Inverse Kinematics Solution Research Articles

Development of the LSTM Model and Universal Polynomial Equation for All the Sub-Phases of Human Gait

Human gait can be measured using a change in the joint angles value of the lower limb joints during walking. Inverse kinematics (IK) of a human leg refers to calculating joint angle values from different leg positions during locomotion. This paper calculates a real-time IK for a 3-link kinematic leg using a musculoskeletal model in OpenSim. The model provides the analytical solution of IK, which is quick and accurate. But, the model-based approach is very much dependent on the morphology of the bipedal robot. The existing bipedal robots are mainly planned for walking on flat terrain and unconstrained environment. So, these limitations lead to the developing of a generalised polynomial equation for generating walking trajectories. The model-based approaches rely on the degree of similarity between the virtual human model and the actual human body, which does not fully describe the human body. Due to the difference in real and virtual models, the model-based approaches suffer during the optimisation process of the boundary conditions and the mass-inertial parameters, leading to an unstable numerical solution. The learning-based method using long short-term memory (LSTM) model for gait generation is proposed to overcome the limitation of model-based approaches.

Inverse kinematics solution of demolition manipulator based on global mapping

In solving the inverse kinematics of the redundant hydraulic manipulator of the demolition robot, there are problems of multiple solutions and the contradiction between the real-time and accuracy of the calculation. A series calculation strategy combining global mapping and local search was proposed. Firstly, the inverse kinematics solution was mapped from the global space to the local space of the working point by the global neural network model, and then the inverse solution results were obtained by the local search of the gravitational search algorithm. To avoid the GSA falling into the local minima and improve the search speed and accuracy, an improved gravitational particle adaptive step search strategy was proposed to balance the exploration and development stage of the population. The simulation and experimental results show that the global than local inverse solution algorithm can avoid the multi-solution problems and ensure the stability and accuracy of the solution on the basis of real-time inversion.

A Research on Manipulator-Path Tracking Based on Deep Reinforcement Learning

The continuous path of a manipulator is often discretized into a series of independent action poses during path tracking, and the inverse kinematic solution of the manipulator’s poses is computationally challenging and yields inconsistent results. This research suggests a manipulator-route-tracking method employing deep-reinforcement-learning techniques to deal with this problem. The method of this paper takes an end-to-end-learning approach for closed-loop control and eliminates the process of obtaining the inverse answer by converting the path-tracking task into a sequence-decision issue. This paper first explores the feasibility of deep reinforcement learning in tracking the path of the manipulator. After verifying the feasibility, the path tracking of the multi-degree-of-freedom (multi-DOF) manipulator was performed by combining the maximum-entropy deep-reinforcement-learning algorithm. The experimental findings demonstrate that the approach performs well in manipulator-path tracking, avoids the need for an inverse kinematic solution and a dynamics model, and is capable of performing manipulator-tracking control in continuous space. As a result, this paper proposes that the method presented is of great significance for research on manipulator-path tracking.

An Improved Unit Quaternion for Attitude Alignment and Inverse Kinematic Solution of the Robot Arm Wrist

This paper introduces a new method for kinematic modeling of the robot arm by deriving a new elegant mathematical formula based on the axis vector with the tangent of the rotation angle. For this purpose, an innovative analytical quaternion is introduced through integration between Axis-Invariants and unit quaternion features named Ju-Gibbs quaternion, which expresses the body rotation with non-redundant parameters compared with the quaternions in literature. Two theorems based on the new form of the quaternion are developed and proved for the kinematic modeling of the robot arm. The first is attitude alignment, which is essential in multiaxial rotation systems. The second theorem for the wrist inverse kinematic (IK) solution is utilized to obtain the joint variables for the last joints of the end effector. In order to verify the effectiveness and accuracy of the proposed method, a numerical example and simulation of different structural configurations of robot and human arms are intensively studied. The novel quaternion provides a new tool for kinematic analysis and reduces the computational complexity of the kinematic solutions of the Robot-Arms wrist. Furthermore, the method laid a new foundation for the IKs of multi-axis systems based on Axis-Invariant and tangent quaternion.

