Serial Manipulators Research Articles

Kinematic Reliability of Manipulators Based on an Interval Approach

Robotic manipulators inevitably experience the impact of uncertainties and errors, such as dimensional tolerances and joint clearances. Therefore, this paper proposes a novel method based on an interval approach to evaluate the kinematic reliability of manipulators. Kinematic reliability quantifies the probability of positioning errors that fall within allowable boundaries. As a result, reliability evaluates the probability that the interval end-effector error produced by dimensional tolerances exceeds an acceptable rate. The proposed reliability index is based on the interval error that conveys an alternative approach to the kinematic reliability methods based on probabilistic frameworks reported in the literature based on probabilistic approaches. The obtained numerical results demonstrate the viability of the proposed methodology by evaluating the reliability of a serial manipulator subjected to joint clearances and a parallel manipulator with dimensional tolerances.

Automatic differential kinematics of serial manipulator robots through dual numbers

Dual Numbers are an extension of real numbers known for its capability of performing exact automatic differentiation of one-valued functions theoretically without error approximation. Also, Differential Kinematics of robots involves the computation of the Jacobian, which is a matrix of partial derivatives of the Forward Kinematic equations with respect to the robot’s joints. Thus, to perform the automatic calculation of the Jacobian matrix, this paper presents an extension of dual numbers composed of a scalar real part and a vector dual part, where the real part represents the angular value of the robot joint, and the dual part represents the direction of the corresponding partial derivative for each joint. The presented method was implemented in Matlab through Object Orientes Programming (OOP), and the results for calculating the Jacobian of the KUKA KR 500 robot model for 1000 random postures were subsequently compared in terms of execution time and Mean Squared Error (MSE) with other conventional methods: the geometric method, the symbolic method, and the finite difference method. The results showed a significant improvement in the computing time for calculating the Jacobian of the robotic model compared to the other methods, as well as a minimum MSE having as reference the numerical value of the symbolic calculations.

A Screw Theory Approach for Instantaneous Kinematic Analysis of Parallel–Serial Manipulators

Abstract The paper presents an approach to perform an instantaneous kinematic analysis of parallel–serial (hybrid) manipulators using screw theory. In this study, we focus on non-kinematically redundant manipulators that include a single parallel mechanism. The proposed systematic procedure allows deriving Jacobian matrices for such manipulators, which provide mathematical relations between the end-effector velocities and speeds in the actuated joints. A generalized structure of the obtained matrices also reflects the constrained motions of the end-effector and the parallel mechanism. To illustrate the developed techniques, we consider three examples where we analyze three well-known parallel–serial manipulators with six, five, and four degrees-of-freedom. Following the proposed method, we determine Jacobian matrices for each manipulator. Next, we apply the presented approach for velocity analysis of a novel parallel–serial manipulator with five degrees-of-freedom. Numerical simulations validate the proposed theoretical techniques. The suggested approach represents the basis for subsequent singularity and performance analysis, and it can be adapted to hybrid manipulators with other architectures.

A passive convex optimal control algorithm for teleoperating a redundant robotic arm in minimally invasive surgery

AbstractIn recent years, the remote center of motion (RCM) constraint has moved from purely mechanical to software implementation, enabling the use of serial manipulators in robotic‐assisted minimal invasive surgery. However, ensuring safety with software‐based RCM presents challenges. This article addresses this issue by introducing a novel control algorithm for a 7‐DOF redundant robotic arm, taking into account a software RCM while considering system passivity and kinematic constraints. The algorithm is both a control optimizer and a robot kinematics inversion, enabling precise and dexterous control for various surgical tasks and other control applications. By formulating a quadratic optimization problem under linear constraints, the algorithm guarantees the robotic arm's performance, safety, and stability under communication delay. Experimental validation demonstrates the effectiveness and accuracy of the control algorithm in executing a surgical training task (peg‐and‐ring) during bilateral teleoperation. The results highlight the successful implementation of the RCM constraint, ensuring patient safety and optimizing the manipulation capabilities of the robotic arm.

