Inverse Kinematics Problem Research Articles

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.

A Novel General Inverse Kinematics Optimization-Based Solution for Legged Robots in Dynamic Walking by a Heuristic Approach

This work presents a new optimization-based solution to the Inverse Kinematics Problem (IKP) of legged robots, including a modified Walking Pattern Generator that automatically avoids singularity configurations regarding position. The approach uses a numeric constrained problem solved with heuristic algorithms, where the joint vector is calculated to minimize the position errors, while orientation errors are handled as equality constraints, and threshold values are used to set the maximum error for each foot along the trajectories. The optimization model can generalize the IKP for robots with any number of legs and any number of poses within the physically consistent trajectories for the Center of Mass and the feet, considering the dynamics of the robot for a stable walking. The case study was a 12-DOF biped robot, and the resulting joint trajectories were validated by a dynamic simulation, using a Gazebo-ROS platform, where the walking was successfully performed without requiring a feedback control for correcting the torso tilt, showing the solution quality.

NUMERICALLY STABLE SOLUTION TO THE 6R PROBLEM OF INVERSE KINEMATICS.

In this paper, a stable and accurate algorithm to compute all solutions of the inverse kinematics problem of a 6 revolute manipulator chain is presented. A system of equations is constructed based on the fundamental closure conditions, leading to a closed algebraic system of 20 equations involving 16 quantities, composed of trigonometric functions of five among the six unknown joint angles. Two among these five are stably eliminated using singular value decomposition (SVD) avoiding the need to consider special cases. The resulting system of equations involving three unknowns is solved by conversion to a generalized eigenvalue problem. The remaining three unknown angles are obtained using the previously computed pseudoinverse. In this formulation we exploit the inherently complex form of the system reducing it to 10 complex equations in 9 quantities, which substantially accelerates the SVD computation. The method's robustness is demonstrated through a comparison to current methods and several examples including known problematic cases where some axis or link lengths vanish, or some joint angles are 180 degrees, as well as cases where multiple eigenvalues arise.

Generating quality grasp rectangle using Pix2Pix GAN for intelligent robot grasping

Intelligent robot grasping is a very challenging task due to its inherent complexity and non-availability of sufficient labeled data. Since making suitable labeled data available for effective training for any deep learning-based model including deep reinforcement learning is so crucial for successful grasp learning, in this paper we propose to solve the problem of generating grasping poses/rectangles using a Pix2Pix Generative Adversarial Network (Pix2Pix GAN), which takes an image of an object as input and produces the grasping rectangle tagged with the object as output. Here, we have proposed an end-to-end grasping rectangle generating methodology and embedding it to an appropriate place of an object to be grasped. We have developed two modules to obtain an optimal grasping rectangle. With the help of the first module, the pose (position and orientation) of the generated grasping rectangle is extracted from the output of Pix2Pix GAN, and then, the extracted grasp pose is translated to the centroid of the object, since here we hypothesize that like the human way of grasping of regular shaped objects, the center of mass and centroids are the best places for stable grasping. For other irregular shaped objects, we allow the generated grasping rectangles as it is to be fed to the robot for grasp execution. The accuracy has significantly improved for generating the grasping rectangle with limited number of Cornell Grasping Dataset augmented by our proposed approach to the extent of 87.79%. Rigorous experiments with the Anukul/Baxter robot, which has 7 degrees of freedom, causing redundancy have been performed. At the grasp execution level, we propose to solve the inverse kinematics problems for such robots using Numerical Inverse-Pose solution together with Resolve-Rate control which proves to be more computationally efficient due to the common sharing of the Jacobian matrix. Experiments show that our proposed generative model-based approach gives the promising results in terms of executing successful grasps for seen as well as unseen objects (refer to demonstrative video).

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.

