Reachable Workspaces Research Articles

Kinematic analysis, workspace definition, and self-collision avoidance of a quasi-spherical parallel manipulator

Abstract Bilateral teleoperation has witnessed significant development since the mid-20th century, addressing challenges related to human presence in environments with constraints or a lack of skilled professionals. This article presents the kinematic and self-collision analyses of the quasi-spherical parallel manipulator, a three-legged parallel robot used as a haptic master device. The device is designed for remote center of motion-constrained operation in the telesurgical field. Inverse and forward kinematics are thoroughly analyzed to study working modes, singular configurations, and implement a haptic control architecture. The research explores the operative and reachable workspaces of the possible working modes, comparing them to find the most suitable one. Results highlight how the addition of the self-collision phenomenon impacts the working mode choice, drastically reducing most of the modes’ operative workspaces. An anti-collision control algorithm is finally introduced to maintain the architecture within its reachable workspace.

Mechanism Design and Workspace Analysis of a Hexapod Robot With Changeable Morphology

Abstract Here, the morphology of a legged robot refers to the standing/crawling pose of the robot and the forward/backward orientation of the knee, which are related to the configurations of all leg mechanisms. The standing/crawling pose of the robot determines the body height and the leg supporting region size, which are related to the obstacle-traversing and arch-traversing capability. The proper knee orientation can reduce the leg–ground interference risk and help select a good foothold. Therefore, the terrain adaptability can be enhanced if the morphology of the legged robot is changeable. Motivated by this, a hexapod robot capable of morphology conversion is designed in this study. For the leg mechanism, a double-parallelogram transmission mechanism is used to change the forward/backward orientation of the knee. The hexapod robot can transform between the crawling pose and the standing pose and can also transform among four standing morphologies (i.e., the knee–elbow, knee–knee, elbow–knee, and elbow–elbow morphologies). The appropriate robot morphology can be determined according to the terrain type. The lateral reachable body workspaces are derived analytically for different morphologies, which is useful for motion planning. Simulations and experiments are used to verify the design and analysis of the hexapod robot.

Efficient Reachable Workspace Division under Concurrent Task for Human-Robot Collaboration Systems

Division of the reachable workspace of upper limbs under different visual and physical conditions, finding the efficient reachable area under concurrent task conditions, and using it as a basis to divide the incorporation boundaries that require robot assistance are the focus of this paper. These could be used to rationalize the allocation of human and robot workspaces to maximize the efficiency of multitask completion, which has significant applications in the enhancement of human–robot collaboration (HRC) capabilities. However, research on this has rarely been conducted due to the complexity and diversity of arm movements. In this paper, we considered the physical and visual restrictions of the human operator, extracted the movement data of 10 participants while completing the reaching task, and divided the workspace into five areas (their angles are 0°~44.761°, 44.761°~67.578°, 67.578°~81.108°, 81.108°~153.173°, and 153.173°~180°). Measuring the concurrent task completion times when the target object is in each area, respectively, we demonstrated that areas I~II are efficient, reachable workspaces for the human. In the non-efficient reachable workspaces, the average completion times for HRC were 86.7% for human operators (in area III) and 70.1% (in area IV), with the average number of warnings reduced from 2.5 to 0.4. The average completion time for HRC in area V was 59.3% for the human operator, and the average number of warnings was reduced from 3.5 to 0.5. Adding robotic assistance in this area could improve the efficiency of the HRC systems. This study provided a quantitative evaluation of human concurrent task completion capabilities and the incorporation boundaries of robots, which is a useful reference for achieving efficient HRC.

Design of a New Family of Kinematically Redundant Parallel Mechanisms With Two Rotations and One Translation

Abstract This article presents a new family of kinematically redundant parallel mechanisms (KR-PMs) with two rotations and one translation (2R1T) based on the Lie group method. Compared with the 2-UPR/RPU PM, these PMs have two main advantages, namely, larger reachable workspaces of the moving platforms and higher motion/force transmission performance, as verified by three typical cases. The inverse kinematics, velocities, singularities, and workspaces of the 2-UPR/PRPU PM are analyzed in detail. A new method for motion/force transmission performance evaluation of KR-PMs in accordance with the indices for nonredundant PMs is proposed. Moreover, the local and global motion/force transmission performances of the 2-UPR/PRPU PM are determined using the new method.

