Serial Robot Research Articles

An error compensation controller for milling robots

This paper presents a method of controlling a serial robot for milling by an inverse kinematic controller combined with an outer PD loop (Inverse Dynamics + PD controller), with calibration and compensation of errors in calculating the cutting forces. Because the cutting forces are generated at the time of cutting, at the contact area between the workpiece and the cutting tool, the generalized forces of the cutting forces in the differential equations of motion of robot is always variable and difficult to determine precisely. The cutting forces depend on the cutting mode, the geometric parameters of the cutting layer, the cutting conditions, etc. This study shows an inverse dynamic controller with the outer PD loop and an additional calibration block to compensate the differences between the actual cutting forces and calculated cutting forces (which are caculated by the empirical formula). The cutting forces at each machining time of the calibration block is determined based on the differential equation of motion. The efficiency (convergence time and accuracy) of the proposed controller is evaluated by comparison between the numerical simulation results of the controller with cutting force calibration and the conventional PD controller. In the conventional PD controller, the dynamic model of the robot is assumed to define precisely. The results contribute to design and manufacture the controllers for robotic milling, and to improve the quality of the machined surface.

Design of a Reconfigurable Mobile Collaborative Manipulator for Industrial Applications

Abstract This paper addresses the design of a reconfigurable mobile manipulator consisting of a mobile base and a collaborative serial robot. The robotic system is meant to work in an industrial environment and perform different logistic tasks. Unlike commercial solutions, the mobile base and the anthropomorphic arm are free to decouple and work separately as two different entities, thus optimizing working times and maximizing the hardware utilization ratio. The proposed mobile manipulator is equipped with an automatic braking system to ensure safety and stability during manipulation, a lifting system that allows the robotic arm to work at different heights, and a spatial referencing process to compensate for positioning error of the mobile base. An illustrative working cycle is implemented in an industrially relevant environment to test all features and show potentialities, in terms of flexibility and reconfigurability, of the presented solution.

A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of Parallel Kinematic Manipulators

Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory control of parallel kinematics manipulators (PKM) equipped with SEAs has not yet been pursued. Key element for this is the computationally efficient evaluation of the second time derivative of the inverse dynamics solution. This has not been presented in the literature, and is addressed in the present paper for the first time. The special topology of PKM is exploited reusing the recursive algorithms for evaluating the inverse dynamics of serial robots. A Lie group formulation is used and all relations are derived within this framework. Numerical results are presented for a 6- DOF Gough-Stewart platform (as part of an exoskeleton), and for a planar PKM when a flatness-based control scheme is applied.

Kinetostatics of a serial robot in screw form

Kinetostatics of a robot is an essential component of robotic analysis that includes actuation distribution and torque control. The extant methods mainly include the static transfer formulae and force Jacobian matrix algorithms based on the Denavit-Hartenberg (D-H) method. They can calculate the joint driving torque, but there are some limitations. This paper proposes a kinetostatics approach for analyzing the driving torque of serial manipulators. The instantaneous work done by the external load is expressed with reciprocal screw. It is the key idea of the approach to derive the kinetostatics equation in screw form and determine the required torque at each joint. This methodology is straightforward for programming. Through kinetostatic analysis of some typical serial manipulators, this paper shows the process of establishing the kinetostatics of every joint to calculate the torque in Plücker coordinates. The general spatial manipulator was analyzed and the solution demonstrates the universality of the method presented in this paper. In addition, the kinetostatic analysis method applies to all kinds of serial manipulators.

Novel Discrete-Time Recurrent Neural Network for Robot Manipulator: A Direct Discretization Technical Route.

Controlling and processing of time-variant problem is universal in the fields of engineering and science, and the discrete-time recurrent neural network (RNN) model has been proven as an effective method for handling a variety of discrete time-variant problems. However, such model usually originates from the discretization research of continuous time-variant problem, and there is little research on the direct discretization method. To address the aforementioned problem, this article introduces a novel discrete-time RNN model for solving the discrete time-variant problem in a pioneering manner. Specifically, a discrete time-variant nonlinear system, which originates from the mathematical modeling of serial robot manipulator, is presented as a target problem. For solving the problem, first, the technique of second-order Taylor expansion is used to deal with the discrete time-variant nonlinear system, and the novel discrete-time RNN model is proposed subsequently. Second, the theoretical analyses are investigated and developed, which shows the convergence and precision of the proposed discrete-time RNN model. Furthermore, three distinct numerical experiments verify the excellent performance of the proposed discrete-time RNN model. In addition, a robot manipulator example further verifies the effectiveness and practicability of the proposed novel discrete-time RNN model.