Hand model with dependency constrained joints for applications in rehabilitation robotics

Aim: This work presents a method for developing a simplified but efficient model of the complex human hand kinematics with the aim of its implementation in rehabilitation robotics. Material and methods: The approach incorporates modularity by simplifying the available model comprising 24 degrees of freedom (DOFs) to 9 DOFs, with the introduction of additional joint coupling parameters specific to different grasp types. The effect of dependent joints to the ranges-of-motion (ROMs) of the model is investigated and compared to the anatomical one. The index, middle, ring and little finger solutions to forward and inverse kinematics problems are then acquired. The implementation of the model, based on the median male bones dimensions, is made available in the open-source Robot Operating System (ROS) framework. Results: By including additional four inclination angles per finger, the devised kinematic hand model encompasses also finger curvatures, resulting in significant positioning accuracy improvements compared to the conventional model. The used 3D spatial position improvement metrics are the mean absolute (MAE) and mean relative errors (MRE). The dependent joint position MAEs range from 0.22 to 0.34 cm, while MREs range from 2.8 and 3.5 %, whereas the highest absolute and relative errors during fingertip positioning can reach 0.5 cm and 10.5 %, respectively. Conclusion: The performed investigation allowed establishing that by modelling finger curvature and assuring the adaptability of the model to a variety of human hands and rehabilitation modalities through joint dependency, represents the best approach towards a relatively simple and applicable rehabilitation model with functional human-like hand movements.

Сравнение результатов работы алгоритмов обратной кинематики на основе FABRIK для многосекционных непрерывных роботов

Flexible bend link robots, also called continuum or soft robots, are an urgent research topic. Various algorithms were developed to solve the inverse problem of the multi-section continuum robot kinematics including those based on the FABRIK (Forward And Backward Reaching Inverse Kinematics) algorithm. This algorithm was originally created to solve the inverse kinematics problem of robots consisting of rigid links connected by spherical joints and could also be used in regard to continuum robots, which are arcs smoothly transiting into each other. To work with the FABRIK algorithm, each bend section is approximated to the virtual rigid link. Two known approaches are known to solve the inverse kinematics problem: the first is based on constructing the tangents (bend section transformation into two tangents), and the second is based on constructing the chords (bend section reduction to a chord). Both approaches demonstrate good results in solving the inverse kinematics problem compared to algorithms based on the Jacobian matrix construction. However, scientific literature misses data on comparing methods that use the FABRIK algorithm. In this regard, two approaches were compared to solve the inverse kinematics problem based on implementing the FABRIK algorithm. Results of numerical experiments with three-, five- and ten-sectional robots are presented. Characteristics of the algorithms and boundaries of their application were determined.

A Neural Network Based Approach to Inverse Kinematics Problem for General Six-Axis Robots.

Inverse kinematics problems (IKP) are ubiquitous in robotics for improved robot control in widespread applications. However, the high non-linearity, complexity, and equation coupling of a general six-axis robotic manipulator pose substantial challenges in solving the IKP precisely and efficiently. To address this issue, we propose a novel approach based on neural network (NN) with numerical error minimization in this paper. Within our framework, the complexity of IKP is first simplified by a strategy called joint space segmentation, with respective training data generated by forward kinematics. Afterwards, a set of multilayer perception networks (MLP) are established to learn from the foregoing data in order to fit the goal function piecewise. To reduce the computational cost of the inference process, a set of classification models is trained to determine the appropriate forgoing MLPs for predictions given a specific input. After the initial solution is sought, being improved with a prediction error minimized, the refined solution is finally achieved. The proposed methodology is validated via simulations on Xarm6-a general 6 degrees of freedom manipulator. Results further verify the feasibility of NN for IKP in general cases, even with a high-precision requirement. The proposed algorithm has showcased enhanced efficiency and accuracy compared to NN-based approaches reported in the literature.

FABRIKx: Tackling the Inverse Kinematics Problem of Continuum Robots with Variable Curvature

A continuum robot is a unique type of robots which move because of the elastic deformation of their bodies. The kinematics of such robots is typically described using constant curvature assumption. Such an assumption, however, does not completely describe the kinematics of a real-life continuum robot. As a result, variable curvature assumptions describe the kinematics of the continuum robot better, however, they are more complicated to formulate and work with. In particular, the existing methods of solving the inverse kinematics problem of multisection continuum robots with variable curvature suffer from a variety of deficiencies. Those deficiencies include complex matrix calculations, singularity problems, unscalability, and inability to find a numeric solution in some cases. In this work, we present FABRIKx: fast and reliable algorithm to solve the problem of inverse kinematics of the multisection continuum robot with variable curvature. In particular, to describe the variable curvature, we utilize a piecewise constant curvature assumption. The proposed algorithm combines both tangent and chord approaches to solve the inverse kinematics problem. The inverse kinematics of a single bending section of piecewise constant curvature is also described. To evaluate FABRIKx effectiveness, we compare it with the Jacobian-based and FABRIKc-based algorithms via simulation studies for different robots. The obtained results show that FABRIKx demonstrates a higher success rate and a lower solution time.

