Inverse Kinematics Research Articles

LSC50: Colombian Sign Language Video and Inertial Measurement dataset

In Colombia, approximately more than 500.000 people have disabling hearing loss, representing around 1% of the population in Colombia, and only 400 professional interpreters of Colombian Sign Language (LSC) are available in the whole country. In this data descriptor, we present a dataset with recordings of Colombian Sign Language (LSC) as an important effort to develop technologies that facilitate social inclusion and equity for the deaf community in Colombia. This dataset includes multimodal recordings of native and non-native signers signing different elements of the LSC lexicon. In particular, we provide recordings of video and inertial measurement units, along with detected body landmarks and computed information on the inverse kinematics of the upper body such as flexion, extension, and rotation of arms and wrists. This dataset is the first of its kind for LSC and it is key for the development of technologies needed to better understand the language and reduce communication barriers between people with and without hearing loss.

Path planning for flexible needle based on both insertion mechanism kinematics and needle bending model.

Due to the limited operating space in the magnetic resonance (MR) environment, there is coupled motion in the insertion mechanism, which not only reduces the flexibility of the robot but also challenges the insertion path planning. Meanwhile, the path planning is also restricted by the bending rule of the flexible needle, thus the bending model of the needle is also essentially built. This paper proposes a path planner for the flexible needle based on both the coupled motion kinematics of the insertion robot and the bending model of the flexible needle. A kinematic analysis for the coupled motion of insertion robot is performed. And the bending model of flexible needle is established based on the needle-tissue interactions. The position and posture of the needle insertion at the entry point are obtained by the calculation of the target position and the analysis of the bending model. And the rotation or translation coordinates of each robot joint are calculated by the inverse kinematics of the insertion robot. Then the path planning based on the coupled kinematics and the bending model is realized. The insertion experiments were performed for each target of G1 and G2. The root mean square errors were 0.83 mm and 0.74 mm, and the maximum errors were 1.1 mm and 0.9 mm for G1 and G2, respectively. The experimental results show that the effectiveness and accuracy of the path planning can meet the requirements for a general minimally invasive surgery, so the proposed path planning algorithm is feasible. This study provides a new solution for the path planning of insertion robots for the minimally invasive surgery. This method can meet the insertion mechanism working within the limited operating space in the MR environment and has a high application value in future clinical medicine.

SK-PSO: A Particle Swarm Optimization Framework with SOM and K-Means for Inverse Kinematics of Manipulators

In this paper, a particle swarm optimizer that integrates self-organizing maps and k-means clustering (SK-PSO) is proposed. This optimizer generates an asymmetric Cartesian space from random joint configurations when addressing the inverse kinematics of manipulators, followed by K-means clustering applied to the Cartesian space. The resulting clusters are used to reduce the dimensionality of the corresponding joint space using Self-Organizing Maps (SOM). During the solving process, the target point’s clustering region is determined first, and then the joint space point closest to the target point is selected as the initial population for the particle swarm algorithm. The simulation results demonstrate the effectiveness of the SK-PSO algorithm. Given the inherent asymmetry among different algorithms in handling the problem, SK-PSO achieves an average fitness value that is 0.02–0.62 times better than five other algorithms, with an asymmetric solving time that is only 0.03–0.34 times that of the other algorithms. Therefore, compared to the other algorithms, the SK-PSO algorithm offers high accuracy, speed, and precision.

A novel inverse kinematics and shape reconstruction method for continuum robots

A novel inverse kinematics and shape reconstruction method for continuum robots

Design and Performance Analysis of a Parallel Pipeline Robot

A parallel four-legged pipeline robot is designed to mitigate the issue of uneven motor loading on the single-leg linkage responsible for movement along the pipe diameter. This issue occurs because the drive motor located closer to the robot body requires higher torque when the serial robot operates along the inner wall of a circular polyethylene gas pipe in an urban environment. The forward and inverse kinematic equations for a single-leg linkage are derived to establish the relationship between joint angles and foot trajectories. Building on this analysis, the forward and inverse kinematic solutions for all four legs are also derived. An optimized diagonal trotting gait is selected as the robot’s walking pattern to ensure a balance between stability and movement efficiency, considering the robot’s structural configuration. Motion simulations for both the serial and parallel robots are performed using simulation software, with a detailed analysis of the displacement of the robot’s center of mass and the leg centers during movement. The driving torque of the leg motors in both configurations is controlled and examined. Simulation results indicate that the designed parallel four-legged pipeline robot achieves lower motion error and smoother leg movements within the pipe. Compared to the serial robot, the maximum torque required to drive the leg motors is reduced by approximately 33%, demonstrating the effectiveness and validity of the overall structural design.