Inverse Kinematics Solution Based on Redundancy Modeling and Desired Behaviors Optimization for Dual Mobile Manipulators

Inverse Kinematics Solution Based on Redundancy Modeling and Desired Behaviors Optimization for Dual Mobile Manipulators

Kinematics modeling method of continuum space manipulator based on virtual discrete-jointed manipulator models

Continuum space manipulators (CSMs) have key application prospects in the maintenance of spacecrafts in narrow environments and space debris removal. Similar to conventional articulated space manipulators (ASMs), CSMs encounter a number of kinematic, dynamic, and control problems caused by the dynamic coupling between the continuum manipulator and its microsatellite platform. However, the continuum manipulator has no obvious kinematic joints. In addition, its motion is generated by the continuum deformation of its elastic body; thus, the virtual manipulator (VM) model of ASM in the free-floating state becomes inappropriate for CSMs. In this study, we propose a kinematic equivalent method for a free-floating CSM, which is equivalent to a virtual discrete-jointed manipulator (VDJM) connected to a virtual ground. First, the constraint relationship is used to establish the virtual vector manipulator (VVM) model for the CSM such that its center of mass in the free-floating mode remains unchanged. Furthermore, on the basis of the VVM model and D-H parameters of the CSM, virtual discrete joints are introduced, and a VDJM model for the CSM is proposed. Compared with the VVM model, the developed VDJM model can more intuitively express the motion characteristics of the CSM. Finally, we demonstrate the application potential of the developed VDJM model in the inverse kinematics solution, workspace, and dynamic coupling of CSMs.

An Analytical Solution for Inverse Kinematics of SSRMS-Type Redundant Manipulators

Compared with non-redundant manipulators, the self-motion of 7-DOF redundant manipulators results in an infinite number of inverse kinematics solutions for a desired end-effector pose. This paper proposes an efficient and accurate analytical solution for inverse kinematics of SSRMS-type redundant manipulators. This solution is applicable to SRS-type manipulators with the same configuration. The proposed method involves introducing an alignment constraint to restrain the self-motion and to decompose the spatial inverse kinematics problem into three independent planar subproblems simultaneously. The resulting geometric equations depend on the part of the joint angles, respectively. These equations are then computed recursively and efficiently using the sequences of (θ1,θ7), (θ2,θ6), and (θ3,θ4,θ5), generating up to sixteen sets of solutions for a given desired end-effector pose. Additionally, two complementary methods are proposed for overcoming the possible singular configuration and judging unsolvable poses. Finally, numerical simulations are conducted to investigate the performance of the proposed approach in terms of average calculation time, success rate, average position error, and the ability to plan a trajectory with singular configurations.

A kinematic modeling scheme of three-axis "Satcom-on-the-Move" antenna based on modified Denavit-Hartenberg method

The current three-axes Satcom-on-the-Move(SOTM) antenna modeling method has some shortcomings, such as low model accuracy, poor portability and so on. In order to solve the above-mentioned shortcomings, a new modified Denavit-Hartenberg(NMDH) kinematics modeling scheme for the three-axes SOTM antenna was proposed. To overcome the modeling difficulties caused by the inherent mechanical structure of the antenna, and meet the requirements of the modified Denavit-Hartenberg(MDH) method, the virtual coordinate system and auxiliary coordinate systems are designed and added respectively on the basis of the MDH method, the forward kinematics model and inverse kinematics solution of the three-axes SOTM antenna are obtained. The correctness of the NMDH modeling scheme is verified by digital simulation. Finally, the system tests are carried out. The test results show that the NMDH modeling scheme proposed in this paper achieves good effect of antenna tracking satellite, and has stronger portability than the system identification modeling method commonly used in engineering.

Design and multi-objective optimization of a novel 5-DOF parallel mechanism with two double-driven chains

AbstractThis paper focuses on the design, analysis, and multi-objective optimization of a novel 5-degrees of freedom (DOF) double-driven parallel mechanism. A novel 5-DOF parallel mechanism with two double-driven branch chains is proposed, which can serve as a machine tool. By installing two actuators on one branch chain, the proposed parallel mechanism can achieve 5-DOF of the moving platform with only three branch chains. Afterwards, analytical solution for inverse kinematics is derived. The 5 $\times$ 5 homogeneous Jacobian matrix is obtained by transforming actuator velocities into linear velocities at three points on the moving platform. Meanwhile, the workspace, dexterity, and volume are analyzed based on the kinematic model. Ultimately, a stage-by-stage Pareto optimization method is proposed to solve the multi-objective optimization problem of this parallel mechanism. The optimization results show that the workspace, compactness, and dexterity of this mechanism can be improved efficiently.