A Design of a 2-DoF Planar Parallel Manipulator with an Electro-Pneumatic Servo-Drive

This paper presents the design of a planar parallel manipulator with a pneumatic drive. Such manipulators are used in production lines for sorting, selecting, packing, and palletizing workpieces. This paper presents simulation studies of the designed manipulator in Matlab/Simulink software and using the SimMechanics library. A simple kinematics problem and an inverse kinematics problem were solved in order to carry out simulation studies of the designed manipulator. Simulation studies were also carried out on the dynamics of the manipulator using a mathematical model describing the physical phenomena occurring during the operation of the manipulator’s electro-pneumatic servo-drives. The main objective of the simulation study was to determine the manipulator working space and the possibility of positional control of the manipulator end-effector using a fuzzy logic controller.

Comparative studies and performance analysis on neural-dynamics-driven control of redundant robot manipulators with unknown models

This paper proposes an inverse-free and model-free control scheme based on gradient neural dynamics (GND), which avoids the calculation of pseudo-inverse, to achieve the tracking control of redundant robot manipulators without knowing their kinematic models. Specifically, two GND models are deployed to solve the inverse kinematics problem and to estimate the unknown Jacobian matrix of manipulators respectively. We prove that the residual tracking error associated with the proposed scheme theoretically converges to an arbitrarily small upper bound in finite-time. Besides, combining GND and zeroing neural dynamics (ZND), this paper also proposes two control schemes based on hybrid neural dynamics to further achieve better performance. Moreover, the proposed continuous-time control schemes are improved to discrete-time algorithms to facilitate the deployment. Finally, the feasibility and merits of the proposed control schemes are revealed by experiments and comparisons.

Inverse kinematics and workspace analysis of a novel SSRMS-type reconfigurable space manipulator with two lockable passive telescopic links

This study proposes a novel space station remote manipulator system (SSRMS)-type reconfigurable space manipulator to enhance the adaptability of the traditional SSRMS-type manipulators in complex on-orbit tasks. The proposed manipulator has two lockable passive telescopic links (LPTLs) and allows changing their lengths to achieve reconfigurability. The inverse kinematics (IK) and the workspace for this manipulator are minutely analyzed. We develop a new CCDJAP-IK method to solve the IK problem by combining the cyclic coordinate descent (CCD) and joint angle parameterization (JAP) methods. This new method addresses the CCD method's convergence instability and the JAP method's high dependence on the pre-set value of the redundancy parameter. In particular, our approach is insensitive to the initial and singular configurations and can generate multiple exact solutions that satisfy the joint limit constraints. A reachability sphere map captures the proposed manipulator's kinematic capability for the workspace analysis. Then the effects of the two LPTLs on this capability are deeply explored. Based on the results, we propose an information-driven optimal configuration search method. Several typical simulations validate the proposed methods’ effectiveness.

Optimization of Robotic Task Sequencing Problems by Crowding Evolutionary Algorithms

This study solved the robotic task sequence planning problem of scheduling joint-space tours so that each task point visit is made according to expected manufacturing criteria. Multiple solutions for robotic inverse kinematic (RIK) problems were obtained for two task sequencing problems: 1) preset manufacturing sequence planning (Preset-MSP) and 2) optimal manufacturing sequence planning (Opt-MSP). First, a real-coded twin-space crowding evolutionary algorithm (TC-EA) was developed and used to explore multiple RIK joint configurations for each task point. Then, a heuristic bidirectional reference mechanism (BRM) was developed and used for efficiently solving Preset-MSP problems. By integrating BRM, the proposed discrete-coded TC-EA also efficiently solved Opt-MSP problems. To validate the proposed approach, multiple multimodal benchmark functions and task sequencing test cases were used to compare the solving capability of the proposed TC-EA and other evolutionary multimodal solvers. The experimental results showed that the proposed methods obtained better or at least comparable solutions for all test problems. For decision makers, the proposed methods have practical applications for exploring and comparing multiple robotic manufacturing plans.