Kinematic Analysis and Trajectory Planning Based on a Six-Axis Robotic Arm

Kinematic analysis and time-optimal trajectory planning are applied to the robot in order to enhance its operational efficiency and preserve its continuous, smooth running trajectory. In this paper, the robot kinematics model is established based on the D-H parametric method with the Daqi Elfin series E05 six-axis robot as the research object. After that, forward and inverse kinematic analysis is carried out. And the segmented polynomial interpolation trajectory planning model of robotic arm is optimized in time based on the improved particle swarm algorithm. And MATLAB robot toolbox is used to build the robotic arm simulation model. From there, the trajectory planning simulation experiments are performed. As well as the experimental results show that the improved particle swarm algorithm effectively reduces the trajectory planning time. In the simulation experiment the time is reduced by 40.78% compared to the initial setting. The effectiveness of the robotic arm is greatly increased by this research.

A novel kinematic modeling method for (1+n) type parallel mechanism: applied to obtain the position and posture space simultaneously

Abstract In this study, a novel kinematic modeling method of parallel mechanism is proposed. It can obtain position and posture space simultaneously in a single model. Compared with the traditional method only based on inverse kinematics, the novel method can significantly improve computational performance. The original evaluation metric $\mathfrak{R}$ is proposed to evaluate the performance of the two modeling methods. Three groups of experiments with different calculation times are carried out for the classical PPU-3RUS parallel mechanism, and the new RS-3UPRU parallel mechanism after the effectiveness and wide applicability of the novel modeling method is proved. The calculation time and output rate are recorded, respectively, and then the respective $\mathfrak{R}$ values are obtained by weighting. The results show that the novel modeling method has better performance.

Type synthesis of a new class of 4-3T1R(y) parallel mechanisms for parallel machine tools design

Unlike previous design procedures for parallel machine tools (PMTs), this paper first analyzes the path and posture requirements of the tools in universal processing, then proposes and constructs a new class of PMs that can provide the required path and posture. This opens up new ideas for the design of PMTs. Based on the reciprocal screw theory, a type synthesis process of asymmetrical lower-mobility PMs was proposed. Through this process, a novel class of four-limbed parallel mechanisms (PMs) providing three translations and one rotation around a horizontal axis (y-axis), denoted as 4-3T1R(y) PMs, was successfully proposed and constructed. Such PMs can be applied to the design of PMTs, especially the design of micro-electrical discharge machining (micro-EDM) PMTs. The structural design of a new 2RRC-2CRU PM, which was a member of 4-3T1R(y) PMs, was performed, and its mobility was analyzed in detail to demonstrate the efficiency of the proposed type synthesis process. The inverse, forward, and velocity kinematics problems of the 2RRC-2CRU PM were solved for further applications.

Inverse kinematics analysis of a wrist rehabilitation robot using artificial neural network and adaptive Neuro-Fuzzy inference system

This paper offers a comprehensive investigation into the forward and inverse kinematics of a wrist rehabilitation robot, utilizing the Denavit-Hartenberg method for forward kinematics (FK) and a geometric approach, as well as artificial neural networks (ANN) and adaptive Neuro-Fuzzy inference systems (ANFIS) for inverse kinematics (IK) analysis. While the geometric method entails precise parameter measurements and faces uncertainties, ANN and ANFIS are explored as potential remedies to enhance accuracy and robustness. Evaluating 11 different training functions sourced from existing literature, our study conducts a thorough assessment of their performance within an ANN network. We aim to pinpoint the most suitable training function for achieving optimal IK solutions in the context of a wrist rehabilitation robotic. Additionally, the ANFIS model, trained using Fuzzy C-Means (FCM), sets itself apart from Grid Partitioning (GP) and Subtractive Clustering (SC). Among the ANN training functions, Bayesian regularization with 5 hidden layers emerges as the most effective, yielding low root mean square error (RMSE) values of 0.003, 0.004, and 0.007 degrees for pronation/supination (P/S), abduction/adduction (AB/AD), and flexion/extension (F/E), respectively. Conversely, ANFIS, trained with FCM, demonstrates satisfactory yet less precise results, with RMSE values of 0.191, 0.082, and 0.165 degrees for P/S, AB/AD, and F/E, respectively. Despite its adequacy, ANFIS trails behind ANN, showcasing RMSE reductions of 98.4%, 95.1%, and 95.7% for P/S, AB/AD, and F/E angles, respectively. This study contributes to leveraging ANN and ANFIS for IK analysis in wrist rehabilitation robotics, highlighting the efficacy of ANN, particularly when employing Bayesian regularization, to enhance accuracy.

