families of circles obtained in the work into four-dimensional space. As a result, three-dimensional hypersurfaces in four-dimensional space were obtained. It is proposed to study them by constructing hypersurface sections models by hyperplanes. Such models in visualization mode allow solving direct and inverse kinematics problems of the manipulator under study.

Design and implementation of a 2-DOF 5R parallel mechanism with a coaxial-driven layout

In order to expand and improve the reachable workspace of planar parallel manipulators, a 2-DOF 5R parallel mechanism with a coaxial-driven layout is proposed. The configuration analysis and structural design are carried out, and the kinematic model is presented to conduct simulation analysis. The results indicate that the layout with the axes of the two driving devices overlapping has a larger workspace and a more compact structure. Meanwhile, a closed-loop PID control system is established to evaluate the accuracy of the proposed mechanism and analyse the kinematic error under different gain parameters. Simulation results indicate that the kinematic performance of the mechanism has improved. The control system is constructed based on using a motion control card as the primary control component and two servo motors as the drive device. Additionally, gain values are adjusted by the driver to reduce the deviation of the servo motors. Finally, the design of the prototype is deployed, and the experiment proved that the 2-DOF 5R planar parallel mechanism (PPM) with a coaxial-driven layout has the advantages of a large workspace, fast dynamic response, high stiffness, and easy control. The design of the 2-DOF 5R PPM solves the problem of single operation and high repeatability, which is increasingly utilized in the fields of electronics, food, daily chemicals, and pharmaceuticals.

Моделирование границ рабочего пространства планарного трёхзвенного манипулятора

A study of the boundaries of the working space of a three-link planar manipulator, specified by analytical equations, is carried out. A new geometric interpretation of these samples is proposed. On its basis, it is established that outer space consists of two-parameter volumes of eccentric and concentric circles. When transforming such environments into four-dimensional space, two types of hypersurfaces are obtained, which represent a geometric model of the manipulator's workspace. The discriminants of these hypersurfaces on the hyperplane are two two-dimensional surfaces. Both an analytical description of these surfaces and their computer models are obtained. As a result, it is established that the boundaries of the working space on the plane of the mechanism are the discriminants of such surfaces. To confirm the reliability of the results obtained, as an example, an inverse kinematics problem is solved on discriminant surfaces — the values of generalized coordinates at the boundary points of the manipulator’s workspace are determined for their given Cartesian coordinates.

Kinematics, dynamics and multi-objective optimization based on singularity-free task workspace for a novel SCARA parallel manipulator

Kinematics, dynamics and multi-objective optimization based on singularity-free task workspace for a novel SCARA parallel manipulator

Unifying the Generalized Jacobian Matrix and prioritized task hierarchies, with application to free-floating VMSs

Free-floating vehicle manipulator systems (VMSs), such as those in space or underwater, experience a coupling effect between the motion of the manipulator arm and the vehicle base, since the motion of the joints induces a motion of the base relative to the system's center of gravity (CG). In this work a control framework is proposed that takes this coupling effect into account, selecting the motion of the CG as the highest priority task in a dynamically consistent task hierarchy in order to reduce the need for counteracting disturbances while controlling the position of the manipulator workspace. The proposed approach generalizes previous works using the Generalized Jacobian matrix to allow the completion of several prioritized tracking tasks. Control allocation is performed in a manner ensuring that the thrusters are used only for controlling the overall position of the VMS, while the joints are used for tasks requiring higher accuracy. The set in which all tracking error dynamics are zero is shown to be uniformly asymptotically stable, and the performance of the proposed control method is validated in a simulation study.

In-hand manipulation using a 3-PRS-finger-based parallel dexterous hand with bidirectional pinching capability

Considering the defects of the traditional dexterous hand in precise in-hand manipulation and bidirectional pinching capability, this paper proposes a 3-PRS-finger-based parallel dexterous hand (PDH). The PDH structure is composed of three 3-PRS parallel fingers. First, a pinching shape analysis is conducted to demonstrate the PDH's bidirectional pinching capability. Then, by analyzing the workspace of the PDH pinching nine objects, the influence on the in-hand manipulation workspace of different objects is determined. The PDH can perform symmetrical in-hand manipulation to address the issue that almost all humanoid dexterous hands pinch objects in a single direction. The force transmission capability of the PDH is compared with that of the 3R serial dexterous hand (SDH) under the same trajectory. The results indicate that the PDH have the possibility to possess a good pinching force performance through the specific trajectory planning. Bidirectional pinching experiments are conducted, and the experimental results demonstrate that the PDH can realize the accurate in-hand manipulation under almost frictionless conditions. The proposed PDH provides a feasible design for the theoretical development and practical application of dexterous hands.

