Inverse Kinematics Solution Research Articles

Upper limb exoskeleton rehabilitation robot inverse kinematics modeling and solution method based on multi-objective optimization

The inverse kinematics problem of exoskeleton rehabilitation robots is challenging due to the lack of a standard analytical model, resulting in a complex and varied solution process. This complexity is especially pronounced in redundant upper limb exoskeleton robots, where inefficient solutions hinder the robot’s ability to adapt to the kinematic shape of the upper limb. This paper proposes a modeling and solution method based on multi-objective optimization to address the inverse kinematics of upper limb exoskeleton robots. We analyzed and validated this method using a redundant upper limb exoskeleton rehabilitation robot system developed by ourselves. First, we established a multi-objective inverse kinematics solution model by defining the end-position function, joint motion comfort function, system energy consumption function, motion safety, and human-like constraints. Then, the solution was designed based on the Improved Equilibrium Optimization (IEO) algorithm and validated its computational performance in terms of optimization ability, accuracy, and robustness. Finally, we experimentally tested the inverse kinematics solution model with the IEO algorithm on discrete objectives and continuous training trajectories using a redundant upper limb exoskeleton rehabilitation robot system. The results show that by incorporating the joint comfort function, system energy consumption function, and human-like constraints into the inverse kinematics model, we can not only quickly solve the inverse kinematics of redundant upper limb exoskeleton robots but also significantly improve the robot’s motion shape. Furthermore, it has better solution accuracy and stronger robustness than other algorithms when solving this inverse kinematics model based on the IEO algorithm.

Design and kinematics of a novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair

PurposeThis paper aims to present the mechanical design and kinematics of a novel rigid-flexible coupling hybrid robot to develop a promising aeroengine blades in situ repair technology.Design/methodology/approachAccording to requirements analysis, a novel rigid-flexible coupling hybrid robot is proposed by combining a three degrees of freedom (DOF) parallel mechanism with a flexible continuum section. Then the kinematics models of both parallel mechanism and flexible continuum section are derived respectively. Finally, based on equivalent joint method, a two-step numerical iterative inverse kinematics algorithm is proposed for the whole robot: (1) the flexible continuum section is equivalently transformed to a 2-DOF spherical joint, thus the approximate analytical inverse kinematic solution can be obtained; (2) the accurate solution is derived by an iterative derivation of both parallel mechanism and flexible continuum section.FindingsTo verify structure scheme and the proposed kinematics modeling method, numerical simulations and prototype experiments are implemented. The results show that the proposed kinematics algorithm has sufficient accuracy and computational efficiency in the whole available workspace, that is end-effector position error and orientation error are less than 0.2 mm and 0.01° respectively, and computation time is less than 0.22s.Originality/valueA novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair is designed. A two-step numerical iterative inverse kinematics algorithm is proposed for this unique hybrid robots, which has good accuracy and computational efficiency.

Deep Learning-Driven Analysis of a Six-Bar Mechanism for Personalized Gait Rehabilitation

Abstract Recent advances in robotics and artificial intelligence have highlighted the potential for the integration of computational intelligence in enhancing the functionality and adaptability of robotic systems, particularly in rehabilitation. Designing robotic exoskeletons for the lower limb rehabilitation of post-stroke patients requires frequent adjustments to accommodate individual differences in leg anatomy. This complex engineering challenge necessitates a deep understanding of human physiology, robotics, and optimization to develop adaptive robotic systems and also to swiftly quantify the required adjustments and implement them for each patient. The conventional approaches, which mostly rely on heuristics and manual tuning, often struggle to achieve optimal results. This paper presents a novel method that integrates a genetic algorithm (GA) with a deep learning approach to generate a gait trajectory of the ankle joint from a six-bar linkage mechanism of fixed dimensions. Later, using the same approach, the inverse kinematics solution for this mechanism is also devised whereby, the set of the link dimensions of the six-bar linkage mechanism is obtained for the given gait trajectory of an individual to achieve customization. We simulated the kinematic behavior of the six-bar linkage mechanism within defined mechanical constraints and utilized the generated data for training a feedforward neural network and long short-term memory models. The proposed model, when trained, can produce accurate lengths for the desired gait trajectories in the sagittal plane and vice-versa which further validates our proposed approach for inverse kinematics solution.

