Inverse Kinematics Solution Research Articles

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.

Mathematical modeling and kinematic analysis of 5 degrees of freedom serial link manipulator for online real-time pick and place applications

<span lang="EN-US">Modeling and kinematic analysis are crucial jobs in robotics that entail identifying the position of the robot’s joints in order to accomplish particular tasks. This article uses an algebraic approach to model the kinematics of a serial link, 5 degrees of freedom (DOF) manipulator. The analytical method is compared to an optimization strategy known as sequential least squares programming (SLSQP). Using an Intel RealSense 3D camera, the colored object is picked up and placed using vision-based technology, and the pixel location of the object is translated into robot coordinates. The LOBOT LX15D serial bus servo controller was used to transmit these coordinates to the robotic arm. Python3 programming language was used throughout the entire analysis. The findings demonstrated that both analytical and optimized inverse kinematic solutions correctly identified colored objects and positioned them in their appropriate goal points.</span>

Inverse Kinematic Solver Based on Bat Algorithm for Robotic Arm Path Planning

The bat algorithm (BA) is a nature inspired algorithm which is mimicking the bio-sensing characteristics of bats, known as echolocation. This paper suggests a Bat-based meta-heuristic for the inverse kinematics problem of a robotic arm. An intrinsically modified BA is proposed to find an inverse kinematics (IK) solution, respecting a minimum variation of the joints’ elongation from the initial configuration of the robot manipulator to the proposed new pause position. The proposed method is called IK-BA, it stands for a specific bat algorithm dedicated to robotic-arms’ inverse geometric solution, and where the elongation control mechanism is embedded in bat agents update equations. Performances analysis and comparatives to related state of art meta-heuristics solvers showed the effectiveness of the proposed IK bat solver for single point IK planning as well as for geometric path planning, which may have several industrial applications. IK-BA was also applied to a real robotic arm with a spherical wrist as a proof of concept and pertinence of the proposed approach.

An Intelligent Human-like Motion Planner for Anthropomorphic Arms Based on Diversified Arm Motion Models

In this paper, the human-like motion issue for anthropomorphic arms is further discussed. An Intelligent Human-like Motion Planner (IHMP) consisting of Movement Primitive (MP), Bayesian Network (BN) and Coupling Neural Network (CPNN) is proposed to help the robot generate human-like arm movements. Firstly, the arm motion model is decoupled in the aspects of arm structure and motion process, respectively. In the former aspect, the arm model is decoupled into different simple models through the Movement Primitive. A Hierarchical Planning Strategy (HPS) is proposed to decouple a complete motion process into different sub-processes. Based on diversified arm motion models, the Bayesian Network is used to help the robot choose the suitable motion model among these arm motion models. Then, according to the features of diversified arm motion models, the Coupling Neural Network is proposed to obtain the inverse kinematic (IK) solutions. This network can integrate different models into a single network and reflect the features of these models by changing the network structure. Being a major contribution to this paper, specific focus is on the improvement of human-like motion accuracy and independent consciousness of robots. Finally, the availability of the IHMP is verified by experiments on a humanoid robot Pepper.

Boomerang Algorithm based on Swarm Optimization for Inverse Kinematics of 6 DOF Open Chain Manipulators

In this study, a feasible swarm intelligence algorithm is proposed that computes the inverse kinematics solution of 6 degree of freedom (DOF) industrial robot arms, which are frequently used in industrial and medical applications. The proposed algorithm is named as Boomerang algorithm due to its recursive structure. The proposed algorithm aims to reduce the computation time to feasible levels without increasing the position and orientation errors. In order to reduce the computational time in swarm optimization algorithms and increase feasibility, an alternative definition method was used instead of the DH method in defining the robot arm kinematic configuration. The effect of the proposed alternative definition method in reducing the computational time is presented through example inverse kinematic analysis. The proposed algorithm was compared with 3 different particle swarm optimization (PSO) variants that include orientation in the inverse kinematic solution of 6 DOF robot arms. Comparative simulation studies were carried out with 20 randomly selected position and orientation data from the workspaces of PUMA 560 and ABB IRB120 manipulators to measure performance of the algorithms. Using the error and computation time values obtained from the simulation results, the algorithms are compared using the Wilcoxon nonparametric statistical test. When the simulation results are analysed by considering the calculation time, positioning accuracy and solution finding rates, it is seen that the Boomerang algorithm is more feasible than the other PSO variants. Verification of the simulation results, and the physical applications were carried out with the ABB IRB120 6 DOF robot arm. Simulation studies and experimental studies showed that the proposed algorithm may be an efficient method for inverse kinematics of time-critical applications.