Serial metamorphic manipulator dynamics formulation implementing screw theory tools

Abstract In this work, a framework is proposed for the analytical formulation of dynamic equations for serial metamorphic manipulators using screw theory tools. The integration of structure reconfiguration is achieved in a compact and comprehensive manner. Based on the previously proposed Modular Structure Representation, additional statements are provided to strictly define the metamorphic structure assembly. To validate the precision of the extracted dynamics, two simulations are performed for paths defined in cartesian space. The generated trajectory is evaluated by comparing the dynamic matrices produced by the proposed method with those from an established dynamic modeling algorithm. Additionally, the trajectory is simulated in an open-source simulator, and the torques extracted from system dynamics are compared with the corresponding simulator torques under the same kinematic constraints.

Patch-free streaming contrast-rebalanced dichoptic cartoons versus patching for treatment of amblyopia in children aged 3 to 5 years: a pilot, randomized clinical trial

BackgroundWe developed and tested a dichoptic treatment designed for younger children that can be viewed freely and involves a dichoptic manipulation of a popular animation series that enables contrast-rebalancing without disrupting fusion. Our aim was to assess whether this novel amblyopia treatment is superior to patching in children aged 3-5 years. MethodsA total of 34 children with amblyopia were randomly assigned to contrast-rebalanced dichoptic cartoons (4 hours/week) or patching (14 hours/week) for 2 weeks. Children in the cartoon group continued watching cartoons for an additional 2 weeks. Designed to target the youngest and most treatable children, the dichoptic cartoons presented the entire scene to the amblyopic eye at 100% contrast, while the fellow eye view was presented at reduced contrast with the main character omitted. Best-corrected visual acuity (BCVA), stereoacuity, suppression, and manual dexterity were measured at each visit. ResultsAfter 2 weeks, improvement in amblyopic eye BCVA was greater for dichoptic treatment than for patching, with a mean improvement of 0.11 ± 0.08 versus 0.06 ± 0.09 logMAR, respectively (P = 0.04). Stereoacuity, suppression, and manual dexterity did not improve significantly more in the dichoptic group than the patching group at 2 weeks. After 4 weeks of dichoptic cartoon treatment, mean visual acuity improvement in the dichoptic group was 0.16 logMAR (95% CI, 0.10-0.21). ConclusionsIn our study cohort, a contrast-rebalanced dichoptic cartoon was more effective than patching in treating childhood amblyopia after 2 weeks. Dichoptic cartoons that rebalance contrast to overcome suppression provide an additional treatment option for amblyopia in young children.

Simple Inverse Kinematics Computation Considering Joint Motion Efficiency.

Inverse kinematics (IK) is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple IK calculation scheme for an industrial serial manipulator. The proposed technique can calculate appropriate values of the joint variables to realize the desired end-effector position and orientation while considering the motion costs of each joint. Two scalar functions are defined for the joint variables: one is to evaluate the end-effector position and orientation, whereas the other is to evaluate the motion efficiency of the joints. By combining the two scalar functions, the IK calculation of the manipulator is formulated as a numerical optimization problem. Furthermore, a simple algorithm for solving the IK via the aforementioned optimization is constructed on the basis of the simultaneous perturbation stochastic approximation with a norm-limited update vector (NLSPSA). The proposed scheme considers not only the accuracy of the position and orientation of the end-effector but also the efficiency of the robot movement. Therefore, it yields a practical result of the inverse problem. Moreover, the proposed algorithm is simple and easy to implement owing to the high-calculation efficiency of NLSPSA. Finally, the effectiveness of the proposed method is verified through numerical examples using a redundant manipulator.

