Serial Manipulators Research Articles

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.

Kinematics analysis of a novel hybrid manipulator for optomechanical modules assembly

A novel hybrid manipulator is proposed in this work, in order to assemble optomechanical modules in an inertial confinement fusion facility (SG-Ⅲ). Differ from general serial and parallel manipulators, both the inverse and forward kinematics problems of hybrid manipulators are difficult to be solved. Based on an analytic method, the position and orientation mapping functions between the optomechanical module and the parallel manipulators are established, and then the method of transformation matrix is employed to obtain the inverse kinematics solution. The forward kinematics of this hybrid manipulator is highly nonlinear and coupled, so a back propagation neural network using all class one network strategy is trained to approximate the mapping relation. Aiming to improve the accuracy, the network is split into two sub-networks corresponding to the natural property of the outputs. In the end, an improved back propagation neural network is proposed to optimize the network, results illustrate that the kinematic accuracy is increased significantly.

An explicit solution of forward and inverse kinematics for a serial manipulator with insufficient intersection joints based on finite and instantaneous screw theory

An explicit solution of forward and inverse kinematics for a serial manipulator with insufficient intersection joints based on finite and instantaneous screw theory

Multi-Objective Optimization of a Three Degree-of-Freedom Translational Parallel Kinematic Machine with Coplanar Rails

Several advancements in the field of parallel manipulators have taken place in recent days as they offer many advantages over serial manipulators in terms of accuracy, agility, stiffness, speed, etc. The Parallel Kinematic Machines (PKMs) with lower Degree of Freedom (DoF) joints are being explored for a variety of industrial applications and, in particular, machining applications as these offer more accuracy, high machining capability, and more stiffness. This research work focuses on the modeling, kinematics, workspace and dexterity analyses of a 3DoF Translational PKM having coplanar rails along the Cartesian axes: -X, +X, +Y. Actuation of sliders, independently along the respective rails, offer the tool platform pure translational motion. Fixed length links are used to connect the sliders and tool platform. The PKM under study is modeled in CATIA. Inverse kinematics and workspace analysis are carried out using the performance indices, namely, Workspace Volume Index (WVI) and Global Condition Index (GCI). Attempts are also made to find the optimal dimensions of the PKM through multi-objective optimization using Genetic Algorithms in MATLAB. The methodology presented is helpful to predict the PKM's performance capability while the results obtained are helpful for the development of a physical prototype necessary for further experimental investigations.

Multiple Working Mode Control of Robotic Operations on Mechanisms With Unmodelled Constraints With Online Mode Switching

Robotic operations such as opening doors in an unstructured environment pose a challenge for robot control due to unmodelled constraints. In this article, a multiple working mode approach is proposed to control a mobile serial robot manipulator to perform operations on mechanisms with unmodelled constraints. The multiple working mode control switches the working mode of a number of active joints during the operation to relax the problem of over-actuation of the constrained robot manipulator when modeling errors cause excessive internal and external reaction forces. Three practical criteria are derived for the assignment of active and passive control modes; two based on the coordinate partitioning method for multibody dynamics, and another based on minimizing task friction forces. The proposed control method has been implemented on a mobile reconfigurable robot, performing constrained motion along an elliptical trajectory, similar to a door-opening task. Simulation and experimental results are presented to show the effectiveness of the proposed control approach.

A hybrid method using FABRIK and custom ANN in solving inverse kinematic for generic serial robot manipulator

A hybrid method using FABRIK and custom ANN in solving inverse kinematic for generic serial robot manipulator

Leveraging pleat folds and soft compliant elements in inflatable fabric beams.

Inflatable fabric beams (IFBs) integrating pleat folds can generate complex motion by modifying the pleat characteristics (e.g., dimensions, orientations). However, the capability of the IFB to return to the folded configuration relies upon the elasticity of the fabrics, requiring additional pressure inputs or complementary mechanisms. Using soft compliant elements (SCEs) assembled onto pleat folds is an appealing approach to improving the IFB elasticity and providing a range of spatial configurations when pressurized. This study introduces an actuator comprising an IFB with pleat folds and SCEs. By methodologically assembling the SCEs onto the pleat folds, we constrain the IFB unfolding to achieve out-of-plane motion at 5 kPa. Besides, the proposed actuator can generate angular displacement by regulating the input pressure ( 5 kPa). A matrix-based representation and model are proposed to analyze the actuator motion. We experimentally study the actuator's angular displacement by modifying SCE shapes, fold dimensions, and assembly distances of SCEs. Moreover, we analyze the effects of incorporating two SCEs onto a pleat fold. Our results show that the actuator motion can be tuned by integrating SCEs with different stiffness and varying the pleat fold dimensions. In addition, we demonstrate that the integration of two SCEs onto the pleat fold permits the actuator to return to its folded configuration when depressurized. In order to demonstrate the versatility of the proposed actuator, we devise and conduct experiments showcasing the implementation of a planar serial manipulator and a soft gripper with two grasping modalities.