Inverse attitude solution of manipulator based on improved quaternion

Typically, quaternions or rotational matrices are used to establish kinematic equations and produce inverse kinematic solutions for the attitude of 6R decoupled manipulators. These approaches have certain drawbacks, such as duplicate equations and manual solution processes that cannot be eliminated automatically. In this study, we introduce the Ju-Gibbs quaternion to establish the kinematic equations, which are isomorphic to the Euler quaternion and share the same mathematical characteristics. Using this modeling method, one can create non-redundant kinematic equations wherein the number of equations equals the number of unknowns. A novel Dixon elimination method is then used to resolve the multilinear problem. Since no division operations are involved in the solution process, the solution has the advantage of being free of computation singularity issues. The experiment verifies that the proposed method can accomplish the autonomous modeling and elimination solution process of 6R manipulators with low computation complexity and high precision.

Formalization of the inverse kinematics of three-fingered dexterous hand

As an effective extension of human limbs, dexterous robotic hands based on cyber-physical systems (CPS) are used to perform diverse tasks in industrial production, medical operation, outer-space exploration, etc. The reliable functioning of dexterous robotic hands depends on the proper modeling and solving of inverse kinematics problems in the design phase. The traditional D-H parameter method for modeling and solving inverse kinematics problems suffers from the singularity problem, which is avoided by methods based on the screw theory. However, the manual or computer-simulation-based development of these methods could suffer from human errors and software defects. In this paper, we address this problem by using formal techniques and tools to develop a screw-theory-based method. Firstly, we formalize theories related to the Paden-Kahan sub-problem in an interactive theorem prover. Secondly, we construct a formal model for solving the inverse kinematics problem for robotic systems. Lastly, taking the three-fingered dexterous hand as a case study, we formally verified its inverse kinematics solutions. The results presented in this article help guarantee a level of safety for robotic systems that is beyond achievable by manual and computer-simulation-based development methods.

An inverse kinematics framework of mobile manipulator based on unique domain constraint

This paper presents the collision-free solution to the inverse kinematics of a mobile manipulator. The main contribution is to propose a novel inverse kinematics solution framework combining unique domains. The inverse kinematics problem is formulated as an optimization problem in this work. Firstly, the objective function is simplified by the kinematics decoupling method based on improved disconnection and re-connection. Then, the joint variables are decoupled and constrained, and an approach to initialize the variables is proposed. An inverse kinematic solution framework for the manipulator body to avoid obstacles is further presented, and CMA-ES is applied to the framework. Finally, the simulation results demonstrate the effectiveness of the proposed method.

Matrix Chain Multiplication and Equivalent Reduced-Order Parallel Calculation Method for a Robotic Arm

Intelligence development has put forward increasing requirements of real-time planning and dynamic feedback in controlling robotic arms. It has become essential in engineering applications to complete the kinematics calculation of complex manipulators in real time. This paper proposes a matrix cascading multiplication equivalent reduced-order parallel computing method for the multiplication of homogeneous matrices in the process of forward and inverse kinematics solutions, which reduces the order of the matrix according to the distribution of zero vectors in the homogeneous matrix calculations. The method removes the unnecessary multiplication in joint homogeneous matrixes containing zero vectors. It obtains the optimal calculation order of the cascade matrix multiplication through dynamic planning searches, improving the efficiency of effective dot product calculation by parallel computation. Calculation processes and specific examples are presented in this paper. Compared with the previous algorithms, the proposed algorithm reduces the calculation cycle by 90%, effectively improving the real-time calculation efficiency in the complex control process.

Time-optimal trajectory planning based on event-trigger and conditional proportional control.