Task and motion planning using mixed integer linear programming for solving fetch-and-carry tasks by a mobile manipulator

This manuscript describes a TAsk and Motion Planning (TAMP) method for mobile manipulators. We focus on fetch-and-carry tasks, and we aim to simultaneously generate both a sequence of actions and a motion sequence for each action. The number of factors to be considered in solving such a problem, and the interactions among them are complex due to the multifaceted characteristics of mobile manipulation. As a result, straightforwardly performing simultaneous TAMP may require a significant amount of processing time. Therefore, we reduce the complexity of the problem by formulating fetch-and-carry planning for a Mixed Integer Linear Programming (MILP) problem. The proposed method can obtain the sequence of actions and the movement of the mobile manipulator in less than one second in many cases. The effectiveness of the proposed method is verified in environments in which delivery objects and obstacles are placed in various patterns, using a robot with an omnidirectional mobile platform and a serial link manipulator.

A dynamic identification method for general serial manipulators from an analytical perspective based on Lie theory

A dynamic identification method for general serial manipulators from an analytical perspective based on Lie theory

Automatic robotic doppler sonography of leg arteries

PurposeRobot-assisted systems offer an opportunity to support the diagnostic and therapeutic treatment of vascular diseases to reduce radiation exposure and support the limited medical staff in vascular medicine. In the diagnosis and follow-up care of vascular pathologies, Doppler ultrasound has become the preferred diagnostic tool. The study presents a robotic system for automatic Doppler ultrasound examinations of patients’ leg vessels.MethodsThe robotic system consists of a redundant 7 DoF serial manipulator, to which a 3D ultrasound probe is attached. A compliant control was employed, whereby the transducer was guided along the vessel with a defined contact force. Visual servoing was used to correct the position of the probe during the scan so that the vessel can always be properly visualized. To track the vessel’s position, methods based on template matching and Doppler sonography were used.ResultsOur system was able to successfully scan the femoral artery of seven volunteers automatically for a distance of 20 cm. In particular, our approach using Doppler ultrasound data showed high robustness and an accuracy of 10.7 (±3.1) px in determining the vessel’s position and thus outperformed our template matching approach, whereby an accuracy of 13.9 (±6.4) px was achieved.ConclusionsThe developed system enables automated robotic ultrasound examinations of vessels and thus represents an opportunity to reduce radiation exposure and staff workload. The integration of Doppler ultrasound improves the accuracy and robustness of vessel tracking, and could thus contribute to the realization of routine robotic vascular examinations and potential endovascular interventions.

A multi-objective trajectory planning approach for vibration suppression of a series–parallel hybrid flexible welding manipulator

Although the series–parallel hybrid welding manipulator has advantages over the traditional series manipulator, its must run continuously and smoothly according to a specific trajectory at the rated velocity. Considering a flexible manipulator with a complex series–parallel hybrid structure as the research object, this paper proposes a multi-objective approach to indirectly suppress the vibration. In view of the complex flexible mechanism with a multi-kinematic pair arrangement and a multi-motor drive, a system comprehensive elastodynamics model is established, and the effectiveness of the model is verified through the hammer test method. To achieve synchronous and coordinated planning of the end position and attitude, the spatial arc welding trajectory is planned on the basis of the synchronous planning controller and the dual-S velocity profile interpolation function. Then, a multi-objective optimization model considering the travel time, energy consumption and terminal amplitude fluctuations is proposed, the trajectory planning problem is transformed into a parameter optimization problem in the interpolation function, and then the elite non-dominated sorting genetic algorithm (NSGA-II) is employed to determine the optimal trajectory. The optimal trajectory thus obtained effectively suppresses the vibration of the system. Finally, compared with the classic fifth-degree polynomial trajectory planning method, the system vibration suppression effect is significant, which verifies the effectiveness and feasibility of the proposed method and provides a theoretical basis for further realizing real-time control.

