Planar Manipulator Research Articles

Motion planning of planar and redundant underwater serial link manipulator based on minimization of energy consumption

Motion planning of planar and redundant underwater serial link manipulator based on minimization of energy consumption

Workspace Boundary Estimation for Soft Manipulators Using a Continuation Approach

Considering a soft manipulator configuration, controlled via installed bounded actuators, this paper addresses the end-effector workspace estimation problem for such a soft robot. For this, the Discrete Cosserat method is adopted to deduce the mathematical model of soft manipulators, based on which a continuation method that accounts for simple and multiple bifurcation points to solution curves is developed to map its workspace boundaries. Difficulties encountered in calculating tangents at simple and multiple bifurcation points are studied, and an efficient solution is provided. Numerical simulations applied to planar and spatial soft manipulator configurations are presented to emphasize the validity of the proposed methodology.

Continuous Control Strategy of Planar 3-Linkage Underactuated Manipulator Based on Broad Neural Network

For the position control of a planar 3-linkage underactuated manipulator (PTUM) with a passive first linkage, a continuous control strategy is developed in this paper. In particular, a broad neural network (BNN)-based model is first established to accurately describe the motion coupling relationship between the passive linkage and the second linkage. Based on this model, by using the particle swarm optimization algorithm, the target angles of all linkages are calculated combining the start states of all linkages and the target position of the PTUM. Then, the target angles of the active linkages are directly achieved by their respective actuators, and that of the passive linkage is also achieved by the rotation of the second linkage. By carrying out several experiments, the effectiveness of the above strategy is verified.

Analysis of Singular Configuration of Robotic Manipulators

Robotic manipulators inevitably encounter singular configurations in the process of movement, which seriously affects their performance. Therefore, the identification of singular configurations is extremely important. However, serial manipulators that do not meet the Pieper criterion cannot obtain singular configurations through analytical methods. A joint angle parameterization method, used to obtain singular configurations, is here creatively proposed. First, an analytical method based on the Jacobian determinant and the proposed method were utilized to obtain their respective singular configurations of the Stanford manipulator. The singular configurations obtained through the two methods were consistent, which suggests that the proposed method can obtain singular configurations correctly. Then, the proposed method was applied to a seven-degree-of-freedom (7-DOF) serial manipulator and a planar 5R parallel manipulator. Finally, the correctness of the singular configurations of the 7-DOF serial manipulator was verified through the shape of the end-effector velocity ellipsoid, the value of the determinant, the value of the condition number, and the value of the manipulability measure. The correctness of singular configurations of the planar 5R parallel manipulator was verified through the value of the determinant, the value of the condition number, and the value of the manipulability measure.

Acoustophoretic patterning of microparticles in a microfluidic chamber driven by standing Lamb waves

The contactless manipulation of microparticles and cells by using acoustic forces is important in many applications. However, multi-band acoustophoresis has been rarely investigated in the literature. In this Letter, we propose a microscale acoustofluidic system that has multiple orders of available Lamb modes for the acoustic trapping of microparticles at various frequencies. In our device, standing Lamb waves (SLWs) of specific orders can be selectively excited in a 300-μm-thick piezoelectric lithium-niobate (LiNbO3) crystal plate by a pair of interdigitated transducers (IDTs) at the corresponding frequency. We demonstrate the acoustophoretic trapping and patterning of 7-μm particles in a single acoustofluidic device with multiple available actuating frequencies. The approach to the proposed design and the working mechanisms are explained by using thin plate and a full-wave models that solve the dispersion relations and coupling fields of the piezoelectric SLW acoustofluidic system, respectively. Furthermore, we experimentally show that the stable and tight trapping of particles in the chamber can be achieved independently along two mutually orthogonal directions. This provides the essential ground for planar manipulations of microparticles and cells based on the proposed device. The results here can trigger more innovative designs and applications of acoustofluidic devices for microparticle manipulation and microfluidic mixing, with multi-frequency channels and a wide span of different actuating frequencies in one system.