Mechanism design and workspace analysis of a hexapod robot

Mobile robots are essential for inspection, surveillance, and disaster relief. The legged robot can adapt to challenging terrains such as stairs and debris. The hexapod robot has better stability, payload capability, and fault-tolerant ability than the biped and quadruped robot. This paper proposes a novel hexapod robot composed of two walking platforms and an actively actuated waist joint. The mechanical topology of the robot is determined by comprehensively considering the walking stability, energy consumption, and operating dexterity. The modular leg mechanism is selected by analyzing the reachable workspaces of three typical 2-DOF parallel leg mechanisms. Besides, the analytical method of calculating the reachable workspace of the robot body with shank-ground interferences is studied for the first time, which helps to enhance the efficiency of foothold selection. The feasibility of integrating the analytical workspace in obstacle-surmounting is verified by climbing a 45-degree staircase. Simulations including avoiding obstacles, spot turning, and climbing a staircase are carried out to verify the correctness of the theoretical analysis. A robot prototype is fabricated, and the field experiments corroborate the results of the computational simulations.

Erratum to “Comparative study on the reachable workspaces of regular and irregular axially symmetric hexapod robots”

Six-legged hexapod walking robots are well-known for their intrinsic stability during navigation and 6-DoF object manipulation. The robot must be operated under a stable workspace envelope to attain effective manipulation. The structural parameters of the robot dramatically influence the characteristics of the workspace. Most studies analyze the workspace only by varying the leg parameter of the robot, maintaining the base configuration constant. This study aims to investigate the effect of change in the base plate characteristics on the workspace for an axially symmetric hexapod robot with cyclic and elliptical configurations. Superimposing the lateral 2D workspace of each pair of legs evolved to obtain a 3D workspace. The quantitative data analysis of the workspace shows that the cyclic configuration has an average increase of 23.74 %, and the elliptical configuration has a reduction of 1.97 % reachable workspace volume compared with regular hexapods. Furthermore, regular, cyclic, and elliptical hexapods are fabricated and validated with the selective workspace analysis data to reinforce the results. This study shows that the change in the hexagonal base plate configuration has a significant influence on workspace characteristics.

Comparative study on the reachable workspaces of regular and irregular axially symmetric hexapod robots

Comparative study on the reachable workspaces of regular and irregular axially symmetric hexapod robots

A Study on the Feasibility of Robotic Harvesting for Chile Pepper

This paper presents a study on the robotic harvesting of New Mexico type chile pepper, in a laboratory setting, using a five degrees of freedom (DoF) serial manipulator. The end-effector of the manipulator, a scissor-type cutting mechanism, was devised and experimentally tested in a lab setup which cuts the chile stem to detach the fruit. Through a MATLAB™-based program, the location of the chile pepper is estimated in the robot’s reference frame, using Intel RealSense Depth Camera. The accuracy of the 3D location estimation system matches the maximum accuracy claimed by the manufacturer of the hardware, with a maximum error to be in Y-axis, which is 5.7 mm. The forward and inverse kinematics are developed, and the reachable and dexterous workspaces of the robot are studied. An application-based path planning algorithm is developed to minimize the travel for a specified harvesting task. The robotic harvesting system was able to cut the chile pepper from the plant based on 3D location estimated by MATLAB™ program. On the basis of harvesting operation, on 77 chile peppers, the following harvesting indicators were achieved: localization success rate of 37.7%, detachment success rate of 65.5%, harvest success rate of 24.7%, damage rate of 6.9%, and cycle time of 7 s.