Trajectory planning is an important issue for manipulators and robots. To get a optimal trajectory, many constraints including actuators specifications, motion range of joints, workspace limitations, etc, and many objectives including the shortest time, the shortest distance, the lowest energy consumption, the minimum oscillations, obstacles-avoiding, etc, should be considered both. In this paper, firstly, the forward kinematics and inverse kinematics of a five axis manipulator are deduced. And, a simple method to choose one appropriate solution from multi solutions of inverse kinematics is proposed. Secondly, an easy-implemented optimization method of trajectory planning is proposed based on seventh order polynomial interpolation, event-trigger mechanism and conditional proportional control (P control). The proposed optimization method can capture the time optimal trajectory, and the actuators specifications including velocity, acceleration of motor can be guaranteed as well. Thirdly, comparative simulations and experiments validate the effectiveness and efficiency of proposed optimization method. The research provides an insight for the application of trajectory optimization on the micro controller with low computing capability and high real-time performance requirement.

Performance Analysis of Hybrid Kinematic Mechanism for Fusion Reactor Maintenance

The hybrid kinematic mechanism (HKM) as an alternative remote handling subsystem of the Demonstration Fusion Power Plant (DEMO) breeding blanket (BB) is undergoing extensive theoretical analysis and feasibility verification. In this paper, the forward and inverse kinematic models of the HKM are derived by combining the Newtonian iterative method and the analytical method. Cartesian space trajectory planning is designed based on the trajectories of the HKM lifting of inboard and outboard BBs. The continuous smooth inverse kinematic solutions in the HKM joint space are obtained based on the polynomial interpolation method. For the characteristics of the HKM piston thread driving, the end-effector position error caused by the degradation of the spherical joint into a universal joint is analyzed and calculated. During the lifting of the left inboard BB, there is a maximum absolute error ∆P = 3.1 mm, and as the error continues to expand to the bottom of the BB it causes a risk of collision. Combining the overall effects of driving control, rigid–flexible coupling, etc., on position accuracy, an open-loop variable parameter error compensation plan based on the Levenberg–Marquardt (LM) nonlinear damping least-squares algorithm is proposed and validated in this paper. The simulation results show that the maximum absolute error after compensation is less than 1 mm as the mesh density increases, and the absolute position accuracy can be further improved by local mesh encryption. This study verifies the feasibility of the HKM as a BB remote handling subsystem and provides an option for high-precision control of the HKM.

Generation of Configuration Space Trajectories Over Semi-Constrained Cartesian Paths for Robotic Manipulators

Serial-link manipulators are required to execute trajectories that enable a robot end-effector or a tool to track a Cartesian path. Practical applications may not require constraining all six degrees of freedom (position and orientation) of the tool resulting in semi-constrained paths. Semi-constrained paths allow improved success rates and better quality trajectories as the robot has more freedom to meet the kinematic and dynamic constraints. Additionally, robotic applications will need to use multiple tool center points (TCPs) on the tool to generate feasible paths for the robot. We present an iterative graph construction method to find trajectories for semi-constrained Cartesian paths that also use multiple TCPs. Our graph-based method finds multiple inverse kinematic solutions for possible Cartesian poses that the robot can take and connects them to build a graph. The algorithm uses cues from the Cartesian space to prioritize poses that produce a better quality solution. A biasing scheme is also developed to selectively sample the starting Cartesian poses from available choices. Our method finds near-optimal solutions with significantly fewer nodes and edges in the graph. The algorithm’s performance results on complex industrial test cases are provided. Note to Practitioners—Industrial applications permit the relaxation of one or more degrees of freedom of the tool while following the Cartesian paths. The relaxation of constraints is introduced by defining tolerances between the tool and the workpiece. Multiple TCPs have to be employed for many tasks to use different surfaces of the tool. In this paper, we present a planning algorithm for semi-constrained Cartesian paths that can incorporate the use of multiple TCPs. The user can define discrete TCPs over the tool contact points or surfaces. The tolerances can be easily defined as angular limits on tool orientation along the Cartesian path. Our planning algorithm can work with others via point constraints in Cartesian space or joint space of the robot. Practitioners from the industry can use the method presented in this paper to develop automated robotic cells that do cutting, sanding, polishing, welding, painting, composite layup, additive manufacturing, and several other common applications.

