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）
Carina Veil, Moritz Flaschel, Ellen Kuhl, Cosimo Della Santina
For fully actuated rigid robots, kinematic inversion is a purely geometric problem, efficiently solved by closed-loop inverse kinematics (CLIK) schemes that compute joint velocities to position the robot body in space. For underactuated soft robots, however, not all configurations are attainable through control action, making kinematic inversion extremely ill-posed. Extensions of CLIK address this by introducing end-to-end mappings from actuation to task space for the controller to operate on, but typically assume finite dimensions of the underlying virtual configuration space. In this work, we formulate CLIK in the infinite-dimensional domain to reason about the entire soft robot shape while solving tasks, thereby skipping intermediate approximation steps. We do this by composing an actuation-to-shape map with a shape-to-task map, deriving the differential end-to-end kinematics via an infinite-dimensional chain rule, and thereby obtaining a Jacobian-based CLIK algorithm. Since complex soft-robot models are rarely available in closed form, and neither the actuation-to-shape mapping nor its Jacobian can typically be obtained analytically, we propose to learn it using differentiable neural operator networks. We first present an analytical study on a constant-curvature segment, and then apply the neural version of the algorithm to a three-fiber soft robotic arm whose underlying model relies on morphoelasticity and active filament theory.
University of Bengkulu（明古鲁大学）；Pusat Penelitian Elektronika dan Telekomunikasi Lembaga Ilmu Pengetahuan Indonesia（印度尼西亚科学院电子学与电信研究中心）
This paper presents the development of vision-based robotic arm manipulator control by applying Proportional Derivative-Pseudoinverse Jacobian (PD-PIJ) kinematics and Denavit Hartenberg forward kinematics. The task of sorting objects based on color is carried out to observe error propagation in the implementation of manipulator on real system. The objects image captured by the digital camera were processed based on HSV-color model and the centroid coordinate of each object detected were calculated. These coordinates are end effector position target to pick each object and were placed to the ri…
An analysis of higher-order kinematics formalisms for an innovative surgical parallel robot
Technical University of Cluj-Napoca（克卢日-纳波卡技术大学）；Gheorghe Asachi Technical University of Iasi（雅西格奥尔基·阿萨基技术大学）；Technical Sciences Academy of Romania（罗马尼亚技术科学院）；École Centrale Nantes（南特中央理工学院）；Nantes Université（南特大学）；CNRS（法国国家科学研究中心）；LS2N（南特数字科学实验室）
Information Fusion and Mining Laboratory（信息融合与挖掘实验室）
This is a follow-up tutorial article of our previous article entitled "Robot Basics: Representation, Rotation and Velocity". For better understanding of the topics covered in this articles, we recommend the readers to first read our previous tutorial article on robot basics. Specifically, in this article, we will cover some more advanced topics on robot kinematics, including robot motion, forward kinematics, inverse kinematics, and robot dynamics. For the topics, terminologies and notations introduced in the previous article, we will use them directly without re-introducing them again in this …
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
In this paper, WALK-VIO, a novel visual-inertial odometry (VIO) with walking-motion-adaptive leg kinematic constraints that change with body motion for localization of quadruped robots, is proposed. Quadruped robots primarily use VIO because they require fast localization for control and path planning. However, since quadruped robots are mainly used outdoors, extraneous features extracted from the sky or ground cause tracking failures. In addition, the quadruped robots' walking motion cause wobbling, which lowers the localization accuracy due to the camera and inertial measurement unit (IMU). …
Considering the difficulty of students in calculating the direct and inverse kinematics of a robotic manipulator using only conventional tools of a classroom, this article proposes the application of Project Based Learning (ABP) through the design, development, mathematical modeling of a robotic manipulator as an integrative project of the disciplines of Industrial Robotics, Microcontrollers and Computer Assisted Design with students of the Control and Automation Engineering of the University of Fortaleza. Once designed and machined, the manipulator arm was assembled using servo motors connect…
KU Leuven – University of Leuven（鲁汶大学）；University of Cambridge（剑桥大学）
This work addresses the inverse kinematics of serial robots using conformal geometric algebra. Classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time or the development of particular geometric strategies that cannot be generalized to arbitrary serial robots. In this work, we present a compact, elegant and intuitive formulation of robot kinematics based on conformal geometric algebra that provides a suitable framework for the closed-form resolution of the inverse kinematic problem for manipulators with a spherical wrist. For…
University of California, Santa Cruz（加州大学圣克鲁兹分校）；NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）
Voxel-based structures provide a modular, mechanically flexible periodic lattice which can be used as a soft robot through internal deformations. To engage these structures for robotic tasks, we use a finite element method to characterize the motion caused by deforming single degrees of freedom and develop a reduced kinematic model. We find that node translations propagate periodically along geometric planes within the lattice, and briefly show that translational modes dominate the energy usage of the actuators. The resulting kinematic model frames the structural deformations in terms of user-…
Self-Motions of General 3-RPR Planar Parallel Robots
Institut National des Sciences Appliquées (INSA)（国立应用科学学院）；École de Technologie Supérieure (ÉTS)（高等技术学院）；Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
Robotics Research Center IIIT Hyderabad（国际信息技术研究所海得拉巴机器人研究中心）
Real time calculation of inverse kinematics (IK) with dynamically stable configuration is of high necessity in humanoid robots as they are highly susceptible to lose balance. This paper proposes a methodology to generate joint-space trajectories of stable configurations for solving inverse kinematics using Deep Reinforcement Learning (RL). Our approach is based on the idea of exploring the entire configuration space of the robot and learning the best possible solutions using Deep Deterministic Policy Gradient (DDPG). The proposed strategy was evaluated on the highly articulated upper body of a…