Instantaneous Kinematics and Free-from-Singularity Workspace of 3-XXRRU Parallel Manipulators

3-XXRRU parallel manipulators (PMs) constitute a family of six-degrees-of-freedom (DOF) PMs with three limbs of type XXRRU, where R and U stand for revolute pair and universal joint, respectively, and XX indicates any actuated two-DOF mechanism that moves the axis of the first R-pair. The members of this family share the fact that they all become particular 3-RRU structures when the actuators are locked. By exploiting this feature, the present paper proposes a general approach, which holds for all the members of this family, to analyze the instantaneous kinematics, workspace, and kinetostatic performances of any 3-XXRRU PM. The results of this study include the identification of singularity conditions without reference to a specific actuation system, the proposal of two specific dimensionless performance indices ranging from 0 to 1, the determination of the optimal actuation system, and the demonstration that 3-XXRRU PMs, when appropriately sized and actuated, possess a broad singularity-free workspace that is also fully isotropic. These findings hold significance in the context of the dimensional synthesis and control of 3-XXRRU PMs. Moreover, when combined with the closed-form solutions for their positional analysis, as demonstrated in a previous publication by the same authors, 3-XXRRU PMs emerge as intriguing alternatives to other six-DOF PMs. The efficacy of the proposed approach is further illustrated through a case study.

The structural design and simulation of the tubing handling manipulator

The size of the oil pipes in the factory is relatively large, making them inconvenient to handle. There are few existing oil pipe handling devices, and a 2P2R four degree of freedom manipulator device has been innovatively designed to complete the oil pipe handling work. First, the three-dimensional model of the manipulator was established using SolidWorks software, and then the improved D-H method was used to carry out the kinematics modeling of the manipulator system, and the forward and Inverse kinematics equations were derived. Then, the MATLAB software was used to carry out the kinematics analysis of the manipulator, and the manipulator workspace was calculated. The movement trajectory, as well as the displacement, speed, and acceleration curves under the trajectory were obtained using the fifth order Polynomial interpolation method, Finally, the 3D model was imported into Adams software, and an Adams virtual prototype was established for dynamic analysis. The force and torque curves of each joint were obtained, laying the foundation for further design and research in the future.

A novel framework to improve motion planning of robotic systems through semantic knowledge-based reasoning

The need to improve motion planning techniques for manipulator robots, and new effective strategies to manipulate different objects to perform more complex tasks, is crucial for various real-world applications where robots cooperate with humans. This paper proposes a novel framework that aims to improve the motion planning of a robotic agent (a manipulator robot) through semantic knowledge-based reasoning. The Semantic Web Rule Language (SWRL) was used to infer new knowledge based on the known environment and the robotic system. Ontological knowledge, e.g., semantic maps, were generated through a deep neural network, trained to detect and classify objects in the environment where the robotic agent performs. Manipulation constraints were deduced, and the environment corresponding to the agent’s manipulation workspace was created so the planner could interpret it to generate a collision-free path. For reasoning with the ontology, different SPARQL queries were used. The proposed framework was implemented and validated in a real experimental setup, using the planning framework ROSPlan to perform the planning tasks. The proposed framework proved to be a promising strategy to improve motion planning of robotics systems, showing the benefits of artificial intelligence, for knowledge representation and reasoning in robotics.

Minimum Friction Coefficient-Based Precision Manipulation Workspace Analysis of the Three-Fingered Metamorphic Hand

Abstract Reconfigurable robotic hands can constitute one of the future trends of dexterous manipulator design, as they can strike a balance between precision, force exertion, flexibility, and adaptability. However, the feasible manipulation workspace of a reconfigurable robotic hand, the metamorphic hand, is complex as the finger operation planes alter with the reconfigurable palm’s motions. Different useful workspace approaches and grasp quality metrics have been introduced, but a precision manipulation workspace (PMW) approach for reconfigurable robotic hands has yet to be presented. This paper presents a hand workspace taxonomy based on previous studies, and a new approach to obtaining a PMW of a robotic hand which satisfies three properties: force closure, singularity avoidance, and interference avoidance. A grasp quality metric, termed the minimum friction coefficient (MFC), is introduced to indicate the force-closure conditions of a robotic hand’s configurations. Unlike the previous grasp quality metrics targeting online grasp-planning tasks, this MFC-based measure focuses on the offline design of robotic hands. This method is essential for conducting grasp planning, design optimization, and actuation reduction for reconfigurable robotic hands. Further, the approach is applied to a three-fingered metamorphic hand, and the results are studied thoroughly.

Dexterous workspace optimization for a six degree-of-freedom parallel manipulator based on surrogate-assisted constrained differential evolution

Parallel manipulators are increasingly applied because of their high stiffness, load capacity, and motion precision. However, the workspace of a parallel manipulator is relatively small compared to that of a serial manipulator. Therefore, appropriate structural designs of parallel manipulators for maximizing the workspace are essential. This paper studies the dexterous workspace maximization problem of a six-degree-of-freedom (DOF) parallel manipulator. First, a constrained optimization model is formulated, in which, the objective is to maximize the dexterous workspace, and the constraints include several kinematic and dynamic indicators, and some general structural limitations. To address the highly constrained, computationally-expensive problem, a surrogate-assisted two-phase constrained differential evolution method is proposed. Its effectiveness and efficiency are verified by the superior performance over two surrogate-free evolutionary methods: differential evolution (DE) and genetic algorithm (GA), and two surrogate-assisted state-of-the-art evolutionary methods: modified constrained expected improvement (CEI) and the lower confidence bounding approach (PCLCB), on ten benchmark functions and the established real-word 6-DOF manipulator design optimization problem.