Analytic and optimization methods for solving inverse kinematics (IK) problems have been deeply studied throughout the history of robotics. The two strategies have complementary strengths and weaknesses, but developing a unified approach to take advantage of both methods has proved challenging. A key challenge faced by optimization approaches is the complicated nonlinear relationship between the joint angles and the end-effector pose. When this must be handled concurrently with additional nonconvex constraints like collision avoidance, optimization IK algorithms may suffer high failure rates. We present a new formulation for optimization IK that uses an analytic IK solution as a change of variables, and is fundamentally easier for optimizers to solve. We test our methodology on three popular solvers, representing three different paradigms for constrained nonlinear optimization. Extensive experimental comparisons demonstrate that our new formulation achieves higher success rates than the old formulation and baseline methods across various challenging IK problems, including collision avoidance, grasp selection, and humanoid stability.
We present an analytical solution for the inverse kinematics (IK) of a robotic arm with one prismatic joint and four revolute joints. This 5-DoF design is a result of minimizing weight while preserving functionality of the device in a wearable usage context. Generally, the IK problem for a 5-DoF robot does not guarantee solutions due to the system being over-constrained. We obtain an analytical solution by applying geometric projections and limiting the ranges of motion for each DoF. We validate this solution by reconstructing randomly sampled end-effector poses, and find position errors below…
Changzhou University（常州大学）；CNRS（法国国家科学研究中心）；Dalian University of Technology（大连理工大学）
According to the topological design theory and method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, this paper studied a 3-DOF translational PM that has three advantages, i.e., (i) it consists of three fixed actuated prismatic joints, (ii) the PM has analytic solutions to the direct and inverse kinematic problems, and (iii) the PM is of partial motion decoupling property. Firstly, the main topological characteristics, such as the POC, degree of freedom and coupling degree were calculated for kinematic modeling. Thanks to these properties, the dire…
Collision Detection with Analytical Derivatives of Contact Kinematics
Department of Mechanical and Nuclear Engineering, Khalifa University of Science and Technology（卡利法大学科学与技术学院机械与核工程系）；Khalifa University Center for Autonomous Robotic Systems (KUCARS)（卡利法大学自主机器人系统中心）；The BioRobotics Institute, Scuola Superiore Sant’Anna（圣安娜高等学院生物机器人研究所）；Department of Excellence in Robotics and AI, Scuola Superiore Sant’Anna（圣安娜高等学院机器人与人工智能卓越部门）；LS2N Laboratory, Institut Mines Telecom Atlantique（Atlantique电信学院LS2N实验室）
Oregon State University（俄勒冈州立大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Olin College of Engineering（奥林工程学院）
We present a novel general model that unifies the kinematics of constant curvature and constant twist continuum manipulators. Combining this kinematics with energy-based physics, we derive a linear mapping from actuator configuration to manipulator deformation that is analogous to traditional robot forward kinematics. Our model generalizes across manipulators with different sizes, types of bending, and types of actuators, without the need for parameter re-fitting. The combination of generality and linearity makes the model useful for control and planning algorithms. Finally, our model is shown…
NTNU, Norwegian University of Science and Technology（挪威科技大学）；SINTEF DIGITAL（挪威科技工业研究院数字部门）
A Python module for rapid prototyping of constraint-based closed-loop inverse kinematics controllers is presented. The module allows for combining multiple tasks that are resolved with a quadratic, nonlinear, or model predictive optimization-based approach, or a set-based task-priority inverse kinematics approach. The optimization-based approaches are described in relation to the set-based task approach, and a novel multidimensional "in tangent cone" function is presented for set-based tasks. A ROS component is provided, and the controllers are tested with matching a pose using either transfor…
TU Wien（维也纳工业大学）；University of Liverpool（利物浦大学）；Austrian Institute of Technology GmbH (AIT)（奥地利技术研究院有限公司）
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 t…
University of Bremen（不来梅大学）；German Research Center for Artificial Intelligence (DFKI GmbH)（德国人工智能研究中心）