Pose Determination System for a Serial Robot Manipulator Based on Artificial Neural Networks

Achieving the highest levels of repeatability and precision, especially in robot manipulators applied in automation manufacturing, is a practical pose-recognition problem in robotics. Deviations from nominal robot geometry could produce substantial errors at the end effector, which can be more than 0.5 inches for a 6 ft robot arm. In this research, a pose-recognition system is developed for estimating the position of each robot joint and end-effector pose using image processing. To generate the joint angle, the system is developed via the modeling of a pose obtained by combining a convolutional neural network (CNN) and a multi-layer perceptron network (MLP). The CNN categorizes the input image generated by a remote monocular camera and generates a classification probability vector. The MLP generates a multiple linear regression model based on the probability vector generated by a CNN and describes the values of each joint angle. The proposed model is compared with the P-n-Perspective problem-solving method, which is based on marker tracking using ArUco markers and the encoder values. The system was verified using a robot manipulator with four degrees of freedom. Additionally, the proposed method exhibits superior performance in terms of joint-by-joint error, with an absolute error that is three units less than that of the computer vision method. Furthermore, when evaluating the end-effector pose, the proposed method showed a lower average standard deviation of 9mm compared with the computer vision method, which had a standard deviation of 13 mm.

Modeling and calibration of high-order joint-dependent kinematic errors of serial robot based on local POE

PurposeThis paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.Design/methodology/approachRobot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.FindingsLaguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg–Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224 mm.Originality/valueThe results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.

High-order inverse dynamics of serial robots based on projective geometric algebra

High-order inverse dynamics of serial robots based on projective geometric algebra

Inverse solution of six-degrees-of-freedom serial robot with adjacent three joint axes parallel based on screw theory

Inverse kinematics occupies a vital role in robotics and is the fundation of robot trajectory planning as well as rigid body motion, which directly affects the rapidity and accuracy of control. Compared with the traditional Denavit-Hatenberg parameter modeling, the screw method has its unique advantages. The paper establishes the kinematic model of a six-degree-of-freedom serial robot using screw theory. The Paden-Kahan sub-problem, orientation separation reduction technique and matrix transformation are used to resolve the inverse kinematics. The effectiveness and validity of the above algorithm are verified by data calculation. A new inverse solution algorithm is designed in this paper to propose an idea for the inverse kinematic solution with the second, third, and fourth joints being parallel to each other in the robot.

Application of Elliptic Jerk Motion Profile to Cartesian Space Position Control of a Serial Robot

The paper discusses the application of a motion profile with an elliptic jerk to Cartesian space position control of serial robots. This motion profile is obtained by means of a kinematic approach, starting from the jerk profile and then calculating acceleration, velocity and position by successive integrations. Until now, this profile has been compared to other motion laws (trapezoidal velocity, trapezoidal acceleration, cycloidal, sinusoidal jerk, modified sinusoidal jerk) considering single-input single-output systems. In this work, the comparison is extended to nonlinear multi-input multi-output systems, investigating the application to Cartesian space position control of serial robots. As case study, a 4-DOF SCARA-like architecture with elastic balancing is considered; both an integer-order and a fractional-order controller are applied. Multibody simulation results show that, independently of the controller, the behavior of the robot using the elliptic jerk profile is similar to the case of adopting the sinusoidal jerk and modified sinusoidal jerk laws, but with a slight reduction in the position error (−3.8% with respect to the sinusoidal jerk law and −0.8% with respect to the modified sinusoidal jerk law in terms of Integral Square Error) and of the control effort (−8.2% with respect to the sinusoidal jerk law and −1.3% with respect to the modified sinusoidal jerk law in terms of Integral Control Effort).

Fans Optimizer: A human-inspired optimizer for mechanical design problems optimization

This paper proposes a human-inspired algorithm for optimizing various practical engineering problems, specifically, the Fans Optimization (FO) algorithm that is inspired by the Fans economy fused in the entertainment domain. Opposing current algorithms, the FO algorithm introduces a Multi-groups mechanism (Cooperation–Competition) and a Two-characteristic individual update mechanism to balance the exploration and exploitation (E&E). Additionally, the multi-phase optimization algorithm includes Roles information and Fans-community, Fans-community Switching, Resource Competition, Information Sharing, and K-Update. In the experiments, the FO algorithm is first compared with 12 meta-heuristic algorithms in four groups of benchmark functions (selected from the IEEE CEC and GECCO competitions), demonstrating that the FO algorithm has a superior convergence performance and E&E. Moreover, the Williams test prove the superiority of the FO algorithm over the competitor algorithms. Additionally, eight class practical engineering problems verify the FO’s practical engineering applicability. Finally, the FO algorithm solves the inverse kinematic solution problem of the 9-degree of freedom serial robot arm (9-DFSRA) , demonstrating superior results over the competitor schemes. Overall, the test results prove that the FO algorithm is superior to its competitor algorithms for complex engineering problems.