Robot inverse kinematics solution for center selection battle royale optimization algorithm

In order to solve the problems of high time complexity and insufficient global exploration ability of the battle royale optimization algorithm, this paper proposes an improved battle royale optimization algorithm based on chaos mapping, center selection and elite adaptive strategy. Through benchmark function testing, compared to particle swarm optimization algorithm, whale optimization algorithm, and the battle royale optimization algorithm, the improved algorithm significantly reduces time complexity and notably enhances convergence precision, speed, and stability. The improved algorithm is applied to the inverse kinematics problem of robots. The accuracy and The stability of the improved algorithm is better than those of the traditional battle royale optimization algorithm, it demonstrates superior solving precision and stability, proving its practicality and potential for development in solving robot inverse kinematics problems.

EMSA-IK: a real-time evolutionary multi-objective semi-analytical inverse kinematics algorithm for redundant manipulators

Purpose This paper aims to propose a real-time evolutionary multi-objective semi-analytical inverse kinematics (IK) algorithm (EMSA-IK) for solving the multi-objective IK of redundant manipulators. Design/methodology/approach Within EMSA-IK, the parameterization method is applied to reduce the number of optimization variables of the evolutionary algorithm and calculate semi-analytical solutions that meet high target pose accuracy. The original evolutionary algorithm is improved with the proposed adaptive search sub-space strategy so that the improved evolutionary algorithm can be used to efficiently perform global search within the parametric joint space to obtain the global optimal parametric joint angles that satisfy multi-objective constraints. Findings Ablation experiments show the effectiveness of the improved strategy used for evolutionary algorithms. Comparative experiments on different manipulators demonstrate the advantages of EMSA-IK in terms of generalizability and balancing multiple objectives, for example, motion continuity, joint limits and obstacle avoidance. Real-world experiments further validate the effectiveness of the proposed algorithm for real-time application. Originality/value The semi-analytical IK solution that simultaneously satisfies high target pose accuracy and multi-objective constraints can be obtained in real time. Compared to existing semi-analytical IK algorithms, the proposed algorithm achieves obstacle avoidance for the first time. The proposed algorithm demonstrates superior generalizability, applicable to not only redundant manipulators with revolute joints but also those with prismatic joints.

Kineto-static analysis of a hybrid manipulator consisting of rigid and flexible limbs with locking function for planar shape morphing

The incorporation of lockable passive backbones into active compliant morphing systems efficiently results in lightweight, high-load, and large deformation systems. However, there exist challenges in kineto-static analysis due to the interaction between rigid reconfigurable kinematic constraints and the nonlinear deformation of actuated flexible limbs. This paper addresses these issues by developing a kineto-static method to analyze the motion in a novel planar 3-DOF shape-morphing manipulator. The manipulator features two actuated flexible limbs with a lockable variable geometry truss (LVGT). In this study, two isostatic topologies are selected for reconfigurable motion control under external tip loads. A multi-step sequential control strategy is proposed to maneuver the manipulator's platform for desired poses. Then, a constrained-trajectory-based kinematic model is proposed for an inverse kinematic solution considering motion planning. Subsequently, a kineto-static model is introduced, considering constraints from rigid and flexible limbs, aiming to distribute distributing redundant actuation forces. Finally, nonlinear finite element analysis (FEA) and experiments are carried out to validate the effectiveness of the proposed method.

Kinematics-guided data-driven energy surrogate model for robotic additive manufacturing

With the increase in the usage of industrial robots for manufacturing applications, there will be a corresponding rise in energy consumption. Especially, robotic additive manufacturing (AM) has demonstrated significant potential for working autonomously in hazardous or extraterrestrial settings, as well as for producing large-scale structures. Recent advancements have made it possible for teams of robots to collaborate for printing structures even larger than their sizes together. Utilizing robots efficiently for AM is essential for achieving energy sustainability goals. The literature on energy models for robots and AM processes lacks a comprehensive energy model for robotic AM. To address this gap, a multi-point trajectory-based energy model is proposed for robotic AM. The model is created to help users manufacture parts in an energy-efficient way. These simulations require a significant amount of computation time, which limits their usage to offline purposes only. Hence, we propose two energy surrogate models for real-time predictions: a pure data-driven model and a kinematics-guided data-driven model. The kinematics-guided approach is an enhanced version of pure data-driven model which learns from inverse kinematics solutions along the trajectory to understand the robot’s dynamics and kinematics. There were two test cases conducted. The first test case consisted of paths that were feasible, printable, and within the robot’s reach, while the second test case consisted of a mixture of paths that were both feasible and infeasible. In comparison to the pure data-driven approach, the kinematics-guided approach stood out in both testing cases. Two real-world case studies have been used to demonstrate that the proposed approach can be used in lieu of simulations for real-time applications. Especially in the second case, where the part was placed very close to the robot making a portion of the part infeasible to print, the proposed approach correctly identified that it was not possible to print the geometry due to the robot’s kinematics. The proposed kinematics-guided approach is 195 and 700 times faster than the simulation results, respectively, in two case studies, and thus supporting the use of the proposed approach for real-time applications.