The method of task-driven structural synthesis for the creative design of the planar manipulator

In this paper, a new structural design method based on MATLAB is developed for the configuration design and optimization of real-life planar manipulators in the high-speed press line. To explore planar manipulators with better performance, the developed method provides a suite of analysis procedures including demonstrating structural synthesis in graph theory, building conversion relations between different models, and generating new configurations of the planar manipulator. In the structural synthesis, the whole family of non-isomorphism planar 8-link kinematic chains with up to 3 prismatic pairs is generated, which lays a solid foundation for the generation of new configurations of planar manipulators. Under the expected requirements and constraints, the original planar manipulator is compared with new planar manipulators in which the developed method. The result shows that the developed method of task-driven structural synthesis is effective in generating configurations of planar manipulators and enriches related research of structural design and optimization in the field.

Tetrabenzo[a,c]phenazine Backbone for Highly Efficient Orange–Red Thermally Activated Delayed Fluorescence with Completely Horizontal Molecular Orientation

AbstractThree thermally activated delayed fluorescence (TADF) molecules, namely PQ1, PQ2, and PQ3, are composed of electron‐accepting (A) tetrabenzo[a,c]phenazine (TBPZ) and electron‐donating (D) phenoxazine (PXZ) units are designed and characterized. The combined effects of planar acceptor manipulation and high steric hindrance between D and A units endow high molecular rigidity that suppresses nonradiative decay of the excitons with improved photoluminescence quantum yields (PLQYs). Particularly, the well‐aligned excited states involving a singlet and a triplet charge‐transfer excited states and a localized excited triplet state in PQ3 enhances the reverse intersystem crossing rate constant (kRISC) with a short delay lifetime (τd). The orange–red OLED based on PQ3 displays a maximum external EL quantum efficiency (EQE) of 27.4 % with a well‐suppressed EL efficiency roll‐off owing to a completely horizontal orientation of the transition dipole moment in the film state.

Tetrabenzo[a,c]phenazine Backbone for Highly Efficient Orange-Red Thermally Activated Delayed Fluorescence with Completely Horizontal Molecular Orientation.

Three thermally activated delayed fluorescence (TADF) molecules, namely PQ1, PQ2, and PQ3, are composed of electron-accepting (A) tetrabenzo[a,c]phenazine (TBPZ) and electron-donating (D) phenoxazine (PXZ) units are designed and characterized. The combined effects of planar acceptor manipulation and high steric hindrance between D and A units endow high molecular rigidity that suppresses nonradiative decay of the excitons with improved photoluminescence quantum yields (PLQYs). Particularly, the well-aligned excited states involving a singlet and a triplet charge-transfer excited states and a localized excited triplet state in PQ3 enhances the reverse intersystem crossing rate constant (kRISC ) with a short delay lifetime (τd ). The orange-red OLED based on PQ3 displays a maximum external EL quantum efficiency (EQE) of 27.4 % with a well-suppressed EL efficiency roll-off owing to a completely horizontal orientation of the transition dipole moment in the film state.

Actuation and Motion Control of Flexible Robots: Small Deformation Problem

AbstractThis paper introduces a new computational approach for the articulated joint/deformation actuation and motion control of robot manipulators with flexible components. Oscillations due to small deformations of relatively stiff robot components which cannot be ignored, are modeled in this study using the finite element (FE) floating frame of reference (FFR) formulation which employs two coupled sets of coordinates: the reference and elastic coordinates. The inverse dynamics, based on the FFR formulation, leads to driving forces associated with the deformation degrees of freedom. Because of the link flexibility, two approaches can be considered to determine the actuation forces required to achieve the desired motion trajectories. These two approaches are the partially constrained inverse dynamics (PCID) and the fully constrained inverse dynamics (FCID). The FCID approach, which will be considered in future investigations and allows for motion and shape control, can be used to achieve the desired motion trajectories and suppress undesirable oscillations. The new small-deformation PCID approach introduced in this study, on the other hand, allows for achieving the desired motion trajectories, determining systematically the actuation forces and moments associated with the robot joint and elastic degrees of freedom, and avoiding deteriorations in the vibration characteristics as measured by the differences between the inverse- and forward-dynamics solutions. A procedure for determining the actuation forces associated with the deformation degrees of freedom is proposed and is exemplified using piezoelectric actuators. The PCID solution is used to define a new set of algebraic equations that can be solved for the piezoelectric actuation voltages required to maintain the forward-dynamics oscillations within their inverse-dynamics limits. A planar two-link flexible-robot manipulator is presented to demonstrate the implementation of the joint/deformation actuation approach. The results obtained show deterioration in the robot precision if the deformation actuation is not considered.