Analysis of Reachable Workspace for Spatial Three-Cable Under-Constrained Suspended Cable-Driven Parallel Robots

Abstract The workspace is an important reference for designs of cable-driven parallel robots (CDPRs). Most current researches focus on calculating the workspace of redundant CDPRs. However, few literature study the workspaces of under-constrained CDPRs. In this paper, the static equilibrium reachable workspaces (SERWs) of spatial 3-cable under-constrained CDPRs are solved numerically since expressions describing workspace boundaries cannot be obtained in closed forms. The steps to solve the SERWs are as follows. First, expressions that describe the SERWs and their boundaries are proposed. Next, these expressions are instantiated through a novel anchor points model composed of linear equations, quadratic equations, and tension limits in cables. Then, based on the reformulated linearization technique (RLT), the constraints system is transformed into a system containing only linear equality constraints and linear inequality constraints. Finally, the framework of the branch-and-prune (BP) algorithm is adopted to solve this system. The effect of the algorithm is verified by two examples. One is searching the SERWs boundaries of a special three-cable-driven parallel robot (CDPR) whose anchor points layouts both on the moving platform (MP) and on the base are equilateral triangles, followed by a method to extract the SERW boundary where cables do not interfere with each other. The other is searching the SERWs boundaries of a general three-cable CDPR with randomly selected geometry arrangement. The presented method in this paper is universal for calculating the SERWs of spatial three-cable CDPRs with arbitrary geometry parameters.

Planar Variable Structure Cable-Driven Parallel Robots for Circumventing Obstacles

Abstract This article aims to address some of the current limitations of cable-driven parallel robots (CDPRs) by enabling regional changes in dynamic structure through collisions between cables and fixed objects placed in the work area (such as idler pulleys). This leads to the definition of a new class of robots referred to as variable structure cable-driven parallel robots (VSCRs). One of the major advancements from VSCRs is their ability to cover nonconvex reachable workspaces: a significant relaxation on the constraints of traditional CDPRs that is especially useful for circumventing obstacles and has implications for a wide range of applications. Specific examples of vertical farming and rehabilitation are demonstrated experimentally. It is shown that VSCRs can dramatically improve the reachability and accessible workspace of traditional CDPRs. In addition, an online method for solving the planar VSCR inverse kinematics problem is introduced, which is based on an extended cable model. The method is general and has been validated through experimental studies.

Kinematic analysis of a novel 2-PrRS-PR(P)S metamorphic parallel mechanism

Lower mobility parallel mechanisms have been developed in different structures and widely applied in industry, but still have disadvantages in various tasks and functional requirements. A 2-PrRS-PR(P)S metamorphic parallel mechanism with two working configurations and a transiting configuration is presented. First, the architecture and the way of metamorphosis about the mechanism are described in detail. The mobility of the metamorphic parallel mechanism is obtained with screw theory. Furthermore, the parasitic motions in different configurations are derived based on the geometry constraint conditions. Both the inverse kinematic problem and forward kinematic problem of the mechanism are investigated by the closed-loop equation and validated via numerical examples. Then, the velocity and acceleration in two working configurations are obtained by the derivation of the inverse kinematic problem. Finally, the reachable orientation workspaces are discussed using the three-dimensional search method in different configurations. A comparison with the 3-PRS PM without metamorphic mechanism in workspace is presented and an example of the metamorphic parallel mechanism in robotic supporting leg is presented. The above analyses provide theoretical foundations for application of this mechanism.

Kinematic analysis and comparison of a 2R1T redundantly actuated parallel manipulator and its non-redundantly actuated forms

This paper proposes a novel redundantly actuated parallel manipulator (RAPM) with a topology of 2UPR&1RPS&1RPU, which is expected to be designed as a three-degree-of-freedom spindle to construct 5-axis hybrid machining units. First, the mobility of the RAPM is calculated by using screw theory, which indicates that the RAPM possesses two rotational and one translational motion capabilities. By removing a redundantly actuated limb from the chain system, four non-redundantly actuated forms can be obtained. Second, an inverse position analysis and the singularity analysis is carried out to reveal the reachable workspaces of the RAPM and its non-redundantly actuated forms. It is proved the reachable workspace of an RAPM is the intersection set of the reachable workspaces of its non-redundantly actuated forms. Third, a set of new kinematic indices are proposed to evaluate the RAPM's dexterity. With this index framework, the dexterity of the RAPM and its non-redundantly actuated forms are obtained and compared, showing that the RAPM has better dexterity and more uniform distribution than its non-redundantly actuated forms throughout the reachable workspace. Last, two types of 5-axis hybrid machining units that incorporate the proposed RAPM are constructed to implement high-speed machining for large-scale components and small precision parts.