Fixed-time tracking control of manipulators based on non-singular fast terminal sliding surface

As for the problem of trajectory tracking of a multi-joint serial manipulator, a novel fixed-time control scheme is proposed based on non-singular fast terminal sliding mode control. By employing a fast terminal sliding mode surface, we solve the singularity problem existed in traditional terminal sliding mode surface. In the meantime, in order to improve the rapidity of the system, the fixed-time control is incorporated with the fast terminal sliding mode surface control. Theoretical analysis proves that the proposed control scheme guarantees that better tracking performance is obtained, and its convergence time upper limit is not affected by the initial states. In addition, a reaching law with the exponential approach characteristic is added to the control law, which effectively reduces the chattering phenomenon in the controller design. Finally, the effectiveness and feasibility of the designed controller are verified through a numerical simulation.

Kinematic Analysis of 3-PRPPS Spatial Parallel Manipulator with Circularly Guided Base for Singularity-Free Robotic Motions

Robot manipulators are classified as serial manipulators and parallel manipulators. Parallel manipulators are classified into planar and spatial parallel manipulators (SPMs). The parallel manipulators have moved and fixed platforms connected with serial chains. The parallel manipulators have many linkages, which create a singularity problem. The singular positions of SPMs have also gained substantial attention in various industrial applications due to their intrinsic advantages in precision, flexibility, and load-bearing capabilities. The 3-PRPPS SPM has three prismatic joints, one spherical joint, and one revolute joint. This work changed the fixed base with a circular guided base to avoid singularity issues. The manipulator was modeled with direct kinematic relations. The Jacobian matrix for position and orientation was derived. The workspace was taken as the common area of the three circles, whose radius was the maximum arm length. The position and orientation of the end effector were traced. In the form of the end effector traces, no singularities in the mechanism were observed. The path of the robot manipulator was observed in all the possible positions and orientations. The multi-body simulation was also conducted on the 3-PRPPS manipulator, the main findings of which are presented in this article.

Noise-Suppressing Newton Algorithm for Kinematic Control of Robots

In this paper, armed with the integral control method, a new noise-suppressing Newton (NSN) algorithm is proposed for the redundancy resolution of redundant robot manipulators efficiently. For practical hardware implementation, the discrete-time noise-suppressing Newton (abbreviated as DTNSN) algorithm is discretized from the continues NSN algorithm. Specifically, the distinguishing feature of the proposed DTNSN algorithm is that it can rigorously converge with inherent tolerance to noises induced by communication jamming and computational systematical errors. In contrast, considerable traditional algorithms often dispose of noises with the high-degree filter from the viewpoint of signal processing, which requires a complex system structure and further results in a heavy computational burden. Note that theoretical analyses are provided to elaborate the convergent property of the DTNSN algorithm polluted with constant bias, time-dependent linear noises and bounded random noises. Besides, by the proposed DTNSN algorithm, the end effector of both serial and parallel redundant robot manipulators complete the allocated motion planning and are impervious to the noisy simulated environment.

Parameter Identification of Hydraulic Manipulators Considering Physical Feasibility and Control Stability

In the challenging applications of hydraulic robots, control performance in the full workspace is required for successful task completion. The model-based controller of the hydraulic manipulator is an effective means to improve control performance. However, most of the existing identification methods rely on least squares or weighted least squares, which may lead to the physically infeasible parameters. Although the physical feasibility of inertial parameters can be solved by the linear matrix inequality, physical feasibility and prior knowledge constraints of hydraulic parameters, such as bulk modulus and valve port coefficients, have not been considered in the identification process. Parameters that do not satisfy constraints will affect system stability in the model-based controller. In this paper, an identification framework is proposed, which integrates inertial, friction, hydraulic parameters physical feasibility. Compared with the non-identified parameters, the ratio of tracking error to maximum velocity with the proposed method is reduced by 50%-56%. Compared with the least squares identification, the control stability in the full workspace is guaranteed. The proposed method is applicable to serial hydraulic manipulators with arbitrary degrees of freedom and is supported by experimental analysis of a hydraulic manipulator.

Hybrid Tension-Position Control of Cable-Driven Serial Manipulator to Improve Accuracy and Avoid Cable Slack and Breakage

Hybrid Tension-Position Control of Cable-Driven Serial Manipulator to Improve Accuracy and Avoid Cable Slack and Breakage

Online Trajectory Generation with Local Replanning for 7-DoF Serial Manipulator in Unforeseen Dynamic Environments

Online Trajectory Generation with Local Replanning for 7-DoF Serial Manipulator in Unforeseen Dynamic Environments

Obstacle Avoidance in Operational Configuration Space Kinematic Control of Redundant Serial Manipulators

Kinematic control of redundant serial manipulators has been carried out for the past half century based primarily on a generalized inverse velocity formulation that is known to have mathematical deficiencies. A recently developed inverse kinematic configuration mapping is employed in an operational configuration space differentiable manifold formulation for redundant-manipulator kinematic control with obstacle avoidance. This formulation is shown to resolve deficiencies in the generalized inverse velocity formulation, especially for high-degree-of-redundancy manipulators. Tracking a specified output trajectory while avoiding obstacles for four- and twenty-degree-of-redundancy manipulators is carried out to demonstrate the effectiveness of the differentiable manifold approach for applications with a high degree of redundancy and to show that it indeed resolves deficiencies of the conventional generalized inverse velocity formulation in challenging applications.