Joint Stiffness Identification Based on Robot Configuration Optimization Away from Singularities

Recently, industrial robots are mostly used in many areas because of their high dexterity and low price. Nevertheless, the low performance of robot stiffness is the primary limiting factor in machining applications. In this paper, a new method for identifying the joint stiffness of serial robots. The method considers the coupling of the end-effector’s rotational and translational displacements. Then, a new criterion is presented for optimizing the robot configuration. Next, the influence of each joint on the criterion is analyzed, and the corresponding joint is selected to simplify the experiment. After that, the method’s robustness, the sensitivity of the number of tests, and the experimental errors are analyzed. Finally, the KUKA KR60-3 robot is used as a descriptive example.

Inverse Kinematics for Serial Robot Manipulators by Particle Swarm Optimization and POSIX Threads Implementation

Inverse kinematics is a fundamental problem in manipulator robotics: a set of joint angles must be calculated so that the robot arm can be manipulated to the corresponding desired end effector position and orientation (also known as “pose”). Traditional solution techniques include analytical kinematics solvers, which provide the closed-form expressions for the joint positions as functions of the end-effector pose. When analytical inverse kinematics solvers are not possible due to the manipulator structure, numerical methods such as Newton–Raphson or Jacobian inverse can be used to achieve the task, but at a much slower speed due, to the iterative nature of the computation. Recent swarm intelligence technology has also contributed to manipulator inverse kinematics solutions. In this paper, the use of the Particle Swarm Optimization (PSO) approach in solving the inverse kinematics problem is investigated for the general serial robotic manipulators. Many of the reviewed robotic manipulator inverse kinematics solvers using swarm intelligence only deal with end effector position and not its orientation. Our PSO approach provides the convergence of a complete end-effector pose and will be demonstrated using the Baxter Research Robot, which has two seven-joint arms, although the method is applicable to any general serial robotic manipulator. For computational efficiency, the inverse kinematic calculations were implemented in parallel using Portable Operating Interface (POSIX) threads to take advantage of the independent swarm particle dynamics.

Kinegami: Algorithmic Design of Compliant Kinematic Chains From Tubular Origami

Origami processes can generate both rigid and compliant structures from the same homogeneous sheet material. In this article, we advance the origami robotics literature by showing that it is possible to construct an arbitrary rigid kinematic chain with prescribed joint compliance from a single tubular sheet. Our “Kinegami” algorithm converts a Denavit–Hartenberg specification into a single-sheet crease pattern for an equivalent serial robot mechanism by composing origami modules from a catalogue. The algorithm arises from the key observation that tubular origami linkage design reduces to a Dubins path planning problem. The automatically generated structural connections and movable joints that realize the specified design can also be endowed with independent user-specified compliance. We apply the Kinegami algorithm to a number of common robot mechanisms and hand-fold their algorithmically generated single-sheet crease patterns into functioning kinematic chains. We believe this is the first completely automated end-to-end system for converting an abstract manipulator specification into a physically realizable origami design that requires no additional human input.

Kinetostatic Optimization for Kinematic Redundancy Planning of Nimbl’Bot Robot

AbstractIn manufacturing industry, computer numerical control (CNC) machines are often preferred over industrial serial robots (ISR) for machining tasks. Indeed, CNC machines offer high positioning accuracy, which leads to slight dimensional deviation on the final product. However, these machines have a restricted workspace generating limitations in the machining work. Conversely, ISR are typically characterized by a larger workspace. ISR have already shown satisfactory performance in tasks like polishing, grinding, and deburring. This paper proposes a kinematic redundant robot composed of a novel two degrees-of-freedom mechanism with a closed kinematic chain. After describing a task-priority inverse kinematic control framework used for joint trajectory planning exploiting the robot kinematic redundancy, the paper analyses the kinetostatic performance of this robot depending on the considered control tasks. Moreover, two kinetostatic tasks are introduced and employed to improve the robot performance. Simulation results show how the robot better performs when the optimization tasks are active.