Control of Parallel Quadruped Robots Based on Adaptive Dynamic Programming Control

With the rapid development of robotics technology, quadruped robots have shown significant potential in navigating complex terrains due to their excellent stability and adaptability. This paper proposes an adaptive dynamic programming control method based on policy iteration, aimed at improving the motion performance and autonomous adaptability of parallel quadruped robots in unknown environments. First, the study establishes a kinematic model of the robot and performs inverse kinematics calculations to determine the angular functions for each joint of the robot’s legs. To improve the robot’s mobility on challenging terrains, we design an optimal tracking controller based on Generalized Policy Iteration (GPI). This approach reduces the model’s dependency on strict requirements and is applied to the control of quadruped robots. Finally, kinematic simulations are conducted based on pre-planned robot gaits. In addition, experiments are then conducted based on the simulation results. The results of simulation experiments indicate that the quadruped robot, under the adaptive optimal control algorithm, can achieve smooth walking on complex terrains, verifying the rationality and effectiveness of the parallel quadruped robot in handling such conditions. The experimental results further demonstrate that this strategy significantly improves the stability and robustness of the robot across various terrains.

Manipulator Differential Kinematics: Part I: Kinematics, Velocity, and Applications [Tutorial

Manipulator kinematics is concerned with the motion of each link within a manipulator without considering mass or force. In this article, which is the first in a two-part tutorial, we provide an introduction to modelling manipulator kinematics using the elementary transform sequence (ETS). Then we formulate the first-order differential kinematics, which leads to the manipulator Jacobian, which is the basis for velocity control and inverse kinematics. We describe essential classical techniques which rely on the manipulator Jacobian before exhibiting some contemporary applications. Part II of this tutorial provides a formulation of second and higher-order differential kinematics, introduces the manipulator Hessian, and illustrates advanced techniques, some of which improve the performance of techniques demonstrated in Part I. We have provided Jupyter Notebooks to accompany each section within this tutorial. The Notebooks are written in Python code and use the Robotics Toolbox for Python, and the Swift Simulator to provide examples and implementations of algorithms. While not absolutely essential, for the most engaging and informative experience, we recommend working through the Jupyter Notebooks while reading this article. The Notebooks and setup instructions can be accessed at https://github.com/jhavl/dkt.

Kinematic Inversion of Aseismic Fault Slip During the Nucleation of Laboratory Earthquakes

AbstractDecades of geophysical monitoring have revealed the importance of slow aseismic fault slip in the release of tectonic energy. Although significant progress have been made in imaging aseismic slip on natural faults, many questions remain concerning its physical control. Here we present an attempt to study the evolution of aseismic slip in the controlled environment of the laboratory. We develop a kinematic inversion method, to image slip during the nucleation phase of a dynamic rupture within a saw‐cut sample loaded in a tri‐axial cell. We use the measurements from a strain gauge array placed in the vicinity of the fault, and the observed shortening of the sample, to invert the fault slip distribution in space and time. The inversion approach relies both on a deterministic optimization step followed by a Bayesian analysis. The Bayesian inversion is initiated with the best model reached by the deterministic step, and allows to quantify the uncertainties on the inferred slip history. We show that the nucleation consists of quasi‐static aseismic slip event expanding along the fault at a speed of the order of 200 m., before degenerating into a dynamic rupture. The total amount of aseismic slip accumulated during this nucleation phase reaches m locally, about 8%–15 % of the coseismic slip. The resolution of the method is evaluated, indicating that the main limitation is related to the impossibility of measuring strain inside the rock sample. The results obtained however show that the method could improve our understanding of earthquake nucleation.