University of Michigan（密歇根大学）；Toyota Research Institute（丰田研究院）
State-of-the-art robotic perception systems have achieved sufficiently good performance using Inertial Measurement Units (IMUs), cameras, and nonlinear optimization techniques, that they are now being deployed as technologies. However, many of these methods rely significantly on vision and often fail when visual tracking is lost due to lighting or scarcity of features. This paper presents a state-estimation technique for legged robots that takes into account the robot's kinematic model as well as its contact with the environment. We introduce forward kinematic factors and preintegrated contact…
A polynomial solution to the inverse kinematic problem of the Kinova Gen3 Lite robot is proposed in this paper. This serial robot is based on a 6R kinematic chain and is not wrist-partitioned. We first start from the forward kinematics equation providing the position and orientation of the end-effector, finally, the univariate polynomial equation is given as a function of the first joint variable $θ_{1}$. The remaining joint variables are computed by back substitution. Thus, an unique set of joint position is obtain for each root of the univariate equation. Numerical examples, simulated in ROS…
Kinematic analysis of a parallel robot for minimally invasive surgery
CESTER, Technical University of Cluj-Napoca（克卢日-纳波卡技术大学 CESTER）；École Centrale Nantes, Nantes Université, CNRS, LS2N, UMR 6004（南特中央理工大学、南特大学、法国国家科学研究中心、LS2N实验室、UMR 6004）；Technical Sciences Academy of Romania（罗马尼亚技术科学院）
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…
Open-Source, Cost-Aware Kinematically Feasible Planning for Mobile and Surface Robotics
Open Navigation LLC；Carnegie Mellon University（卡内基梅隆大学）；Locus Robotics；QUT Centre for Robotics and School of Electrical Engineering and Robotics（QUT机器人中心和电气工程与机器人学院）
School of Mechanical Engineering, Shanghai Jiao Tong University（上海交通大学机械与动力工程学院）；Intel Labs China（英特尔中国实验室）；Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology（昆明理工大学机电工程学院）
Aerospace production volumes have increased over time and robotic solutions have been progressively introduced in the aeronautic assembly lines to achieve high-quality standards, high production rates, flexibility and cost reduction. Robotic workcells are sometimes characterized by robots mounted on slides to increase the robot workspace. The slide introduces an additional degree of freedom, making the system kinematically redundant, but this feature is rarely used to enhance performances. The paper proposes a new concept in trajectory planning, that exploits the redundancy to satisfy addition…
MineRobot: An Actuator-Centered Kinematic Modeling and Solving Framework for Underground Mining Robots
College of Computer Science and Engineering, Shandong University of Science and Technology（山东科技大学计算机科学与工程学院）；Shandong Lionking Software Co., Ltd.（山东狮王软件有限公司）；College of Intelligent Equipment, Shandong University of Science and Technology（山东科技大学智能装备学院）
Vision-based segmentation of the robotic tool during robot-assisted surgery enables downstream applications, such as augmented reality feedback, while allowing for inaccuracies in robot kinematics. With the introduction of deep learning, many methods were presented to solve instrument segmentation directly and solely from images. While these approaches made remarkable progress on benchmark datasets, fundamental challenges pertaining to their robustness remain. We present CaRTS, a causality-driven robot tool segmentation algorithm, that is designed based on a complementary causal model of the r…
RIKEN Center for AI Project（日本理化学研究所人工智能项目中心）；Istituto Italiano di Tecnologia（意大利技术研究所）；Massachusetts Institute of Technology（麻省理工学院）；Università degli Studi di Genova（热那亚大学）；University College London（伦敦大学学院）
With the recent advances in machine learning, problems that traditionally would require accurate modeling to be solved analytically can now be successfully approached with data-driven strategies. Among these, computing the inverse kinematics of a redundant robot arm poses a significant challenge due to the non-linear structure of the robot, the hard joint constraints and the non-invertible kinematics map. Moreover, most learning algorithms consider a completely data-driven approach, while often useful information on the structure of the robot is available and should be positively exploited. In…
Eindhoven University of Technology（埃因霍温理工大学）；University of Twente（特文特大学）
Soft robots are interesting examples of hyper-redundancy in robotics, however, the nonlinear continuous dynamics of these robots and the use of hyper-elastic and visco-elastic materials makes modeling of these robots more complicated. This study presents a geometric Inverse Kinematic (IK) model for trajectory tracking of multi-segment extensible soft robots, where, each segment of the soft actuator is geometrically approximated with multiple rigid links connected with rotary and prismatic joints. Using optimization methods, the desired configuration variables of the soft actuator for the desir…
A Design and an Implementation of an Inverse Kinematics Computation in Robotics Using Real Quantifier Elimination based on Comprehensive Gröbner Systems
University of Tsukuba（筑波大学）；Tokiwa Senior High School（常盘高等学校）
We present a hierarchical whole-body controller leveraging the full rigid body dynamics of the wheeled bipedal robot Ascento. We derive closed-form expressions for the dynamics of its kinematic loops in a way that readily generalizes to more complex systems. The rolling constraint is incorporated using a compact analytic solution based on rotation matrices. The non-minimum phase balancing dynamics are accounted for by including a linear-quadratic regulator as a motion task. Robustness when driving curves is increased by regulating the lean angle as a function of the zero-moment point. The prop…
Inverse Kinematics (IK) solves the problem of mapping from the Cartesian space to the joint configuration space of a robotic arm. It has a wide range of applications in areas such as computer graphics, protein structure prediction, and robotics. With the vast advances of artificial neural networks (NNs), many researchers recently turned to data-driven approaches to solving the IK problem. Unfortunately, NNs become inadequate for robotic arms with redundant Degrees-of-Freedom (DoFs). This is because such arms may have multiple angle solutions to reach the same desired pose, while typical NNs on…