Direct and inverse kinematics solutions of a particular type of 3-PSP parallel manipulator

Abstract In this paper, the direct and inverse kinematics problems for a particular type of 3-DOF, 3-PSP parallel manipulator are considered. The proposed direct kinematics solution is based on an existing one in the literature, but with an alternative, simplified second stage in the solution’s formulation. An explicit analytical solution of the inverse kinematics problem is also proposed for one of the manipulator’s operational modes, requiring one pass through the direct kinematics solution. The proposed solutions can be seamlessly extended to the inverted parallel structure.

Inverse kinematic solution and singularity avoidance using a deep deterministic policy gradient approach

<p>The robotic arm emerges as a subject of paramount significance within the industrial landscape, particularly in addressing the complexities of its kinematics. A significant research challenge lies in resolving the inverse kinematics of multiple degree of freedom (M-DOF) robotic arms. The inverse kinematics of M-DOF robotic arms pose a challenging problem to resolve, thus it involves consideration of singularities which affect the arm robot movement. This study aims a novel approach utilizing deep reinforcement learning (DRL) to tackle the inverse kinematic problem of the 6-DOF PUMA manipulator as a representative case within the M-DOF manipulator. The research employs Jacobian matrix for the kinematics system that can solve the singularity, and deep deterministic policy gradient (DDPG) as the kinematics solver. This chosen technique offers enhancing speed and ensuring stability. The results of inverse kinematic solution using DDPG were experimentally validated on a 6-DOF PUMA arm robot. The DDPG successfully solves inverse kinematic solution and avoids the singularity with 1,000 episodes and yielding a commendable total reward of 1,018.</p>

Analytical Inverse Kinematics for 2-Segment Extensible Continuum Manipulators

Abstract Fast inverse kinematics (IK) algorithm is significant for real-time precise motion control of continuum and soft manipulator. In this paper, we studied an explicit expression of two-segment continuum manipulator based on the constant curvature assumptions and discussed the existence of the IK solutions. This model used pseudo-rigid-body method, unlike 6-axis rigid industrial robot arm, we found that the two-segment extensible continuum manipulators have limited rotation angle around the direction vector of its tip, i.e., this type manipulator has limited dexterity. Then we pre-constrained five degrees of freedom (DOFs) constrained and discussed the definition of the left DOF. The IK solving process is simplified to realize small calculation cost for most applications. This model will provide a robust and real-time way to control the two-segment extensible continuum manipulators.

An Efficient Quadratic Programming Method for Kinematic Control of Redundant Manipulators under Joint Velocity Constraints

This paper presents an efficient inverse kinematics solution for redundant robotic arms. The proposed method combines the principles of continuation methods, improves the instability of the computation time by increasing the convergence of the kinematics function, and improves the efficiency of traditional numerical methods. The effectiveness and efficient performance of the method are demonstrated through comparative experiments. The computational speed of the method is twice as fast as the Newton–Raphson method under joint limit constraints and equal solution accuracy.

Development of Standalone Extended-Reality-Supported Interactive Industrial Robot Programming System

Extended reality (XR) is one of the most important technologies in developing a new generation of human–machine interfaces (HMIs). In this study, the design and implementation of a standalone interactive XR-supported industrial robot programming system using the Unity game engine is presented. The presented research aims to achieve a cross-platform solution that enables novel tools for robot programming, trajectory validation, and robot programming debugging within an extended reality environment. From a robotics perspective, key design tasks include modeling in the Unity environment based on robot CAD models and control design, which include inverse kinematics solution, trajectory planner development, and motion controller set-up. Furthermore, the integration of real-time vision, touchscreen interaction, and AR/VR headset interaction are involved within the overall system development. A comprehensive approach to integrating Unity with established industrial robot modeling conventions and control strategies is presented. The proposed modeling, control, and programming concepts, procedures, and algorithms are verified using a 6DoF robot with revolute joints. The benefits and challenges of using a standalone XR-supported interactive industrial robot programming system compared to integrated Unity–robotics development frameworks are discussed.

Kinematic Modelling of Humanoid Robot Based on Vectorial Approach

The present work is dedicated to the study of the inverse kinematics solution of a humanoid bipedal robot with 30 degrees of freedom using a newly approach based on vectors that generated from the geometric space of the robot. The solutions of the inverse kinematics problem for all joints articulations are carried out through a simple and linear equations. Finally, simulations of results are performed through harmonization of trajectories of end effectors of the robot's members.