Several publications are concerned with learning inverse kinematics, however, their evaluation is often limited and none of the proposed methods is of practical relevance for rigid-body kinematics with a known forward model. We argue that for rigid-body kinematics one of the first proposed machine learning (ML) solutions to inverse kinematics -- distal teaching (DT) -- is actually good enough when combined with differentiable programming libraries and we provide an extensive evaluation and comparison to analytical and numerical solutions. In particular, we analyze solve rate, accuracy, sample …
Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）
Gaze stabilization is fundamental for humanoid robots. By stabilizing vision, it enhances perception of the environment and keeps points of interest in the field of view. In this contribution, a multimodal gaze stabilization combining classic inverse kinematic control with vestibulo-ocular and optokinetic reflexes is introduced. Inspired by neuroscience, it implements a forward model that can modulate the reflexes based on the reafference principle. This principle filters self-generated movements out of the reflexive feedback loop. The versatility and effectiveness of this method are experimen…
A Universal Vehicle-Trailer Navigation System with Neural Kinematics and Online Residual Learning
Center for Artificial Intelligence and Robotics, Shenzhen International Graduate School, Tsinghua University（人工智能与机器人中心，清华大学深圳国际研究生院）；Department of Mechanical Engineering, University of Hong Kong（机械工程系，香港大学）
In this research, Artificial Neural Networks (ANNs) have been used as a powerful tool to solve the inverse kinematic equations of a parallel robot. For this purpose, we have developed the kinematic equations of a Tricept parallel kinematic mechanism with two rotational and one translational degrees of freedom (DoF). Using the analytical method, the inverse kinematic equations are solved for specific trajectory, and used as inputs for the applied ANNs. The results of both applied networks (Multi-Layer Perceptron and Redial Basis Function) satisfied the required performance in solving complex in…
Real-Time Conformal-Seeded Hybrid Inverse Kinematics for Offset Redundant Manipulators
VinRobotics；Nanyang Technological University（南洋理工大学）；VinRobotics JSC（VinRobotics股份公司）；Center for AI Research (CAIR), VinUniversity（VinUniversity人工智能研究中心）
Infinite-Dimensional Closed-Loop Inverse Kinematics for Soft Robots via Neural Operators
Department of Mechanical Engineering, Stanford University（机械工程系，斯坦福大学）；Institute of Applied Mechanics, Friedrich-Alexander-Universität Erlangen–Nürnberg（应用力学研究所，弗赖堡-艾尔兰根-纽伦堡大学）；Cognitive Robotics Department, Delft University of Technology（认知机器人系，代尔夫特理工大学）
Multi-AUV Kinematic Task Assignment based on Self-organizing Map Neural Network and Dubins Path Generator
College of Information Engineering, Shanghai Maritime University（上海海事大学信息工程学院）；Logistics Engineering College, Shanghai Maritime University（上海海事大学物流工程学院）；Mechanics Institute, University of Shanghai for Science and Technology（上海理工大学力学研究所）
Soft robotic manipulators provide numerous advantages over conventional rigid manipulators in fragile environments such as the marine environment. However, developing analytic inverse models necessary for shape, motion, and force control of such robots remains a challenging problem. As an alternative to analytic models, numerical models can be learned using powerful machine learned methods. In this paper, the Kinematics Transformer is proposed for developing accurate and precise inverse kinematic models of soft robotic limbs. The proposed method re-casts the inverse kinematics problem as a seq…
Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）；Centre Hospitalier Universitaire de Nantes（南特大学中心医院）；Deutsches Forschungszentrum für Künstliche Intelligenz（德国人工智能研究中心）；Universita degli studi di Genova（热那亚大学）
The optimization of parallel kinematic manipulators (PKM) involve several constraints that are difficult to formalize, thus making optimal synthesis problem highly challenging. The presence of passive joint limits as well as the singularities and self-collisions lead to a complicated relation between the input and output parameters. In this article, a novel optimization methodology is proposed by combining a local search, Nelder-Mead algorithm, with global search methodologies such as low discrepancy distribution for faster and more efficient exploration of the optimization space. The effect o…
