Kinematic Modeling Method Research Articles

Design and analysis of a class of two-limb non-parasitic 2T1R parallel mechanism with decoupled motion and symbolic forward position solution - influence of optimal arrangement of limbs onto the kinematics, dynamics and stiffness

The two-limb11Throughout this paper, the two-limb parallel mechanism means that the base and moving platforms of a parallel mechanism are directly connected with two independent limbs, despite the existence of closed sub-loop in one limb (i.e., in this work, it is named as hybrid-single-ordered-chain, and HSOC for short). parallel mechanisms (PMs) can have the advantages, in terms of avoidance of mechanical collision, simple architecture, rapid configuration transformation and large workspace volume. This paper consists of two major contents. The first aspect pertains to the design of a class of two-limb PMs with two translations and one rotation (2T1R), where a family of PMs featuring two translations actuated by sliding units are proposed, with decoupled position and orientation as well as symbolic forward position solution, without parasitic motions. The second aspect is to analyze the influence of the arrangement of limbs onto the kinematic, dynamic and stiffness performance of the PMs. Using the kinematic modeling method based on topological characteristics, the unified symbolic forward and inverse position solutions of the PMs are derived, together with the workspace, rotational capacity and singularity. Finally, a comparative study regarding the kinematics, dynamics and stiffness of the two PMs is carried out to find the optimal PM configuration. This paper presents a systematic analysis for the synthesis, optimal design and performance evaluation of two-limb parallel mechanisms.

Assembly Configuration Representation and Kinematic Modeling for Modular Reconfigurable Robots Based on Graph Theory

A Modular Reconfigurable Robot (MRR) composed of standard joint and link modules has the advantages of rapid changeover of assembly configurations for a diversity of application requirements. To tackle the kinematics analysis issues for an MRR, it is essential to develop a generic method to mathematically represent all possible assembly configurations and automatically generate their kinematic models. In this paper, two types of robot modules, i.e., revolute joint modules and rigid link modules, are considered as the basic building blocks of an MRR. The topological structure of an MRR is represented by a graph, termed an Assembly Graph (AG), in which all robot modules, regardless of their types, are treated as vertices, while the connecting interfaces between any two robot modules are treated as edges. Based on graph theory, a modified adjacency matrix, termed an Assembly Adjacency Matrix (AAM), is proposed to represent the assembly configuration of an MRR, in which the three-dimensional assembly information is specified with connecting port vectors for the adjacent modules. A path matrix derived from the AAM of an MRR is employed to describe the connecting sequence of its constituting modules. The local frame representation of the Product-of-Exponentials (POE) formula is employed, which is configuration-independent. Therefore, for an MRR configuration represented with an AAM, its kinematic model will be automatically generated according to its path matrix. The proposed assembly configuration representation and kinematic modeling method are validated through a dual-branch MRR configuration.

1U-Sized Deployable Space Manipulator for Future On-Orbit Servicing, Assembly, and Manufacturing

Miniaturized, multifunctional, and economical on-orbit service satellites have been increasingly used with the continuous increase of space exploration missions. In this paper, an innovative deployable manipulator is designed, named Cubot, which can be stowed in 1 U-sized ( 10 cm × 10 cm × 10 cm ) space. With CubeSat as the carrier, the deployable Cubot aims to achieve a variety of on-orbit operation tasks including space debris removal and space station on-orbit maintenance, for future on-orbit servicing, assembly, and manufacturing (OSAM). A kinematics modeling method of a space manipulator with passive joints is proposed, and the motion equation of the manipulator is derived. Considered the elastic potential energy stored in the passive joint during deployment, the momentum change of Cubot is simulated and analyzed. As the main forced element, the end effector is analyzed using FEA. Dynamic stress response with respect to the force distribution and the clamping angle is analyzed to evaluate mechanical performances of the end-effector component. Deployment tests are conducted to verify the feasibility of Cubot based on a principled prototype, which aims to provide engineering and practical experience for the development of this field.

Whole-body kinematic and dynamic modeling for quadruped robot under different gaits and mechanism topologies.