Whole-body inverse kinematics robust to base position control error in mobile manipulators

Mobile manipulators require whole-body inverse kinematics (IK), encompassing both the mobile base and arm, to execute manipulation tasks. One of the challenges associated with whole-body IK is the redundancy of degrees of freedom when combining those of the mobile base and arm, which generates an infinite number of solutions. Therefore, in this study, we focus on the trend in mobile manipulators where the positional precision of the mobile base is lower than that of the manipulator. We propose a definition for the robustness value to base position control error and discuss a methodology to quickly obtain robust whole-body IK solutions. In an assessment utilizing a dataset that simulates domestic environments and a human support robot, which is a research platform for mobile manipulators designed to operate with humans, we validated that the quick acquisition of IK solutions robust to base position control error is achievable. In addition, we integrated the proposed IK approach into motion planning and evaluated its performance. Our results revealed that motion planning integrated with the proposed IK approach was superior to conventional methods in terms of both computation time and robustness for base position control error.

Combined classification and regression inverse kinematics modeling for overall shape prediction of soft manipulators

In helping astronauts perform tasks, soft manipulators offer the advantages of softness, lightness, low cost, and interaction safety to interact with. However, modeling their inverse kinematics through traditional methods is subject to truncation errors, complex derivations and inexpressibility equations, owing to geometric singularities. Furthermore, facing the future control requirement for multiple major feature points on manipulators, most neural network approaches that solve the drive space only by the inverse solution of the end task space, cannot obtain the inverse kinematics solutions of all feature points, due to their including redundancy (the dimension n of the drive space of feature points is larger than that of the end task space). Therefore, this paper proposes a method combining classification and regression based on multi-layer perceptron for inverse kinematic modeling, namely the IK-MLP-CR method, with the bending states classified and the whole manipulator shape predicted, greatly reducing the amount of training data and training time. Finally, the performance evaluation of the proposed model is validated through the simulation and ground microgravity experiments. Results show that using the IK-MLP-CR method results in a successful grasping rate of over 97%, and that the trend of the experimental bending conforms to physical motions under different pressures.

ANN Approach for SCARA Robot Inverse Kinematics Solutions with Diverse Datasets and Optimisers

Abstract In the pursuit of enhancing the efficiency of the inverse kinematics of SCARA robots with four degrees of freedom (4-DoF), this research delves into an approach centered on the application of Artificial Neural Networks (ANNs) to optimise and, hence, solve the inverse kinematics problem. While analytical methods hold considerable importance, tackling the inverse kinematics for manipulator robots, like the SCARA robots, can pose challenges due to their inherent complexity and computational intensity. The main goal of the present paper is to develop efficient ANN-based solutions of the inverse kinematics that minimise the Mean Squared Error (MSE) in the 4-DoF SCARA robot inverse kinematics. Employing three distinct training algorithms – Levenberg-Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) – and three generated datasets, we fine-tune the ANN performance. Utilising diverse datasets featuring fixed step size, random step size, and sinusoidal trajectories allows for a comprehensive evaluation of the ANN adaptability to various operational scenarios during the training process. The utilisation of ANNs to optimise inverse kinematics offers notable advantages, such as heightened computational efficiency and precision, rendering them a compelling choice for real-time control and planning tasks. Through a comparative analysis of different training algorithms and datasets, our study yields valuable insights into the selection of the most effective training configurations for the optimisation of the inverse kinematics of the SCARA robot. Our research outcomes underscore the potential of ANNs as a viable means to enhance the efficiency of SCARA robot control systems, particularly when conventional analytical methods encounter limitations.

Inverse kinematics solution and control method of 6-degree-of-freedom manipulator based on deep reinforcement learning

The advent of Industry 4.0 has significantly promoted the field of intelligent manufacturing, which is facilitated by the development of new technologies are emerging. Robot technology and robot intelligence methods have rapidly developed and been widely applied. Manipulators are widely used in industry, and their control is a crucial research topic. The inverse kinematics solution of manipulators is an important part of manipulator control, which calculates the joint angles required for the end effector to reach a desired position and posture. Traditional inverse kinematics solution algorithms often face the problem of insufficient generalization, and iterative methods have challenges such as large computation and long solution time. This paper proposes a reinforcement learning-based inverse kinematics solution algorithm, called the MAPPO-IK algorithm. The algorithm trains the manipulator agent using the MAPPO algorithm and calculates the difference between the end effector state of the manipulator and the target posture in real-time by designing a reward mechanism, while considering Gaussian distance and cosine distance. Through experimental comparative analysis, the feasibility, computational efficiency, and superiority of this reinforcement learning algorithm are verified. Compared with traditional inverse kinematics solution algorithms, this method has good generalization and supports real-time computation, and the obtained result is a unique solution. Reinforcement learning algorithms have better adaptability to complex environments and can handle different sudden situations in different environments. This algorithm also has the advantages of path planning, intelligent obstacle avoidance, and other advantages in dynamically processing complex environmental scenes.