Inverse Kinematics of a Class of 6R Collaborative Robots with Non-Spherical Wrist

The spread of cobotsin common industrial practice has led constructors to prefer the development of collaborative features that are necessary to prevent injuries to operators over the realization of simple kinematic structures for which the joints-to-workspace mapping is well known. An example is given by the replacement in serial robots of spherical wrists with safer solutions, where the danger of crushing and shearing is intrinsically avoided. Despite this tendency, the kinematic map between actuated joints and the Cartesian workspace remains of paramount importance for robot analysis and programming, deserving the attention of the research community. This paper proposes a closed-form solution for the inverse kinematics of a class of 6R robotic arms with six degrees of freedom and non-spherical wrists. The solutions are worked out by a single polynomial, of minimum degree, in terms of one of the positioning parameters chosen for the description of the robot posture. The roots of such a polynomial are then back-substituted to determine all the remaining unknowns. A numerical example is finally shown to verify the validity of the proposed implementation for a commercial collaborative robot.

Tool wear image on-machine detection based on trajectory planning of 6-DOF serial robot driven by digital twin

Tool wear image on-machine detection based on trajectory planning of 6-DOF serial robot driven by digital twin

Optimal adaptive barrier-function super-twisting nonlinear global sliding mode scheme for trajectory tracking of parallel robots

Compared to serial robots, parallel robots have potential superiorities in rigidity, accuracy, and ability to carry heavy loads. On the other hand, the existence of complex dynamics and uncertainties makes the accurate control of parallel robots challenging. This work proposes an optimal adaptive barrier-function-based super-twisting sliding mode control scheme based on genetic algorithms and global nonlinear sliding surface for the trajectory tracking control of parallel robots with highly-complex dynamics in the presence of uncertainties and external disturbances. The globality of the proposed controller guarantees the elimination of the reaching phase and the existence of the sliding mode around the surface right from the initial instance. Moreover, the barrier-function based adaptation law removes the requirement to know the upper bounds of the external disturbances, thus making it more suitable for practical implementations. The performance and efficiency of the controller is assessed using simulation study of a Stewart manipulator and an experimental evaluation on a 5-bar parallel robot. The obtained results were further compared to that of a six-channel PID controller and an adaptive sliding mode control method. The obtained results confirmed the superior tracking performance and robustness of the proposed approach.

추가 잉여 입력 상태에 따른 직렬형 로봇의 속도 타원 사이의 기하적 관계 분석

This paper presents an in-depth analysis of the geometric relationship among the velocity ellipsoids of a serial robot according to the combination of additional extra inputs. In this paper, one or more extra inputs are added to a non-redundant or redundant serial robot, and no assumption is made on the linear independency of the additional extra inputs. First, in the case of one additional input, the relationship of two velocity ellipsoids before and after the addition of extra input is expressed by means of the freezing of the extra input, which defines a constraint hyperplane in the output space. Using the constraint hyperplane, the geometric relationship between two velocity ellipsoids with zero and one extra input is obtained. Second, the case of two additional inputs is treated as the addition of extra input twice in a row, and two constraint hyperplanes corresponding to the freezing of the two extra inputs are defined. Using the two constraint hyperplanes, the geometric relationship among three velocity ellipsoids with zero, one, two extra inputs is obtained. It is shown that the resulting geometric relationship should change depending on the linear independency of the two extra inputs. Third, the analysis for the case of two extra input is extended to the case of r(≥ 3) additional inputs, which is treated as the addition of extra input r times in a row. Using r constraint hyperplanes corresponding to the freezing of the (r+1) extra inputs, the geometric relationship among r velocity ellipsoids with zero up to r extra inputs is identified. It is shown that the inclusion relationship between two velocity ellipsoids before and after the addition of r extra inputs should change depending on the linear independency of the r extra inputs. Fourth, simulation results of planar and spatial serial robots are provided to illustrate the varying geometric relationship among the velocity ellipsoids of a serial robot according to the combination of additional extra inputs.

Encountering singularities of a serial robot along continuous paths at high precision

A new variable step (VS) method rapidly calculates continuous kinematic paths that encounter singularities of a serial robot. Mitigating adverse effects of such encounters by applying small deviations to the intended path achieves high precision. The method is motivated by a simplified geometric model representing the arm extension, overhead and wrist singularities found in a wrist-separable 6-axis robot. A variable step length limits the kinematic closure error in a high-order combined predictor-corrector. Squaring the determinant of the robot Jacobian matrix gives its Taylor series favorable convergence. The resulting estimate of the distance to the nearest singularity affecting convergence of other kinematic variables bounds the step length, avoiding jumps between branches of path bifurcations associated with robot singularities. Finally, a 2nd order bivariate expansion of the squared determinant targets a minimum determinant magnitude by controlling deviation from an intended path. This process obviates the need for matrix regularization giving unintended switches between solution branches. The VS method demonstrates the ability to deviate from an intended path through dead center of any of the above singularities in isolation, pairwise and three-fold combination.