Dynamic locomotion plays a crucial role for legged robots to fulfill tasks in unstructured environments. This paper proposes whole-body kinematic and dynamic modeling method s based on screw theory for a quadruped robot using different gaits and mechanism topologies. Unlike simplified models such as centroid or inverse pendulum models, the methods proposed here can handle 10-dimensional mass and inertia for each part. The only simplification is that foot contact models are treated as spherical joints. Models of three different mechanism topologies are formulated: (1) Standing phase: a system consisting of one end-effector, the body, and four limbs, the legs; (2) Walking phase: a system consisting of one or two lifting legs (depending on the chosen gait), two or three supporting legs; (3) Floating phase: a system in which all legs detach from the ground. Control strategies based on our models are also introduced, which includes walk and trot gait plans. In our control system, two additional types of information are provided: (1) contacting forces are given by force sensors installed under feet; (2) body poses are determined by an inertial measurement unit (IMU). Combined with the sensor data and calibrated mass, inertia, and friction, the joint torque can be estimated accurately in simulation and experiment. Our prototype, the “XiLing” robot, is built to verify the methods proposed in this paper, and the results show that the models can be solved quickly and leads to steady locomotions.

Optimizing Kinematic Modeling and Self-Collision Detection of a Mobile Manipulator Robot by Considering the Actual Physical Structure

In this paper, an optimized kinematic modeling method to accurately describe the actual structure of a mobile manipulator robot with a manipulator similar to the universal robot (UR5) is developed, and an improved self-collision detection technology realized for improving the description accuracy of each component and reducing the time required for approximating the whole robot is introduced. As the primary foundation for trajectory tracking and automatic navigation, the kinematic modeling technology of the mobile manipulator has been the subject of much interest and research for many years. However, the kinematic model established by various methods is different from the actual physical model due to the fact that researchers have mainly focused on the relationship between driving joints and the end positions while ignoring the physical structure. To improve the accuracy of the kinematic model, we present a kinematic modeling method with the addition of key points and coordinate systems to some components that failed to model the physical structure based on the classical method. Moreover, self-collision detection is also a primary problem for successfully completing the specified task of the mobile manipulator. In traditional self-collision detection technology, the description of each approximation is determined by the spatial transformation of each corresponding component in the mobile manipulator robot. Unlike the traditional technology, each approximation in the paper is directly established by the physical structure used in the kinematic modeling method, which significantly reduces the complicated analysis and shortens the required time. The numerical simulations prove that the kinematic model with the addition of key point technology is similar to the actual structure of mobile manipulator robots, and the self-collision detection technology proposed in the article effectively improves the performance of self-collision detection. Additionally, the experimental results prove that the kinematic modeling method and self-collision detection technology outlined in this paper can optimize the inverse kinematics solution.

Kinematics Analysis and Optimization of a 3-DOF Planar Tensegrity Manipulator under Workspace Constraint

Tensegrity mechanisms (TM) are well-appraised for their compliance and lightweight, making their design theory a hot research topic recently. However, due to unconstrained DOFs, the design and analysis of TMs are generally more complicated than traditional mechanisms composed of rigid links and joints. A compact 3-DOF tensegrity manipulator is introduced and an advanced two-step kinematic modeling method is proposed in this paper. This method is first assumed that bars and cables are rigid to estimate the equilibrium state using the energy-based method. Then, the flexibility of bars and cables is considered, and the force density method equations are solved utilizing the equilibrium state obtained by the previous step as the initial guess of iteration for fast computation. Based on the two-step method, the performances of the TM, such as workspace, manipulability, potential energy, and stiffness, are analyzed. Thereafter, the installation position and size of the manipulator are optimized under the workspace constraint. In the optimization process, discrete points on the prescribed task workspace contour are used to simplify the constraint to improve computational efficiency. Finally, study cases are investigated to validate the proposed method, and the feasibility of the discrete sampling method for constraint simplification is also verified.

Kinematic modeling and solution of rigid-flexible and variable-diameter underwater continuous manipulator with load

AbstractThis paper presents a method to solve the kinematics of a rigid-flexible and variable-diameter continuous manipulator. The multi-segment underwater manipulator is driven by McKibben water hydraulic artificial muscle (WHAM). Considering the effect of elasticity and friction, we optimized the static mathematical model of WHAM. The kinematic model of the manipulator with load is established based on the hypothesis of piecewise constant curvature (PCC). We developed an optimization algorithm to calculate the length of the WHAMs according to the principle of minimum strain energy and obtain the configuration space parameters of the kinematic model. Based on the infinitesimal method, the homogeneous transformation matrices of the variable-diameter bending sections are computed, and the terminal position and attitude are obtained. In this paper, we studied the working space of the manipulator by quantitative analysis of the impact factors including pressure and load. A deep neural network (DNN) with six hidden layers is designed to solve inverse kinematics. The forward kinematic results are used to train and test the DNN, and the correlation coefficient between the output and target samples reaches 0.945. We carried out an underwater experiment and verified the effectiveness of the kinematic modeling and solution method.