Composite continuum robots: Accurate modeling and model reduction

Models of continuum robots often trade off accuracy and speed. The constant curvature assumption model can perform fast calculations but with poor accuracy. Static models can obtain good calculation accuracy but with slower computation speed. In this paper, a precise and efficient method for establishing a non-constant curvature kinematic model for composite continuum robots is proposed. First, an algorithm based on the Beam Constraint Model is proposed to establish the static model of the continuum robot. The situation in which friction changes gradually in continuum robots is considered in the static model. Then, the Kepler elliptic curve is used to simplify the static model to build a non-constant curvature kinematic model of the continuum robot. Then, complex inverse kinematics solutions are transformed into explicit sets of equations by mathematical transformation. Finally, simulations and experiments are designed to demonstrate the algorithm proposed in this paper. The simulation results show that the proposed algorithm is 1572 times faster than the Levenberg–Marquardt algorithm. The experimental results show that the average error of the static model is 0.065 mm, accounting for 0.13% of its length. The maximum error is 0.309 mm, accounting for 0.618% of its length. The positioning accuracy of the non-constant curvature model proposed in this paper is 2.02 times that of the constant curvature model. The results show that the simplified kinematic model algorithm based on the static model has high accuracy and computational efficiency. This research is crucial for the practical application of continuum robots in engineering.

An improved inverse kinematics solution method for the hyper‐redundant manipulator with end‐link pose constraint

AbstractHyper‐redundant manipulators have strong flexibility that benefits from their redundant limb structure. However, a large number of redundant degrees of freedom will also lead the solution of inverse kinematics much more difficult, which restricts their motion performance to some extent. Inspired by the FABRIK (Forward and Backward Reaching Inverse Kinematics) method, an improved inverse kinematics solution method for the hyper‐redundant manipulator is proposed. Based on the space vector method, the kinematic model of the manipulator is established to dynamically acquire its endpoint position, and the workspace is further obtained by using the Monte Carlo method. The original search method is optimized, the include angle decoupling mechanism between adjacent links is established to obtain the rotation angles of each joint, and the joint angle limitation is introduced to meet the actual manipulator structural restriction. On this basis, the pose constraint mechanism is established to realize the control of the end‐link pose, and the linear degree of freedom is introduced to realize the solution after the directional expansion of the manipulator's workspace. A series of simulation experiments are carried out. In the experiments, the position error of the manipulator's endpoint is always less than 10−6 mm. Meanwhile, the comparative experimental results show that compared with the original method, the proposed method exhibits higher position accuracy under the condition that the computation time is almost the same. In addition, in the end‐link pose constraint experiment and path motion experiments, the pose error of the end‐link is always less than 10−7°, indicating that the end‐link pose can also meet the high accuracy requirements under the premise of ensuring high position accuracy. Finally, the prototype experiment further verifies its performance.

Design and analysis of redundant electro-hydraulic-driven manipulator for tokamak vacuum vessel

Remote handling (RH), as one of the key technologies for fusion reactors in the future, has been the focus of research by researchers. This paper presents the design and analysis of a redundant manipulator with 10° of freedom (DOF) intended for use in vacuum vessel of the Tokamak. With a span of 3.15 m and a payload of 10 kg, the manipulator is powered by a combination of hydraulics and motors. The manipulator is mainly composed of the macro-operating arm, the micro-operating arm, and an end-effector, each serving its specific functions. This paper introduces and discusses the roles and capabilities of these components in the manipulation process. The finite element analysis (FEA) of the manipulator's structure reveals that the maximum stress of the structure is significantly lower than the permissible stress of the material Aluminium alloy 2A14. By utilizing the modified Denavit-Hartenberg (DH) method, the kinematic model was created, the forward kinematic matrix was established, and the workspace was analysed accordingly. The inverse kinematics solution was elaborated by the combination of geometric and numerical solutions. Given velocity and acceleration of the joints and the mass of the links, the force and torque of each joint were computed by the inward iterations method based on the Newton-Euler equation, and the rationality of the results was verified by ADAMS simulation. The results indicate that the manipulator, with sufficient strength and appropriate kinematic and dynamic properties, can fulfill the design objective and functional requirements.