Redundant Serial Manipulator Inverse Position Kinematics and Dynamics

AbstractA redundant serial manipulator inverse position kinematic mapping is employed to define a new manipulator operational space differentiable manifold and an associated system of well posed operational space differential equations of manipulator dynamics. A review of deficiencies in the conventional generalized inverse velocity approach to manipulator redundancy resolution and a numerical example show that the conventional approach is incompatible with kinematics of redundant serial manipulators. The inverse position kinematic mapping presented is shown to define a differentiable manifold that is parameterized by either input or operational space coordinates. Differentiation of the inverse position mapping yields an inverse velocity mapping that is a total differential, in contrast with generalized inverse velocity mappings, hence avoiding the deficiencies identified. A second differentiation yields an inverse acceleration mapping that is used, without ad-hoc derivation, to obtain well posed operational space ordinary differential equations of redundant manipulator dynamics that are equivalent to the equations of multibody dynamics.

Hierarchical Error Compensation Method for Two-Degree-of-Freedom Manipulator Positioning Error in Hybrid Robots

In this paper, taking a two-degree-of-freedom parallelogram serial manipulator of a hybrid robot as an example, a hierarchical error compensation method that combines geometric and non-geometric error compensation is proposed. First, we establish the geometric kinematic modeling and error model and use the Levenberg-Marquardt (L-M) method to identify the geometric error parameters. Then, we use the grid interpolation method to compensate for non-geometric errors, thereby improving the overall positioning accuracy of the manipulator. Finally, a simulation is presented to verify the correctness and effectiveness of the proposed method. The results show that the positioning accuracy is improved from 4.8568 mm to 0.0036 mm, and the attitude error is improved from 0.9437° to 0.0105°.

High-Order Derivatives of Serial Manipulator Jacobians Using Multidual Differentiation Transform

Abstract The use of robots is continuously growing, from heavy-duty industries to nanotechnology. Exact multilink robot end effector control is required to withstand this tendency in modern robotics. Mapping between joint variables in joint-space coordinate and end effector configuration in task-space coordinate are provided by serial manipulator kinematics. A computation of higher-order Jacobian matrix derivatives is required for accurate trajectory tracking. With conventional numerical derivation, only approximate results can be obtained. Still, the computation of high-order derivatives of multi-DoF manipulators with high accuracy requires long time intervals and it is difficult. This paper investigates a novel derivation method for a multilink robot Jacobian. According to this method, an exact value of higher-order acceleration can be obtained using a multidual differentiation transform. Multidual functions for sine and cosine will be used to get the exact value of acceleration, jerk, and hyper-jerk (jounce) expressions, commonly used for accurate trajectory-tracking.

Noncollocated Proprioceptive Sensing for Lightweight Flexible Robotic Manipulators

This article presents the design of a noncollocated feedback system for flexible serial manipulators. The device is a passive serial chain of encoders and lightweight links, mounted in parallel with the manipulator. This measuring arm effectively decouples the manipulator's proprioception from its actuators by providing information on the actual end effector pose, accounting for both joint and link flexibility. The kinematic redundancy of the measuring chain allows for safe operation in the context of human–robot interaction. A simple yet effective error model is introduced to assess the suitability of the proposed sensor system in the context of robotic control. The practicality of the device is first demonstrated by building a physical joint-encoder assembly and a simplified planar measuring arm prototype. With this additional feedback, a task-space position controller is devised and tested in simulation. Finally, the simulation results are validated with an experimental 3-DoF lightweight manipulator prototype equipped with a five-joint measuring arm.

Message from the editor in Chief

*Message from the editor in Chief
 
 The year 2023 promises many exciting developments for the Global Journal of Computer Sciences: Theory and Research (GJCS). In addition, every year, the number of citations continues to rise strongly in proportion to the increase in the number of articles published. In this respect, first of all, we would like to thank all our authors who have contributed to the success of our journal. While reviewing our new issue, we saw articles from different authors from different countries: Turkey, Argentina, Albania, Algeria.
 The multiculturalism policy followed in our globally-focused journal makes us happy with every new issue. We examine the following research areas in the current issue; “A data warehouse architecture proposal and ETL analysis:a case study of an Albanian banking system”, “Applying developed genetic algorithm operators to knapsack problems”, “Developing a new model for context awareness in ambient intelligence”, “Initial value problems: a didactic tool in evolution”, “Remote control of a serial manipulator using a depth camera” .
 We will continue to contribute to literature within the scope of Computer Science with our strong team.
 Thanks to all our authors the contributors to this issue.
 
 Hope to see you in our new issue.
 
 Assoc. Prof. Dr. Ezgi Pelin YILDIZ
 Global Journal of Computer Sciences: Theory and Research (GJCS) CHEF EDITOR