Inverse kinematics solutions of a newly designed three-link robotic manipulator for the casting process using the ant lion optimizer

Inverse kinematics solutions of a newly designed three-link robotic manipulator for the casting process using the ant lion optimizer

Solution And Visualization 3D Plane Inverse Kinematics Method

The hyper-redundant type of robot is a type of robot that in carrying out its duties in the field of kinematics its degrees of freedom exceed the required minimum degrees. The advantage will be increased capability in operation and performance, if the degrees of freedom are excessive, even in unorganized and complex systems and environments. Algebraic approach method in inverse kinematics algorithm analysis can use; analytic algebra, jacobian basis, analytic KI, exponential multiplication, grobner, and conformal geometry. Iterative approach method in inverse kinematics algorithm analysis can use; genetic algorithm, fuzzy logic, ANFIS, and evolutionary algorithm. The geometric approach method in the inverse kinematics algorithm analysis can use; capital method. The purpose of this study is to analyze a virtual 2 arm robot, which will use axis manipulation in three dimensions using an inverse kinematics solution, using a geometric approach. How to step along on the z axis by rotating and using the reverse kinematics solution to the desired location. The visualization results will be repeated so as to ensure the effectiveness of the algorithm. As for this algorithm will provide a single solution, and this algorithm will prevent and reduce singularities if the link is lower.

Precision fingertip grasp: A human-inspired grasp planning and inverse kinematics approach for integrated arm–hand systems

In this paper, we present a human-inspired approach to solve grasp planning and inverse kinematics (IK) problems, simultaneously. Our proposed solution is for integrated arm–hand systems. Conventional approaches consider the robot manipulator (arm) and the robotic hand separately and solve the problems of grasp planning and IK in sequence. Such separate considerations of the arm and hand often introduce errors in the IK solution. The sequential approaches waste significant computational power in searching for infeasible grasps. To address these issues, we propose to consider the robotic arm and the hand as a kinematically integrated system. We then introduce a coarse-to-fine strategy to solve grasp planning and IK problems simultaneously. The proposed approach achieves force-closure fingertip grasping without using reachability information a priori. Instead, through an integrated grasp planning and IK solution, the reachability information is obtained from the IK solution and is used to filter out infeasible grasps. This strategy will dramatically reduce the search space and save significant computational power. Numerical examples will be used to demonstrate the efficiency of the proposed approach, in comparison to a sequential solution of the grasp planning and IK for integrated arm–hand systems.

Adaptive end‐effector pose control for tomato harvesting robots

AbstractThis paper investigates the development of a tomato‐harvesting robot operating on a plant factory and primarily studies the reachable pose of tomatoes in the nondexterous workspace of manipulator. The end‐effector can only reach the tomatoes with reachable poses when the tomatoes are within the nondexterous workspace. If the grasping pose is not reachable, it will lead to grasping failure. An adaptive end‐effector pose control method based on a genetic algorithm (GA) is proposed to find a reachable pose. The inverse kinematic solution based on analysis method of the manipulator is analyzed and the objective function of whether the manipulator has a solution or not is obtained. The grasping pose is set as an individual owing to the position of the tomatoes is fixed and the grasping pose is variable. The GA is used to solve until a pose that can make the inverse kinematics have a solution is generated. This pose is the reachable grasping pose of the tomato at this position. The quintic interpolation polynomial is used to plan the trajectory to avoid damage to tomatoes owing to fast approaching speed and a distance based background filtering method is proposed. Experiments were performed to verify the effectiveness of the proposed method. The radius of the workspace of the UR3e manipulator with the end‐effector increased from 550 to 800 mm and the grasping range expanded by 208%. The harvesting success rate using the adaptive end‐effector pose control method and trajectory planning method was 88%. The cycle of harvesting a tomato was 20 s. The experimental results indicated that the proposed tomato‐recognition and end‐effector pose control method are feasible and effective.