A Novel Manipulation Technique for Lapidus Fusion in Correction of Hallux Valgus Deformity With Underlying Metatarsus Adductus: A Case Series

Underlying metatarsus adductus (MA) is commonly seen in patients with hallux valgus (HV) deformity, with implications regarding procedure selection and hallux valgus recurrence. Lapidus, or first tarsometatarsal fusion, is commonly performed allowing reduction in intermetatarsal angle (IMA) but this procedure has not been established as an approach to provide partial correction of MA deformity. Retrospective assessment of preoperative and postoperative metatarsus adductus angle (MAA), IMA and hallux abductus angle (HAA) in patients treated with Lapidus fusion for HV. Significance was determined via paired t test with a p value of <.05. All cases involved manual transverse plane manipulation to reduce both IMA and MAA during screw insertion. Intermetatarsal angle and Engel's angle were measured on preoperative AP radiographs to determine the presence of underlying MA in patients undergoing Lapidus fusion for HV. Ten weeks and 1 year postoperative radiographs were measured to determine degree of correction of IMA, HAA, and MAA. Thirty-four patients met inclusion criteria, which is approximately 46% of our sample population. The average preoperative IMA was 19.4˚ (range 12-32) and the average postoperative IMA was 9.7˚ (range 6-14). The average preoperative Engel's angle was 27.4˚ (range 24-34) and the average postoperative Engel's angle was 22.6˚ (range 15-28) with mean improvement in MA of 6.6˚. Of the 34, 27 (79.4%) patients had a normal Engel's angle at 10 weeks postoperatively. All measures of change met level of significance (p < .05). Of the 34 patients, 21 had radiographs taken beyond the 1 year mark (average 53 weeks). These patients were found to have an average Engel's angle of 23.0˚, which is not statistically significantly different from their 10 week measurements. Of the 21 patients, 17 (81%) maintained normal Engel's angle past 1 year. Metatarsus adductus varies regarding degree of reducibility and complicates preoperative angular measurement and correction of HV. Based on these findings, we recommend Lapidus fusion using this specified manipulation technique to obtain comprehensive transverse plane correction.

A novel hybrid Zhang neural network model for time-varying matrix inversion

A new hybrid Zhang neural network (HZNN) model is formulated to solve time-varying matrix inversion problem. The network is designed such that it encompasses the goodness of both gradient neural network (GNN) and Zhang neural network (ZNN). The stability of the network and convergence results are established theoretically. The rate of convergence of HZNN model is much faster compared to the classical GNN model and ZNN model for time-varying matrix inversion problem. Nonlinear activation functions for HZNN need not have to be odd and monotonically increasing for the network to converge, however with certain restrictions. Simulations are carried out to test the efficiency of HZNN over GNN and ZNN. Also, HZNN with odd and non-odd activation functions are examined for convergence. It is observed that the network converges much faster with the proposed non-odd function 3 (nof3). Furthermore, the HZNN model with odd and non-odd functions are applied to the kinematic control of a two-link planar manipulator for tracking a circular path.

Predictive Trajectory Tracking Algorithm of Underactuated Systems Based on the Calculus of Variations

Abstract The tracking control of underactuated systems is a challenging problem due to the structural differences compared to fully actuated systems. Contrarily to fully actuated systems, resolving the inverse kinematics problem of underactuated systems is not possible independently from the dynamic equations. Instead, the inverse dynamics must be addressed. It is common to extend the computed torque control (CTC) technique with servoconstraints. Besides the CTC's clearness, the stability of the system cannot be always guaranteed. A novel predictive controller (PC) is presented in this paper. Our PC applies the variational principle to design the motion of the system in order to achieve a stable motion with the lowest possible tracking error. To demonstrate the applicability and the performance of the PC method, a numerical study is presented for a planar manipulator resulting in about 20% RMS error compared to the CTC method from the literature.