Stability mechanism recognition and failure risk assessment on a high slope by synthesizing different analysis methods

The studied slope is located in the middle reach of the Yalong River in the eastern margin of Qinghai-Tibet Plateau in Southwest China. A large hydropower station is planning to be built near the slope. Understanding the stability mechanism of the slope is important for dam site design. Under a combination of tectonic activity, unloading and weathering, the bedrock mass was fractured. On the basis of field investigation, the GSI classification system and Barton criterion were introduced to determine the strength of the rock mass. The kinematic, limit equilibrium and discontinuum modeling methods were carried out to comprehensively understand the stability of the slope. The kinematic analyses show that only wedge mode is possible for large rock mass failure. However, limit equilibrium analyses show that both wedge failure and circular slip are not expected for rock mass. The slope rock mass is now in the surface rebalance stage. The potentially unstable part is the covering deposit. The 40 million m3 surface deposit is now nearly in a limit equilibrium state. The possibility of failure reaches 41%. Mitigation measures must be put into effect on the deposit to assure the stability of the slope. The results indicated that the failure mechanism of the slope was not controlled by the discontinuities in the rock mass at present but depended on the stability of the surface deposit.

Determination of the feasible setup parameters of a workpiece to maximize the utilization of a five-axis milling machine

The machining industry must maximize the machine tool utilization for its efficient and effective usage. Determining a feasible workpiece location is one of the significant tasks performed in an iterative way via machining simulations. The maximum utilization of five-axis machine tools depends upon the cutting system’s geometry, the configuration of the machine tool, and the workpiece’s location. In this research, a mathematical model has been developed to determine the workpiece’s feasible location in the five-axis machine tool for avoiding the number of iterations, which are usually performed to eliminate the global collision and axis limit errors. In this research, a generic arrangement of the five-axis machine tool has been selected. The mathematical model of postprocessor has been developed by using kinematic modeling methods. The machine tool envelopes have been determined using the post-processor and axial limit. The tooltip reachable workspace is determined by incorporating the post-processor, optimal cutting system length, and machining envelope, thereby further developing an algorithm to determine the feasible workpiece setup parameters accurately. The algorithm’s application has been demonstrated using an example. Finally, the algorithm is validated for feasible workpiece setup parameters in a virtual environment. This research is highly applicable in the industry to eliminate the number of iterations performed for the suitable workpiece setup parameters.

Modeling in Two Configurations of a 5R 2-DoF Planar Parallel Mechanism and Solution to the Inverse Kinematic Modeling Using Artificial Neural Network

This article introduces a new kinematic modeling method used to analyze coupled rigid multibody movements. The method was applied to the study of a 5R planar parallel mechanism’s kinematics and consists of analyzing two fixed configurations of the mechanism to systematize the rotational relationships between the two structures. Mathematical models were developed using complex numbers. The inverse kinematic problem was modeled as a system of eight nonlinear equations and eight unknowns, which was solved with Newton-Raphson’s method. Subsequently, with the inverse problem model, a numerical database related to the mechanism configurations, including singular positions, was generated to train a multilayer neural network. The Levenberg-Marquardt algorithm was used for network training. Finally, an interpolated linear path was used to understand the efficiency of the trained network.

The Kinematic Modeling and Simulation of an Adjustable Pivot Point of Six Degree-of-Freedom (DOF) Parallel Robot

For the pose requirements of secondary mirror in the large aperture space optical remote sensor, the pose adjustment is applied to the pivot point of secondary mirror. So the adjustable pivot point kinematic model must be set up. Based on the characteristics of the pivot point fixed with the moving platform, the corresponding coordinate system is built, and the adjustable pivot point kinematic model is established on the Euler rotation. Then virtual prototype model and the pivot point are built in ADAMS, and the kinematic simulation method is given. Finally, a 6-DOF parallel robot as secondary mirror pose adjustment device of an optical remote sensing system is taken as an example, and the adjustable pivot point kinematic model and ADAMS simulation method are carried out. The results show that the model and simulation method are correct and practical, which can be used in any field of a 6 DOF parallel robot with adjustable pivot point.