Mathematical Analysis and Motion Capture System Utilization Method for Standardization Evaluation of Tracking Objectivity of 6-DOF Arm Structure for Rehabilitation Training Exercise Therapy Robot.

A treatment method for suppressing shoulder pain by reducing the secretion of neurotransmitters in the brain is being studied in compliance with domestic and international standards. A robot is being developed to assist physical therapists in shoulder rehabilitation exercise treatment. The robot used for rehabilitation therapy enables the training of patients to perform rehabilitation exercises repeatedly. However, the biomechanical movement (or motion) of the shoulder joint should be accurately designed to enhance efficiency using a shoulder rehabilitation robot. Furthermore, safely treating patients by accurately evaluating biomechanical movements in compliance with domestic and international standards is a major task. Therefore, an in-depth analysis of shoulder movement is essential for understanding the mechanism of shoulder rehabilitation using robots. This paper proposes a method for analyzing shoulder movements. The rotation angle and range of motion (ROM) of the shoulder joint are measured by attaching a marker to the body and analyzing the inverse kinematics. The first motion is abduction and adduction, and the second is external and internal rotation. The location information of the marker is transmitted to an application software through an infrared camera. For the analysis using an inverse kinematics solution, five males and five females participated in the motion capture experiment. The subjects did not have any disability, and abduction and adduction were repeated 10 times. As a result, ROM of the abduction and adduction were 148° with males and 138.7° in females. Moreover, ROM of the external and internal rotation were 111.2° with males and 106° in females. Because this study enables tracking of the center coordinates of the joint suitably through a motion capture system, inverse kinematics can be accurately calculated. Additionally, a mathematical inverse kinematics equation will utilize follow-up study for designing an upper rehabilitations robot. The proposed method is assessed to be able to contribute to the definition of domestic and international standardization of rehabilitation robots and motion capture for objective evaluation.

Research on Inverse Kinematics Solution of Manipulator Based on FGA Optimized BP Neural Network

In view of the complexity of the traditional inverse kinematics solution, it is solved by the mapping of the BP neural network, but the precision is low and the network performance is not good. By using FGA to optimize BP neural network, the shortcomings of the neural network itself can be overcome. Taking the pose matrix and joint angle of the manipulator as the input and output variables of the prediction network, the inverse solution prediction BP network of the manipulator is constructed, and then samples are selected for training. Finally, the network test and simulation results show that the optimized BP neural network has higher prediction precision and improved network performance.

Inverse Kinematics Solution and Trajectory Planning of Redundant Manipulator Based on Improved Gradient Projection Method

With the rapid development of high-speed railways, the water injection way for the train is developing in the direction of full automation. To enable the water-carrying robot arm on the train to cope with various emergencies during the operation, it is necessary to keep the robot arm more flexible. In this paper, the improved gradient projection algorithm (IGPM) is combined with the rapidly expanding random tree algorithm (RRT), and the optimal goal is to maximize the manipulator’s degradation operability and obtain a path with the best fault tolerance under the continuous joint angle. Finally, with the 4R redundant manipulator serving as an example, the feasibility and superiority of the algorithm in this paper are compared and verified through the numerical simulation method.

Simulation on control system of the parallel ankle rehabilitation mechanism driven by Pneumatic Artificial Muscles

The ankle is the most weight-bearing joint in the body, which plays a vital role in ensuring people’s walking. Aiming at the problems of complex mechanism, rigid drive and difficult control of the current ankle joint rehabilitation equipment, a 3-SPS/S type ankle parallel rehabilitation mechanism based on pneumatic artificial muscles is developed, and a self-tuning PID controller based on BP neural network is proposed to improve the accuracy of the control system. According to the static characteristics of the pneumatic artificial muscle, the physicians mathematical model of the artificial muscle is optimized, the kinematic position inverse solution of the ankle joint parallel rehabilitation mechanism is analysed and the control system is established. Combined with traditional PID control and BP neural network control algorithm, the BP_PID controller is completed, the control system is simulated and analysed. The simulation results show that BP_PID controller can meet design requirements for the ankle joint parallel rehabilitation mechanism, and is obviously superior to the PID controller in response speed and control accuracy.