Adaptive Obstacle Avoidance for a Class of Collaborative Robots

In a human–robot collaboration scenario, operator safety is the main problem and must be guaranteed under all conditions. Collision avoidance control techniques are essential to improve operator safety and robot flexibility by preventing impacts that can occur between the robot and humans or with objects inadvertently left within the operational workspace. On this basis, collision avoidance algorithms for moving obstacles are presented in this paper: inspired by algorithms already developed by the authors for planar manipulators, algorithms are adapted for the 6-DOF collaborative manipulators by Universal Robots, and some new contributions are introduced. First, in this work, the safety region wrapping each link of the manipulator assumes a cylindrical shape whose radius varies according to the speed of the colliding obstacle, so that dynamical obstacles are avoided with increased safety regions in order to reduce the risk, whereas fixed obstacles allow us to use smaller safety regions, facilitating the motion of the robot. In addition, three different modalities for the collision avoidance control law are proposed, which differ in the type of motion admitted for the perturbation of the end-effector: the general mode allows for a 6-DOF perturbation, but restrictions can be imposed on the orientation part of the avoidance motion using 4-DOF or 3-DOF modes. In order to demonstrate the effectiveness of the control strategy, simulations with dynamic and fixed obstacles are presented and discussed. Simulations are also used to estimate the required computational effort in order to verify the transferability to a real system.

Dynamic Modeling of Planar Multi-Link Flexible Manipulators

A closed-form dynamic model of the planar multi-link flexible manipulator is presented. The assumed modes method is used with the Lagrangian formulation to obtain the dynamic equations of motion. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The eigenvalue problem associated with the mass boundary conditions, which changes with the robot configuration and payload, is discussed. The time-domain simulation results and frequency-domain analysis of the dynamic model are presented to show the validity of the theoretical derivation.

Computation of the Available Force Set of a 3-RPRR Kinematically-Redundant Planar Parallel Manipulator

Abstract An algorithm is developed to determine the Available Force Set (AFS) of the 3-RPRR kinematically-redundant planar parallel manipulator. The results of the algorithm are verified against a brute force approach and are found to yield exact results with significantly less computational time. The use of the AFS in a robot design context is illustrated through the analysis of two performance indices: the maximum pure force capable of being applied in any direction and the maximum pure force capable of being applied in a given direction. The algorithm is used to compute the AFS and the performance indices throughout the 3-RPRR robot's workspace. The proposed methodology is a useful tool for the design and analysis of the 3-RPRR robot and could be adapted to other kinematically-redundant planar parallel manipulators.

Decentralized Adaptive Control for Collaborative Manipulation of Rigid Bodies

In this work, we consider a group of robots working together to manipulate a rigid object to track a desired trajectory in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{SE}(3)$</tex-math></inline-formula> . The robots do not know the mass or friction properties of the object, or where they are attached to the object. They can, however, access a common state measurement, either from one robot broadcasting its measurements to the team, or by all robots communicating and averaging their state measurements to estimate the state of their centroid. To solve this problem, we propose a decentralized adaptive control scheme wherein each agent maintains and adapts its own estimate of the object parameters in order to track a reference trajectory. We present an analysis of the controller’s behavior, and show that all closed-loop signals remain bounded, and that the system trajectory will almost always (except for initial conditions on a set of measure zero) converge to the desired trajectory. We study the proposed controller’s performance using numerical simulations of a manipulation task in 3-D, as well as hardware experiments which demonstrate our algorithm on a planar manipulation task. These studies, taken together, demonstrate the effectiveness of the proposed controller even in the presence of numerous unmodeled effects, such as discretization errors and complex frictional interactions.