Reachable workspace determination for a spatial hyper-redundant manipulator formed by several parallel manipulators

Solving the reachable workspaces of spatial hyper-redundant manipulators (SHRMs) formed by serially connected parallel manipulators is an important and challenging work. This study addresses the issue on reachable workspaces and establishes a novel CAD-VBbased workspace determination system for determining the reachable workspaces of SHRMs. The reachable workspace determination of a novel (3-RPS)+(3-SPR)+(3-RPS) SHRM, a triple delta-type SHRM, and a novel (3-RRS)+(3-SPR)+(3-RRS) SHRM shows the generality and effectiveness of the proposed approach. The system proposed in this study can contribute to reachable workspace analysis for SHRMs.

A compact 3-DOF shoulder mechanism constructed with scissors linkages for exoskeleton applications

A novel 3-degrees-of-freedom (DOF) spherical mechanism, singularity-free in the anatomical shoulder joint workspace, is described. The use of curved scissors linkages interconnected by revolute joints, whose axes share the same remote centre-of-motion, achieves the most compact design of its kind. The kinematics of this scissors shoulder mechanism (SSM) are derived and presented. A design equation restricting the linkage's curvature by the central/pitch angle of the fully stretched scissors is obtained. Motion-captured data are used for validating the reachable 3-d workspace while a test-subject is wearing a null protraction/retraction constrained exoskeleton. The embodiment of the SSM as a shoulder joint for an exoskeleton device does not compromise the upper extremity function within the anatomical reachable 3-d workspace. It operates within a volume of 0.236 m3, corresponding to 68.09% and 94.97% of the volumes of the full active (0.350 m3) and null protraction/retraction constrained active (0.223 m3) reachable workspaces of the test-subject, respectively. Thus, the SSM represents a simplification of a spatial spherical mechanism design and overcomes the need for the use of redundant links and optimization routines.

Auto-establishing simulation parallel manipulators with linear legs and auto-solving their workspaces by utilizing CAD variation geometry

A new approach of CAD variation geometry is proposed for automatically establishing the simulation mechanisms of parallel manipulators (PMs) with linear legs, and automatically solving their forward displacements, workspaces, and Euler angles. First, the basic concepts and techniques of the CAD variation geometry are described. Second, a program is developed by utilizing new approach. In the developed software, an interface is constructed for inputting given parameters and outputting solved results of data and graphs, several sub-programs are compiled for automatically establishing various simulation mechanisms, solving the forward displacements, and solving/displaying reachable workspaces and Euler angles of various PMs. Third, the three novel and five existing different PMs are illustrated. When the given parameters of the PMs into the interface are inputted, their simulation mechanisms are established automatically. The displacements, the reachable workspaces, and the Euler angles are solved automatically. Finally, the solved results of the developed software are verified by that of the analytic solutions of several existing PMs and the simulation solutions of several novel PMs.

Geometry-Based Trajectory Planning of a 3-3 Cable-Suspended Parallel Robot

This paper addresses the dynamic trajectory planning of a spatial cable-suspended parallel robot with three cables and three-degree-of-freedom. A new $s-\ddot{s}$ plane ( $s$ is the path parameter) method is presented to devise dynamically feasible point-to-point trajectories and periodic trajectories that are not fully located in the static workspace (SW) of the robot. First, the unilateral cable tension constraints are explicitly converted into geometry constraints in the $s-\ddot{s}$ plane. Then, a set of reachable workspaces is defined, which can be obtained analytically and the volumes of which are all much larger than the volume of the SW. By designing dynamic point-to-point trajectories directly in the $s-\ddot{s}$ plane, any points in the reachable workspaces can be reached in sequence via some intermediate points in the SW. The $s-\ddot{s}$ plane method also offers insights into planning periodic circular trajectory and transition trajectory for oscillations along a straight line, which is considered to be more efficient than the algebraic method provided in the literature. The proposed method always guarantees positive and continuous cable tensions and yields analytical results. The performance of the method is evaluated through numerical simulations and experiments.