Dynamic Parallel Mapping and Trajectory Planning of Robot Arm in Unknown Environment

A high real-time robot arm mapping and dynamic shortest path planning algorithm is proposed, which is used for low-cost depth cameras and robot arms. First of all, an inverse kinematics solution algorithm for a non-spherical wrist joint is proposed for the Kinova Mico2 manipulator. Based on the idea of position and attitude decoupling combined with the numerical solution, the solution of multiple sets of inverse kinematics is acquired. Secondly, a hand-eye system is established on the basis of the depth camera-RealSense. The point cloud is inversely solved through the depth map, which is pre-processed by the pass-through filtering and outlier removal algorithm. A scene parallel mapping method is designed to achieve the real-time reconstruction of the working scene for the robot arm, in which the maintenance of map and large matrix operations can be completed by GPU. Thirdly, a path planning algorithm with the shortest path for the manipulator end in Cartesian space is designed based on D* method and grid map. The attitude interpolation and smoothing are performed on the path points to obtain the executable joint trajectories on the time axis. Finally, the ROS system is used to build a simulation test verification environment, and the effectiveness of the related algorithms is verified through multiple simulation cases.

A closed-form solution for inverse kinematics of redundant space manipulator with multiple joint offsets

This paper proposes a novel parameterization analytical method to solve the inverse kinematics of a redundant space manipulator, which has link offsets at the shoulder, elbow, and wrist parts. Due to the manipulator’s particular configuration, current arm angle concepts cannot provide the analytical solution directly. Hence, this paper defines a new arm angle parameter that describes the manipulator’s redundancy and obtains the closed-form solutions directly. This is because, unlike manipulators without offset links, existing approaches involve parameters that may cause the inverse kinematic solution to fail when applied to the manipulator type considered in this work. Specifically, we analyze the parameter interplay on the inverse kinematic computation and then investigate the relations between the singularity and arm angle based on the singularity conditions of the Jacobian matrix. Besides, a semi-analytical method is proposed to determine the feasible arm angle intervals, while avoiding the singularity and inverse kinematic computation. Finally, a simple approach is proposed to compute the arm angle according to the feasible intervals. The proposed method has obvious geometric significance, is suitable for configuration control, and can be implemented in real-time control systems.

A computationally effective singularity avoidance method for redundant manipulators with non-spherical wrists

For redundant manipulators with non-spherical wrists, we propose a general and computation-effective method of singularity avoidance. Firstly, the dimension of the Jacobian of the redundant manipulator is reduced by the elementary transformation method to obtain the singular factors. Secondly, we use the damped reciprocal method to solve the inverse kinematics solutions of the redundant manipulator. Thirdly, the singularities of the redundant manipulator are divided into non-escapable and escapable singularities, and the singular conditions are determined with the singular factors. Then taking the singularity avoidance as the secondary task of the control system, we propose a singular factor optimization method to avoid both types of singularities of the redundant manipulator. The complexity analysis shows that no need to calculate the pseudo-inverses or partial derivatives of the Jacobian, the proposed method has lower computational complexity. Finally, simulations have been made on the non-escapable and escapable singularities to verify the proposed methods.

A Predictable Obstacle Avoidance Model Based on Geometric Configuration of Redundant Manipulators for Motion Planning

When a manipulator works in dynamic environments, it may be affected by obstacles and may cause danger to people around. This requires the manipulator to be able to plan the obstacle avoidance motion in real time. Therefore, the problem solved in this paper is dynamic obstacle avoidance with the whole body of the redundant manipulator. The difficulty of this problem is how to model the manipulator to reflect the motion relationship between the manipulator and the obstacle. In order to describe accurately the occurrence conditions of the collision, we propose the triangular collision plane, a predictable obstacle avoidance model based on the geometric configuration of the manipulator. Based on this model, three cost functions, including the cost of the motion state, the cost of a head-on collision, and the cost of the approach time, are established and regarded as optimization objectives in the inverse kinematics solution of the redundant manipulator combined with the gradient projection method. The simulations and experiments on the redundant manipulator and the comparison with the distance-based obstacle avoidance point method show that our method improves the response speed of the manipulator and the safety of the system.