Model Predictive Trajectory Optimization With Dynamically Changing Waypoints for Serial Manipulators

Model Predictive Trajectory Optimization With Dynamically Changing Waypoints for Serial Manipulators

On the design of a macro‐micro parallel manipulator for cochlear microrobot operations

AbstractBackgroundThe method of stem cell transfer to narrow cochlear canals in vivo to generate hair cells is still an unclear operation. Thus, the development of any possible method that will ensure the usage of medical microrobots in small cochlear workspaces is a challenging procedure.MethodsThe current study tries to introduce a macro‐micro manipulator system composed of a 6‐DoF industrial serial manipulator as a macro manipulator and a proposed 5‐DoF parallel manipulator with dual end effectors as a micro manipulator carrying permanent magnets for tetherless microrobot actuation inside the cochlea.ResultsThroughout the study, structural synthesis and kinematic analysis of the proposed micro manipulator were introduced. A prototype of the manipulator was manufactured and its hardware verification procedures were carried out using motion capture cameras and surgical navigation registration methodologies.ConclusionsFollowing motion training, the assembled macro‐micro manipulator was successfully utilised to actuate a microrobot placed inside a manufactured cochlea mockup model.

Symmetric Identities Involving the Extended Degenerate Central Fubini Polynomials Arising from the Fermionic p-Adic Integral on ℤp

Since the constructions of p-adic q-integrals, these integrals as well as particular cases have been used not only as integral representations of many special functions, polynomials, and numbers, but they also allow for deep examinations of many families of special numbers and polynomials, such as central Fubini, Bernoulli, central Bell, and Changhee numbers and polynomials. One of the key applications of these integrals is for obtaining the symmetric identities of certain special polynomials. In this study, we focus on a novel generalization of degenerate central Fubini polynomials. First, we introduce two variable degenerate w-torsion central Fubini polynomials by means of their exponential generating function. Then, we provide a fermionic p-adic integral representation of these polynomials. Through this representation, we investigate several symmetric identities for these polynomials using special p-adic integral techniques. Also, using series manipulation methods, we obtain an identity of symmetry for the two variable degenerate w-torsion central Fubini polynomials. Finally, we provide a representation of the degenerate differential operator on the two variable degenerate w-torsion central Fubini polynomials related to the degenerate central factorial polynomials of the second kind.

QCASBC: An algorithm for hardware-in-the-loop simulation of 3-link RRR robotic manipulator

In this paper, a quick convergence adaptive structure is proposed for trajectory tracking of an articulated type robotic manipulator using the Hardware in the Loop (HIL) simulation technique. A novel Nonlinear Quick Convergence Adaptive Sliding Backstepping Control (QCASBC) algorithm is implemented on a C2000 real-time controller board. The performance of the proposed control algorithm is inspected concerning the sliding mode PID (SM-PID) control technique to estimate its correlation with the proposed algorithm. The experimental part of the HIL simulation tests has been carried out on a simulated model of a three-link serial robot manipulator. A dynamic model of the robotic manipulator has been developed using Matlab Simulink software and its performance is analyzed using the HIL technique via a C2000 real-time controller for tracking the desired trajectory. Results show that the speed of convergence while tracking the desired trajectory of the manipulator is better in the proposed algorithm. It is also estimated that the positional error of the QCASBC algorithm is superior to the SM-PID control algorithm. The observed average angle error is improved by 14% and the average response time error is improved by 11% by using the proposed QCASBC algorithm compared to the SM-PID approach.

Several Symmetric Identities of the Generalized Degenerate Fubini Polynomials by the Fermionic p-Adic Integral on Zp

After constructions of p-adic q-integrals, in recent years, these integrals with some of their special cases have not only been utilized as integral representations of many special numbers, polynomials, and functions but have also given the chance for deep analysis of many families of special polynomials and numbers, such as Bernoulli, Fubini, Bell, and Changhee polynomials and numbers. One of the main applications of these integrals is to obtain symmetric identities for the special polynomials. In this study, we focus on a novel extension of the degenerate Fubini polynomials and on obtaining some symmetric identities for them. First, we introduce the two-variable degenerate w-torsion Fubini polynomials by means of their exponential generating function. Then, we provide a fermionic p-adic integral representation of these polynomials. By this representation, we derive some new symmetric identities for these polynomials, using some special p-adic integral techniques. Lastly, by using some series manipulation techniques, we obtain more identities of symmetry for the two variable degenerate w-torsion Fubini polynomials.