A Study on Clearance Effects on Dynamic Responses of Robot Manipulator

Clearances caused by assemblage, manufacturing errors and wear, affect inevitably the dynamic responses of mechanisms such as robot manipulator. In this study, the effects of clearance on a robot manipulator system are investigated numerically. The contact behavior along normal and tangential direction of clearance joint is described by a nonlinear contact force model and a modified Coulomb friction model respectively. Then, the dynamics equations of the robot manipulator system are established considering joint clearance. In order to investigate the effects of clearance on dynamic performances of practical mechanism, a planar robot manipulator system on a spacecraft system with a revolute clearance joint is used as the apply example. Four case studies for various clearance sizes are implemented to investigate and discuss the effects of joint clearance. The simulation results indicate that clearance joints have severe effects on the dynamic performances of mechanism system and the impact in clearance joints represented by contact force models must be considered in dynamics analysis and design of mechanism system. The simulation results in this work can predict the effects of clearance on robot manipulator system preferably and it is the basis of precision analysis, robust control system design of robot manipulator system.

Inverse dynamics of underactuated planar manipulators without inertial coupling singularities

In this paper, we present a model for the inverse dynamics of underactuated manipulators that is free from inertial coupling singularities. The framework’s main idea is to include a small-amplitude wave on the trajectory of the rotating active joints. First, we derive the modified nonlinear dynamics for the multijoint manipulators with multiple degrees-of-freedom (DoF). Next, a 4-DoF mass-rotating underactuated manipulator with two passive and two active joints is chosen. Then, a condition assuming the positive definiteness of the inertia matrix is developed to have the singularity-free inverse dynamics. Finally, we analytically study how singularities can be avoided and show an example simulation with a feed-forward control at the singular configuration.

Design and kinematic analysis of a novel rehabilitative robotic walking simulation device.

This paper presents an original rehabilitative robotic walking simulation device. As a novel feature, it can duplicate the walking motion of the feet completely by including the motion of the metatarsophalangeal joints as well. It is also adjustable to different foot sizes and gait parameters such as speed, step length, and foot elevation. The presented device comprises two identical mechanisms that simulate the right and left feet. Each mechanism is designed as a planar parallel manipulator with three degrees of freedom and thus its platform (i.e. foot plate) can duplicate the sagittal-plane motion of a foot completely. A prototype of the device is already built, patented, and tested by several people, two of whom are physiotherapists. In the paper, the inverse and forward kinematic analyses of each parallel manipulator are also presented. The inverse kinematic analysis is carried out based on a typical gait cycle data of a healthy person gathered from the related literature. The results of the inverse kinematic analysis are then used as reference trajectory data in testing the device with different healthy people at different speeds.

Workspace analysis of 3-DOF U-shape base planar parallel robotic motion stage using shape memory alloy restoration technique (SMART) linear actuators

The applications of lightweight planar parallel robotic manipulators are increasing enormously because of its various desirable characteristics such as low weight, lower inertia and higher stiffness. Higher accelerations and accuracies can be achieved in planar parallel manipulators. Also, shape memory alloy restoration technique (SMART)-based linear actuators are replacing huge and bulky linear actuators. This study presents the kinematic design of smart linearly actuated family of U-shape base planar parallel robotic manipulator. With the aid of solid modelling software, different available configurations were modelled and their workspace was analysed. The developed 3-DOF motion stages (18 unique configurations) were fabricated using fused deposition modelling process, and the top three configurations having higher workspace were further experimented. It is interesting to observe that the actual or experimental workspace of a particular manipulator configuration is further minimised from the predicted or feasible workspace. It is due to the presence of passive links, singularities, friction between the parts, heat dissipation, force distribution, stiffness, etc. The present study depicts the experimental workspace of the top three configurations, namely PPR-PRP-PRR, PRP-PPR-PRP and PRP-PPR-PRR. Since none of the experimental workspace observed is equal or higher than the model workspace, an efficiency loss in terms of workspace reduction was calculated to understand the acceptability of the configurations in different domains. Apart from the loss, the result disclosed that the actual workspace of all the manipulators was within the feasible workspace domain of mobile platform. The PPR-PRP-PRR manipulator was found to possess highest experimental workspace than other configurations. Note: P, P, and R refer to active prismatic, passive prismatic and passive revolute joints respectively.