Integrating artificial immune systems and multi-layer perceptron-biogeography-based optimization for enhanced inverse kinematics in robotic arm

Determining required joint angles to achieve a desired position in a manipulator’s arm is a complicated problem without simple analytical solutions. This paper researches several computational methods based on artificial intelligence (AI) for calculating the joint positions of the 6-DOF robotic arm. We can extrapolate relevance, for example, to the crucial role that robotic manipulator arms play in industrial and medical applications, where enhanced precision and movement efficiency may sharply boost performance and expand applicability. Here, we investigate the effectiveness of methods, such as the artificial immune system (AIS) and multi-layer perceptron-biogeography-based optimization (MLP-BBO). Those AI-driven methods have been applied to determine joint angles for reaching desired positions through simulations for the robotic arm. The results show that the AIS and MLP-BBO approach can handle the intrinsic complexities of the task, thus testifying to the practicability and dependability of these two methods in this application. From the findings in the study, it was indicated that AI-driven techniques can effectively answer the complex problem of the robotic manipulator arm in finding joint angles.

Optimal gait design for a soft quadruped robot via multi-fidelity Bayesian optimization

This study focuses on the locomotion capability improvement in a tendon-driven soft quadruped robot through an online adaptive learning approach. Leveraging the inverse kinematics model of the soft quadruped robot, we employ a central pattern generator to design a parametric gait pattern, and use Bayesian optimization (BO) to find the optimal parameters. Further, to address the challenges of modeling discrepancies, we implement a multi-fidelity BO approach, combining data from both simulation and physical experiments throughout training and optimization. This strategy enables the adaptive refinement of the gait pattern and ensures a smooth transition from simulation to real-world deployment for the controller. Compared to previous result using a fixed gait pattern, the multi-fidelity BO approach improves the robot’s average walking speed from 0.14 m/s to 0.214 m/s, an increase of 52.7%. Moreover, we integrate a computational task off-loading architecture by edge computing, which reduces the onboard computational and memory overhead, to improve real-time control performance and facilitate an effective online learning process. The proposed approach successfully achieves optimal walking gait design for physical deployment with high efficiency, effectively addressing challenges related to the reality gap in soft robotics.

A human digital twin approach for fatigue-aware task planning in human-robot collaborative assembly

Human-robot collaboration (HRC) has emerged as a pivotal paradigm in manufacturing, integrating the strengths of both human and robot capabilities. Neglecting human physical fatigue may adversely affect worker health and, in extreme cases, may lead to musculoskeletal disorders. However, human fatigue has rarely been considered for decision-making in HRC manufacturing systems. Integrating adaptive decision-making to optimise human fatigue in HRC manufacturing systems is crucial. Nonetheless, real-time perception and estimation of human fatigue and decision-making informed by human fatigue face considerable challenges. To address these challenges, this paper introduces a human digital twin method, a bidirectional communication system for physical fatigue assessment and reduction in human-robot collaborative assembly tasks. The methodology encompasses an IK-BiLSTM-AM-based surrogate model, which consists of inverse kinematics analysis (IK), bidirectional long short-term memory (BiLSTM), and attention mechanism (AM), for real-time muscle force estimation integrated with a muscle force-fatigue model for muscle fatigue assessment. An And-Or graph and optimisation model-based HRC task planner is also developed to alleviate physical fatigue via task allocation. The efficacy of this approach has been validated through proof-of-concept assembly experiments involving multiple subjects. The results show that the IK-BiLSTM-AM model achieves a minimum of 8% greater accuracy in muscle force estimation than the baseline methods. The 12-subject assessment results indicate that the task planner effectively reduces the physical fatigue of workers while performing collaborative assembly tasks.

A Neuro-Fuzzy Solution for Inverse Kinematics of Redundant Manipulators

Abstract: This paper presents a novel approach for solving the inverse kinematics (IK) problem of redundant robotic manipulators using an Adaptive Neuro-Fuzzy Inference System (ANFIS). Redundant manipulators, characterized by having more degrees of freedom (DOF) than necessary for a task, introduce complexity in their IK solutions due to their non-linear, time-varying, and transcendental nature. Traditional methods such as algebraic or geometric solutions are often computationally intensive and can suffer from issues such as singularities. This study leverages ANFIS, combining the learning capability of neural networks with the logic-based structure of fuzzy systems, to predict IK solutions for 5-DOF and 7-DOF manipulators. The Denavit-Hartenberg (D-H) notation is employed for the kinematic modeling of robot links. Comparative analysis of the predicted IK values using ANFIS demonstrates its high accuracy and efficiency, as validated by surface and residual plots. The results show that ANFIS can be effectively utilized for fast and reliable IK predictions, offering a robust alternative to traditional approaches. This method can be applied in robotic systems requiring high precision in constrained or dynamic environments.