Kinematic interpretation of Darboux cyclides

Kinematic interpretation of quaternionic–Bézier curves and surfaces is revealed. This combination of kinematic and geometric modeling methods is used to characterize orbits of quadratic surfaces in the Study quadric under the kinematic map as certain Darboux cyclides. In particular, earlier unknown rational parametrizations of one-oval Darboux cyclides are found.

Kinematic Analysis of the Robot Having Closed Chain Mechanisms Based on an Improved Modeling Method and Lie Group Theory

The robot kinematic model is the basis of motion control, calibration, error analysis, etc. Considering these factors, the kinematic model needs to meet the requirements of completeness, model continuity, and minimality. DH model as the most widely used method to build robot kinematic model still has problems in completeness, model continuity, and calculation, especially for robots with complex mechanisms such as closed chain mechanism and branch mechanism. In this paper, an improved kinematic modeling method is proposed based on the cooperation of the DH model and the Hayati and Mirmirani model and considering the Lie group concept. The improved model is complete and continuous, and when combining with Lie group to calculate, it avoids numbers of trigonometric functions and antitrigonometric functions in the process so as to optimize the algorithm. With this method, the kinematic model of the closed chain cascade manipulator developed in our laboratory is established, and a working process of it is numerically calculated. The results of the numerical calculation are basically consistent with those of virtual prototype simulation, which means the established kinematic model is correct and the numerical calculation method can solve the problem correctly. The kinematic model and the results of the kinematic analysis provide a theoretical basis for the subsequent motion control, calibration, and error analysis of the robot.

A Hybrid Active and Passive Cable-Driven Segmented Redundant Manipulator: Design, Kinematics, and Planning

With a light-slender and superior dexterous body, the cable-driven segmented redundant manipulators (CSRMs) are excellent candidates for operations in narrow confined space. However, their application is still largely limited due to their weak stiffness, low load capacity, and complex modeling and planning. In this article, we design a new type of CSRM with high stiffness and load capacity using hybrid active and passive cables, and propose a simplified kinematics modeling and configuration planning method. The manipulator is composed of three active-linkage segments and one active tool end-effector. Each active segment, driven by three active driving cables, has two degrees of freedom (DOFs). By utilizing the passive linkage cables, the segment can be fully constrained with high stiffness, and move with equal joint angles in nearly continuous shape. Based on such structural features, the kinematics equations about the active segment-joint variables (i.e., the equalpitch and yaw angles of the whole segment) are derived. The direct, inverse kinematics and differential kinematics are greatly simplified. To find suitable solutions under environment constraints, extended virtual joint (EVJ) is introduced for quick regional solutions searching and equivalent kinematic constraint analysis. Furthermore, a configuration planning method based on the simplified kinematics and equivalent EVJs is proposed for single obstacle avoidance and continuous narrow space crossing tasks. Finally, a prototype system is developed and typical experiments are performed. The results show the high linkage accuracy, improved stiffness, and load capacity of the developed CSRM and verify the adaptability of the proposed configuration planning method.

A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

This paper proposes a method for kinematic calibration of a 3T1R, 4-degree-of-freedom symmetrical parallel manipulator driven by two pairs of linear actuators. The kinematic model of the individual branched chain is established by using the local product of exponentials formula. Based on this model, the model of the end effector’s pose error is established from a pair of symmetrical branched chains, and a recursive least square method is applied for the parameter identification. By installing built-in sensors at the passive joints, a calibration method for a serial manipulator is eventually extended to this parallel manipulator. Specifically, the sensor installed at the second revolute joint of each branched chain is saved, replaced by numerical calculation according to kinematic constraints. The simulation results validate the effectiveness of the proposed kinematic error modeling and identification methods. The procedure for pre-processing compensation on this 3T1R parallel manipulator is eventually given to improve its absolute positioning accuracy, using the inverse of the calibrated kinematic model.