Forward and Inverse Kinematics Solution of A 3-DOF Articulated Robotic Manipulator Using Artificial Neural Network

In this research paper, the multilayer feedforward neural network (MLFFNN) is architected and described for solving the forward and inverse kinematics of the 3-DOF articulated robot. When designing the MLFFNN network for forward kinematics, the joints' variables are used as inputs to the network, and the positions and orientations of the robot end-effector are used as outputs. In the case of inverse kinematics, the MLFFNN network is designed using only the positions of the robot end-effector as the inputs, whereas the joints’ variables are the outputs. For both cases, the training of the proposed multilayer network is accomplished by Levenberg Marquardt (LM) method. A sinusoidal type of motion using variable frequencies is commanded to the three joints of the articulated manipulator, and then the data is collected for the training, testing, and validation processes. The experimental simulation results demonstrate that the proposed artificial neural network that is inspired by biological processes is trained very effectively, as indicated by the calculated mean squared error (MSE), which is approximately equal to zero. The resulted in smallest MSE in the case of the forward kinematics is 4.592×10^(-8) in the case of the inverse kinematics, is 9.071×10^(-7). This proves that the proposed MLFFNN artificial network is highly reliable and robust in minimizing error. The proposed method is applied to a 3-DOF manipulator and could be used in more complex types of robots like 6-DOF or 7-DOF robots.

Extension of Inverse Kinematic Solution for a Robot to Cope With Joint Angle Constraints

Extension of Inverse Kinematic Solution for a Robot to Cope With Joint Angle Constraints

Machine learning-based framework for optimally solving the analytical inverse kinematics for redundant manipulators

Solving the analytical inverse kinematics (IK) of redundant manipulators in real time is a difficult problem in robotics since its solution for a given target pose is not unique. Moreover, choosing the optimal IK solution with respect to application-specific demands helps to improve the robustness and to increase the success rate when driving the manipulator from its current configuration towards a desired pose. This is necessary, especially in high-dynamic tasks like catching objects in mid-flights. To compute a suitable target configuration in the joint space for a given target pose in the trajectory planning context, various factors such as travel time or manipulability must be considered. However, these factors increase the complexity of the overall problem which impedes real-time implementation. In this paper, a real-time framework to compute the analytical inverse kinematics of a redundant robot is presented. To this end, the analytical IK of the redundant manipulator is parameterized by so-called redundancy parameters, which are combined with a target pose to yield a unique IK solution. Most existing works in the literature either try to approximate the direct mapping from the desired pose of the manipulator to the solution of the IK or cluster the entire workspace to find IK solutions. In contrast, the proposed framework directly learns these redundancy parameters by using a neural network (NN) that provides the optimal IK solution with respect to the manipulability and the closeness to the current robot configuration. Monte Carlo simulations show the effectiveness of the proposed approach which is accurate and real-time capable ($\approx$ \SI{32}{\micro\second}) on the KUKA LBR iiwa 14 R820.

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.

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.

Analytical and deep learning approaches for solving the inverse kinematic problem of a high degrees of freedom robotic arm

Inverse kinematics is the basis for controlling the motion of robotic manipulators. It defines the required joint variables for the robotic end-effector accurately reach the desired location. Due to the derivation difficulty, computation complexity, singularity problem, and redundancy, analytical Inverse kinematics solutions pose numerous challenges to the operation of many robotic arms, especially for a manipulator with a high degree of freedom. This paper develops different Deep Learning networks for solving the Inverse kinematics problem of six- Degrees of Freedom robotic manipulators. The implemented neural architectures are Artificial Neural Network, Convolutional Neural Network, Long–Short Term Memory, Gated Recurrent Unit, and Bidirectional Long–Short Term Memory. In this context, we associate the proposed results with a specific tuning of Deep Learning network hyper-parameters (number of hidden layers, learning rate, Loss function, optimization algorithm, number of epochs, etc.). The Bidirectional Long–Short Term Memory network outperformed all proposed architectures. To be close as possible to the experimental results, we have included two types of noise in the training data set to validate which of the five proposed neural networks is more efficient. Furthermore, in this study, we compare the performance of analytical and soft computing solutions in generating robots’ trajectories. We include this scenario, focusing on the advantage of implementing neural networks in avoiding the singularity problem that can occur using the analytical approach. In addition, we used the RoboDK simulator to show simulation results with real-world meaning. The performance of Deep Learning models depends on the complexity of the posed problem. Moreover, the complexity of the Inverse Kinematics problem is related to the number of Degrees of Freedom. At the end of this work, we evaluate the influence of the complexity of robotic manipulators on the proposed Deep Learning networks’ performance. The results show that the implemented Deep Learning mechanisms performed well in reaching the desired pose of the end-effector. The proposed inverse kinematics strategies apply to other manipulators with different numbers of Degrees of Freedom.

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.