Forward and inverse kinematics solution of a robotic manipulator using a multilayer feedforward neural network

In this paper, a multilayer feedforward neural network (MLFFNN) is proposed for solving the problem of forward and inverse kinematics of the manipulator. For forward kinematics solution, two cases are presented. The first case is that one MLFFNN is designed and trained to find only the position of the robot end-effector. In the second case, another MLFFNN is designed and trained to find both the position and the orientation of the robot end-effector. Both MLFFNNs are designed considering the joints’ positions as the inputs. For inverse kinematics solution, a MLFFNN is designed and trained to find the joints’ positions considering the position and the orientation of the robot end-effector as the inputs. For training any of the proposed MLFFNNs, data are generated in MATLAB using two different cases. The first case is considering incremental motion of the robot joints, whereas the second case is considering a sinusoidal motion. This method is designed to be generalized to any DOF manipulator. For simplicity, it is applied using a 2-DOF planar robot. The results show that the approximation error between the desired and estimated output is very low and approximately zero. The MLFFNN is efficient to solve the forward and inverse kinematics problems.

Learning-Based Approach to Inverse Kinematics of Wheeled Mobile Continuum Manipulators

Continuum manipulators have been the subject of intensive research due to their inherent flexibility, allowing them to have a dexterous positioning, even in restricted environments. However, while research abounds on static continuum manipulators, a few are interested in wheeled mobile continuum manipulators (WMCMs), where the workspace is extended, and additional degrees of freedom can be used to perform more complex tasks. This article proposes a learning framework for solving the inverse kinematics (IK) of the WMCM while maintaining multiple IK solutions. The configuration space of the WMCM is discretized to reduce the infinite number of IK solutions to a finite number. Besides, the WMCM’s IK problem is transformed into a single-section IK problem of the continuum manipulator by parameterizing the mobile platform’s variables and the actuating variables of the first <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(N-1)$</tex-math></inline-formula> sections, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> being the number of sections. The parameterization is carried out by clustering the WMCM workspace using the growing neural gas algorithm. The proposed approach is validated by performing simulations and experiments on a WMCM named Robotino XT.

Kinematic analysis of ankle joint during gait in drop foot patients wearing passive Ankle-Foot Orthosis *

The term ‘drop-foot’ refers to an uncommon presentation of degenerative diseases, derived from neurological, muscular or anatomical complications, resulting in difficulties in performing foot dorsiflexion. This causes an abnormal gait pattern, characterized by two complications: the ‘foot slap’ at the initial contact with the ground, and the ‘toe-drag’ during the swing phase. In order to support gait, a common non-surgical treatment is the use of lightweight ‘L’ shaped ankle-foot orthosis (AFO). In this study we combine gait analysis and biomechanical modeling tools to analyse the kinematics of ankle joint in gait with and without the support of a passive AFO, namely the ‘Codivilla’ spring. The study was conducted on a population of eighteen adult subjects suffering from unilateral drop-foot (7 females, age 58.1 ± 14.5 years, BMI 23.4 ± 4.60). The infrared multicamera system SMART DX by BTS Bioengineering (Milan, Italy), was used to acquire data relating the 3D position of 22 markers placed on patient’s body, following the Davis protocol, during walking trials performed in two conditions: barefoot and with the AFO mounted on the affected limb. Data were then imported in OpenSim (SimTK software) and used to solve an inverse kinematic problem in order to reproduce walking and compute the evolution of body joints angles. Ankle dorsiflexion and subtalar inversion signals were analysed using MATLAB (2022a) to compute the following metrics for each angle: Range of Motion (RoM), angle at Heel Strike (HS) and angle at Toe Off (TO). The two-way ANOVA statistical test was used to analyse the effects of two factors: walking condition (with versus without AFO) and limb (affected versus contralateral). The interaction factor (condition*limb) was also analysed. Fig. 1 shows the evolution over the gait cycle of the ankle and subtalar angles in the two walking conditions for each foot. Solid lines are obtained as the mean value of subjects’ averaged step. Shaded areas represent the variability among subjects. Table 1 reports the results of the two-way ANOVA test in terms of p-value. Results show that the AFO ‘Codivilla’ spring acts on the kinematics of ankle by reducing the RoM during walking, as it limits the plantar flexion of drop foot. However, it does not significantly affect the ankle angle at HS and TO, although the first is lower in the affected foot. Results also show that the evolution of subtalar angle in the affected foot is altered, not in the RoM, rather in values, in particular at the initial phases of gait cycle. However, the considered orthosis does not produce improvements in the kinematics of subtalar angle. This is probably due to the L-shape of the device, which does not limit ankle inversion/eversion. In conclusion our study confirms the alterations of the drop foot in the kinematics of the ankle joint, particularly at Heel Strike in which both the ankle and the subtalar angle are altered compared to the contralateral foot. The use of Codivilla spring results in a more physiological dorsiflexion of the ankle but has no significant effect on the kinematics of the subtalar joint.