Trajectory Tracking of a Planer Parallel Manipulator by Using Computed Force Control Method

Despite small workspace, parallel manipulators have some advantages over their serial counterparts in terms of higher speed, acceleration, rigidity, accuracy, manufacturing cost and payload. Accordingly, this type of manipulators can be used in many applications such as in high-speed machine tools, tuning machine for feeding, sensitive cutting, assembly and packaging. This paper presents a special type of planar parallel manipulator with three degrees of freedom. It is constructed as a variable geometry truss generally known planar Stewart platform. The reachable and orientation workspaces are obtained for this manipulator. The inverse kinematic analysis is solved for the trajectory tracking according to the redundancy and joint limit avoidance. Then, the dynamics model of the manipulator is established by using Virtual Work method. The simulations are performed to follow the given planar trajectories by using the dynamic equations of the variable geometry truss manipulator and computed force control method. In computed force control method, the feedback gain matrices for PD control are tuned with fixed matrices by trail end error and variable ones by means of optimization with genetic algorithm.

Kinematic Performances of a Novel TLPM Parallel Robot

This paper investigates the kinematic performances of kinematics, Jacobian, singularity and interferences of a novel six-degree-of freedom (DOF) parallel manipulator. Analytical solutions of the forward position kinematics have been worked out. Three-dimensional Cartesian space generated by a stroke interval from lmin to lmax fulfils the point workspace are illustrated, and the reachable workspaces are obtained. The notion of pure translational Jacobian of constraint matrix is introduced, and two types of conventional singularities are analyzed. Finally, auxiliary vectors are introduced to determine the link interferences, shown that there are two kinds of interferences in the system, one is angle-interference in one limb, and the other is distance-interference in adjacent limbs.

On the dynamics and control of flexible joint space manipulators

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both in the manipulator and the spacecraft making the positioning of the end-effector very difficult. Here, both types of flexibilities are lumped at the joints and the dynamic equations of a general flexible joint space manipulator are derived. Their internal structure is highlighted and similarities and differences with fixed-base robots are discussed. It is shown that one can exploit the derived dynamic structure in order to design a static feedback linearization control law and obtain an exact linearization and decoupling result. The application of such controllers is desired in space applications due to their small computational effort. In case of fixed-base manipulators, the effective use of a static feedback controller is feasible only if a simplified model is considered. Then, the proposed static feedback linearization control law is applied to achieve end-effector precise trajectory tracking in Cartesian space maintaining a desirable non-oscillatory motion of the spacecraft. The application of the proposed controller is illustrated by a planar seven degrees of freedom (dof) system.

Upper extremity 3-dimensional reachable workspace analysis in dystrophinopathy using Kinect.

An innovative upper extremity 3-dimensional (3D) reachable workspace outcome measure acquired using the Kinect sensor is applied toward Duchenne/Becker muscular dystrophy (DMD/BMD). The validity, sensitivity, and clinical meaningfulness of this novel outcome measure are examined. Upper extremity function assessment (Brooke scale and NeuroQOL questionnaire) and Kinect-based reachable workspace analyses were conducted in 43 individuals with dystrophinopathy (30 DMD and 13 BMD, aged 7-60 years) and 46 controls (aged 6-68 years). The reachable workspace measure reliably captured a wide range of upper extremity impairments encountered in both pediatric and adult, as well as ambulatory and non-ambulatory individuals with dystrophinopathy. Reduced reachable workspaces were noted for the dystrophinopathy cohort compared with controls, and they correlated with Brooke grades. In addition, progressive reduction in reachable workspace correlated directly with worsening ability to perform activities of daily living, as self-reported on the NeuroQOL. This study demonstrates the utility and potential of the novel sensor-acquired reachable workspace outcome measure in dystrophinopathy.