Convex geometric motion planning of multi-body systems on lie groups via variational integrators and sparse moment relaxation

This paper reports a novel result: with proper robot models based on geometric mechanics, one can formulate the kinodynamic motion planning problems for rigid body systems as exact polynomial optimization problems. Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not parameterize 3D rigid body motion efficiently; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space and apply the variational integrator to formulate the forced rigid body dynamics as quadratic polynomials. Then, we leverage Lasserre’s hierarchy of moment relaxation to obtain the globally optimal solution via semidefinite programming. By leveraging the sparsity of the motion planning problem, the proposed algorithm has linear complexity with respect to the planning horizon. This paper demonstrates that the proposed method can provide globally optimal solutions or certificates of infeasibility at the second-order relaxation for 3D drone landing using full dynamics and inverse kinematics for serial manipulators. Moreover, we extend the algorithms to multi-body systems via the constrained variational integrators. The testing cases on cart-pole and drone with cable-suspended load suggest that the proposed algorithms can provide rank-one optimal solutions or nontrivial initial guesses. Finally, we propose strategies to speed up the computation, including an alternative formulation using quaternion, which provides empirically tight relaxations for the drone landing problem at the first-order relaxation.

Treatment Couch Path Planning for Proton Therapy Systems

In the treatment process of proton radiation therapy, the patient needs to be positioned and immobilized before being moved into the treatment position. In this study, the patient was primarily positioned using the 6R robotic treatment couch as the patient support system (PSS). A simplified three-dimensional model of the treatment room was developed based on the relative motion within the treatment room. The forward and inverse kinematics of the 6R robotic treatment couch were analyzed using an improved Denavit-Hartenberg (D-H) representation. A collision interference model was created based on the actual treatment process. The motion path of the treatment couch was planned and simulated in MATLAB using an improved artificial potential field method for obstacle avoidance. The results indicate that the robotic treatment couch can smoothly navigate around obstacles to reach the target point, satisfying the positioning requirements for proton therapy.

Quadruped Robots Gait Planning and Kinematic Analysis

Quadruped robots imitate the gait of animals in nature to achieve flexible and stable movement. Their superior mobility and adaptability have secured an important position in modern robotics. However, quadruped robots still face numerous technical challenges, including complex gait planning. Gait refers to the swinging and supporting movements of the legs and the relative timing of these movements. Different gaits determine various movement forms for quadruped robots, and studying these gaits plays a crucial role in the stable periodic motion of the robot. This paper analyzes three types of gaitsstatic gait, dynamic gait, and quasi-static gaitbased on traditional gait planning methods. Additionally, this paper analyze the movement of the single leg, including the forward and inverse kinematics and the endpoint cycloidal trajectory. Finally, we simulate the stable trot gait in MATLAB, returning the force curve at the foot, joint angles, angular velocity, and angular acceleration curves to complete the verification of the theory.

Real-time optimized inverse kinematics of redundant robots under inequality constraints

Inverse kinematics of redundant robots presents a challenging problem for real-time applications due to the lack of uniqueness of solution and the low computational efficiency caused by redundancy and hard limits. In this work, a general and efficient method for addressing the real-time optimized inverse kinematics of redundant robots is proposed, taking into account hard limits in joint and Cartesian space that can never be violated. The proposed method proceeds by using constrained linear programming instead of quadratic programming to solve the inverse kinematics problem. Various hard limits such as joint range, bounds on velocity and acceleration are handled explicitly as inequality constraints. This method resolves the redundancy in real-time and enable to simultaneously guarantee that the additional motion constraints will never be violated. Its performance allows real-time kinematic control of redundant robots executing sensor-driven online tasks. The effectiveness of this method is demonstrated through simulations and experiments conducted on a 7-DOF KUKA IIWA robot, showcasing its ability to control redundant robots executing sensor-driven tasks in dynamic environments with numerous hard limits.