Human-like redundancy resolution: An integrated inverse kinematics scheme for anthropomorphic manipulators with radial elbow offset

As a mimic of the human arm structure, anthropomorphic manipulators with radial elbow offset (AMREO) are often deployed on humanoid service robots. However, the unique offset leads to difficulties in solving the analytical inverse kinematics (IK), which poses a challenge for further anthropomorphic control. This paper presents an integrated scheme for solving the path-wise IK problem of a 7-DoF AMREO in the position domain. Unlike other approaches, special attention is paid to the naturalness of the arm configuration, with the aim of making AMREO exhibit human-like behavior in human-centered environments. First, an analytical IK solution of AMREO for a single end-effector pose is derived based on the arm angle parameterization. Then, inspired by the habitual arm configurations in human reaching movements, the natural arm configuration mapped to wrist position is proposed for AMREO. To learn the patterns implied therein, a LSTM-based natural arm angle prediction network (NAPN) is designed and trained based on a human demonstration dataset. Finally, a redundancy resolution framework embedded with NAPN is built to generate smooth and natural joint configurations in the path-wise IK tasks. Comparative experiments show that the proposed analytical IK algorithm has better computational efficiency and precision than conventional methods, and can give complete results for one IK call within 4 μs. In addition, continuous path tracking experiments on a real robot validate the effectiveness and anthropomorphism of the redundancy resolution scheme based on NAPN.

МОДЕЛИРОВАНИЕ ПОЛУАВТОМАТИЧЕСКОГО РЕЖИМА УПРАВЛЕНИЯ ДВИЖЕНИЕМ ДВУНОГИХ ШАГАЮЩИХ РОБОТОВ В СИСТЕМАХ ВИРТУАЛЬНОГО ОКРУЖЕНИЯ

The paper considers methods and approaches for semi-automatic motion control of bipedal walking robots in virtual environment systems. The proposed solutions include generating a walking pattern, calculating inverse kinematics, and synthesis of PD-controllers with feedback based on the angle sensor readings. To ensure the static and dynamic stability of the walking robot, generating its movement trajectories is implemented using the criterion of zero mo-ment point (ZMP) and the inverse pendulum model with virtual height. In this case, the walking pattern is generated by solving the problem of inverse kinematics using the Leven-berg-Marquardt method to calculate the rotation angles in the robot joints. To implement semi-automatic motion control of a walking robot in a virtual environment, an approach based on the technology of functional diagrams and virtual control panels is used. Testing the proposed methods and approaches is carried out in the VirSim virtual environment software package and shows their adequacy and efficiency for modelling a walking robot movement while maintaining its balance.

ПРОГРАММНАЯ РЕАЛИЗАЦИЯ РЕШЕНИЯ ОБРАТНОЙ ЗАДАЧИ КИНЕМАТИКИ ШЕСТИЗВЕННОГО МАНИПУЛЯТОРА

A brief review of the existing methods for solving the inverse kinematics problem for multilink mechanical systems is carried out. A geometric model of an industrial manipulator of the KUKA family with six degrees of freedom is developed. A special method for separately solving the inverse kinematics problem for a manipulator with a spherical wrist design is applied to demonstrate this approach efficiency. An approximate numerical solution of the inverse kinematics problem for this manipulator is implemented in software. The effectiveness of the software solution is tested on the example of solving various trajectory problems using the Universal Mechanism software package for modelling mechanical systems