Kinematic Modeling and Performance Analysis of a 5-DoF Robot for Welding Applications

Robotic manipulators are critical for industrial automation, boosting productivity, quality, and safety in various production applications. Key factors like the payload, speed, accuracy, and reach define robot performance. Optimizing these factors is crucial for future robot applications across diverse fields. While 6-Degrees-of-Freedom (DoF)-articulated robots are popular due to their diverse applications, this research proposes a novel 5-DoF robot design for industrial automation, featuring a combination of three prismatic and two revolute (2R) joints, and analyzes its workspace. The proposed techno-economically efficient design offers control over the robot manipulator to achieve any reachable position and orientation within its workspace, replacing traditional 6-DoF robots. The kinematic model integrates both parallel and serial manipulator principles, combining a Cartesian mechanism with rotational mechanisms. Simulations demonstrate the end effector’s flexibility for tasks like welding, additive manufacturing, and material inspections, achieving the desired position and orientation. The research encompasses the design of linear and rotational actuators, kinematic modeling, Human–Machine Interface (HMI) development, and welding application integration. The developed robot demonstrates a superior performance and user-friendliness in welding. The experimental work validates the design’s optimized joint trajectories, efficient power usage, singularity avoidance, easy access in application areas, and reduced costs due to fewer actuators.

Model free sliding mode control for serial robot manipulator: rigid and elastic joint robot

Model free sliding mode control for serial robot manipulator: rigid and elastic joint robot

Redundant Non-Serial Implicit Manipulator Kinematics and Dynamics

Abstract Redundant non-serial manipulators that include a spectrum of parallel and non-parallel heavy load bearing construction and material handling equipment are treated, using foundations of differential geometry. Kinematics of this category of manipulator are defined in manipulator configuration space by algebraic equations in input and output coordinates that cannot be explicitly solved for either as a function of the other. New sets called assembly components of manipulator configuration space are defined that partition the space into maximal, path-connected, disjoint, topological components. All configurations within an assembly component can be connected by one or more continuous paths within that component, but configurations in different assembly components cannot be connected by continuous paths. Forward and inverse kinematically singular configurations are characterized by criteria that partition each assembly component into path-connected, singularity-free assembly components in which equations of kinematics and dynamics are well behaved. It is shown that a generalized inverse velocity-based kinematic formulation that is problematic for serial manipulators is likewise plagued with problems for non-serial implicit manipulators that can be avoided using the methods presented. Singularity-free differentiable manipulator configuration space components are defined and parameterized by both input and operational coordinates, leading to well-posed ordinary differential equations of manipulator dynamics in both input and operational coordinates. Three typical applications and associated model problems are studied throughout the paper to illustrate the methods and results presented.

Simultaneous identification of geometric parameters and structural stiffness of serial robots composing flexible links

It has been a formidable challenge to accurately predict the pose of serial robots composing flexible links due to the difficulties in simultaneously considering geometric errors and link flexibility. This paper presents an approach for simultaneously identifying kinematics and stiffness parameters in the flexible serial robot. A compliance equivalent method is employed to model the flexibility in the joints and links nonlinearly. Based on this, the kinetostatics model of those serial robots can be established analytically. By approximating the force-deflection characteristics of the flexible links, a unified error model containing both geometric and compliance parameters is derived. Moreover, an adaptive total-least-square method is proposed for the identification considering constraints on the compliance coefficient. To verify the effectiveness of the proposed method, simulations on a single flexible link, a serial robot, and experiments on a 3-DOF planar serial manipulator are carried out. The results show that the residual errors of the manipulator can be significantly reduced by identifying the kinematics and stiffness parameters using the proposed approach.