Energy-Efficient Torque Distribution Optimization for an Omnidirectional Mobile Robot with Powered Caster Wheels

A mobile robot with no less than two powered caster wheels (PCWs) has the ability to perform omnidirectional motions and belongs to a redundantly actuated system. Redundant actuation will bring the issue of non-uniqueness of actuating torque distribution, and inappropriate choices of torque distribution schemes will lead to unexpected large required actuating torques and extra energy consumption. This paper proposes a new torque distribution optimization approach based on a gradient projection method (GPM) for the omnidirectional mobile robot (OMR) with direct drive PCWs. It can significantly reduce the maximal required actuating torque and the energy consumption of the system. The modular kinematic and dynamic modeling method is presented first, which is suitable for an arbitrary number of employed PCWs, as well as their install positions in the chassis. The detailed energy consumption model of the OMR, including output energy consumption and electrical energy loss, is formulated through experimental testing. The effectiveness of the proposed algorithms is validated by simulation examples. Lastly, the computational efficiency of the method is verified

Visual Servo Control of a Novel Magnetic Actuated Endoscope for Uniportal Video-Assisted Thoracic Surgery

This letter presents the first case of implementing visual servo control on a magnetic anchored endoscope. The novel magnetic actuated endoscope is designed for uniportal video-assisted thoracic surgery (VATS). It is compact and has a workspace close to the chest wall, which is suitable for operation in constrained space. The visual servo control allows the magnetic endoscope to automatically track a surgical instrument. In surgery, this can prevent human errors and muscle fatigues. The workflow is as follows: the kinematic model and control method are derived first. The control method is then verified in simulation. Experiments are conducted to validate the control method and prove feasibility of the system. Overall, contributions of this letter include the following. First, the development of a magnetic anchored and actuated endoscope capable of instrument tracking, which can improve uniportal VATS. Second, proving the feasibility of visual servo control in magnetic anchored endoscope, which can expand to development of other magnetic systems and surgical robots.

Kinematic calibration for industrial robots using articulated arm coordinate machines

To improve the position accuracy of industrial robots, a novel kinematic model and calibration method using articulated arm coordinate machines (AACMM) is proposed in this paper. The end of the industrial robot is connected to the probe of an AACMM, thus forming a closed kinematic chain. The coordinate systems of the double arms were established, based on which the mapping of the joint angles and the position of the end were derived as well as the nominal value of the kinematic parameters of the industrial robot. A two-step search method was presented for kinematic parameter identification of the industrial robot. The identified kinematic parameters were used to compensate the errors of the nominal kinematic parameters in the controller of the industrial robot. Experiments were conducted to verify the calibration method, which show that after calibration, the average position errors of the industrial robot were decreased greatly.

The influence of reference position deviation on industrial robots positioning precision

Due to industrial robot’s higher precision and better repeatability that human workforce, they have been chosen to replace human workload in all types of industrial activities. Due to the increasing positioning precision and repeatability needed by the industrial operations, it is necessary to use industrial robots that comply with the required technical specifications. For this reason, research on new methods to increase positioning accuracy is necessary. Some of the positioning errors are caused by the reference positioning deviations present in the industrial robot structure. Due to the systematic nature of reference position deviations, by entering the values in a compensation method, the positioning error is permanently minimized. In the paper are presented new methods of reference positioning deviations determination. In the paper is presented a mathematical model based on direct kinematic modeling method, used for calculating the position of the industrial robot end-effector. By applying these method’s, we can determine the reference positioning deviations and by introducing them into a specialized calculation system we can simulate the impact of these deviations. By applying these methods on a six axis articulated industrial robot and introducing the industrial robot’s parameters in a specialized calculating programs the positioning errors are determined and shown in the paper.

Modeling of Continuum Manipulators Using Pythagorean Hodograph Curves.

Research on continuum manipulators is increasingly developing in the context of bionic robotics because of their many advantages over conventional rigid manipulators. Due to their soft structure, they have inherent flexibility, which makes it a huge challenge to control them with high performances. Before elaborating a control strategy of such robots, it is essential to reconstruct first the behavior of the robot through development of an approximate behavioral model. This can be kinematic or dynamic depending on the conditions of operation of the robot itself. Kinematically, two types of modeling methods exist to describe the robot behavior; quantitative methods describe a model-based method, and qualitative methods describe a learning-based method. In kinematic modeling of continuum manipulator, the assumption of constant curvature is often considered to simplify the model formulation. In this work, a quantitative modeling method is proposed, based on the Pythagorean hodograph (PH) curves. The aim is to obtain a three-dimensional reconstruction of the shape of the continuum manipulator with variable curvature, allowing the calculation of its inverse kinematic model (IKM). It is noticed that the performances of the PH-based kinematic modeling of continuum manipulators are considerable regarding position accuracy, shape reconstruction, and time/cost of the model calculation, than other kinematic modeling methods, for two cases: free load manipulation and variable load manipulation. This modeling method is applied to the compact bionic handling assistant (CBHA) manipulator for validation. The results are compared with other IKMs developed in case of CBHA manipulator.