Geometric analysis of generic 3R robots, and necessary and sufficient conditions for a class of orthogonal robots to have four IKS

• URL: http://arxiv.org/abs/2609.00316v1
• Date: Mon, 31 Aug 2026 20:07:32 GMT
• Title: Geometric analysis of generic 3R robots, and necessary and sufficient conditions for a class of orthogonal robots to have four IKS
• Abstract summary: This paper presents the kinematic analysis of a generic 3R robot using the inverse kinematic model inherited from a method based on conformal geometric algebra.<n>The paper discusses a generic framework to study the conditions for a 3R robot to have four inverse kinematic solutions (IKS) and allows to study the distribution of IKS as seen in workspace.
• Score: 1.654371982203344
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The kinematic analysis of a generic 3R robot has been investigated with multiple approaches in the past. The algebraic approaches have established concrete results but are unfortunately limited to special classes or architectural simplifications. Geometric approaches on the other hand have extended the analysis to generic robots while also providing an intuitive understanding of their kinematic properties. We use the best of both approaches to present the kinematic analysis of a generic 3R robot, using the inverse kinematic model inherited from a method based on conformal geometric algebra. The paper discusses a generic framework to study the conditions for a 3R robot to have four inverse kinematic solutions (IKS) and allows to study the distribution of IKS as seen in workspace. The necessary and sufficient conditions for a class of orthogonal robots are presented using the proposed approach.

Related papers

• Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra [1.654371982203344]
  We present the Inverse Kinematic Model (IKM) of 3R robots, using the advantages of Conformal Geometric Algebra (CGA)<n>Our approach directly yields a uni in terms of theta without the need to eliminate theta_3 by reframing the problem as the intersection of two circles.
  arXiv  Detail & Related papers  (2026-08-31T20:01:15Z)
• MineRobot: A Unified Framework for Kinematics Modeling and Solving of Underground Mining Robots in Virtual Environments [6.632835744087224]
  Underground mining robots are increasingly operated in virtual environments (VEs) for training, planning, and digital-twin applications.<n>We present emphMineRobot, a unified framework for modeling and solving the kinematics of underground mining robots in VEs.
  arXiv  Detail & Related papers  (2026-03-23T14:53:26Z)
• Analysis of a Cuspidal 6R Robot [45.88028371034407]
  We present a theoretical and numerical analysis of the kinematics for the "Transpressor", a cuspidal 6R robot.<n>For special target poses, we provide the solutions analytically and present a simple numerical solver for the general case.
  arXiv  Detail & Related papers  (2026-02-16T14:41:26Z)
• URDF-Anything: Constructing Articulated Objects with 3D Multimodal Language Model [76.08429266631823]
  We propose an end-to-end automatic reconstruction framework based on a 3D multimodal large language model (MLLM)<n>URDF-Anything utilizes an autoregressive prediction framework based on point-cloud and text multimodal input to jointly optimize geometric segmentation and kinematic parameter prediction.<n> Experiments on both simulated and real-world datasets demonstrate that our method significantly outperforms existing approaches.
  arXiv  Detail & Related papers  (2025-11-02T13:45:51Z)
• AI Methods for Permutation Circuit Synthesis Across Generic Topologies [1.0499611180329804]
  Our approach uses Reinforcement Learning (RL) techniques to achieve near-optimal synthesis of permutation circuits up to 25 qubits.<n>We train a foundational model on a generic rectangular lattice, and employ masking mechanisms to dynamically select subsets of topologies during the synthesis.<n>This enables the synthesis of permutation circuits on any topology that can be embedded within the rectangular lattice, without the need to re-train the model.
  arXiv  Detail & Related papers  (2025-09-19T14:28:22Z)
• Is Single-View Mesh Reconstruction Ready for Robotics? [78.14584238127338]
  We evaluate single-view mesh reconstruction models for their potential in enabling instant digital twin creation for real-time planning and dynamics prediction using physics simulators for robotic manipulation.<n>Our findings highlight critical gaps between computer vision advances and robotics needs, guiding future research at this intersection.
  arXiv  Detail & Related papers  (2025-05-23T14:35:56Z)
• Pairwise-Constrained Implicit Functions for 3D Human Heart Modelling [60.56741715207466]
  We introduce a pairwise-constrained SDF approach that models the heart as a set of interdependent SDFs.<n>Our method significantly improves inner structure accuracy over single-SDF, UDF-based, voxel-based, and segmentation-based reconstructions.
  arXiv  Detail & Related papers  (2023-07-16T10:07:15Z)
• Structured Prediction for CRiSP Inverse Kinematics Learning with Misspecified Robot Models [39.513301957826435]
  We introduce a structured prediction algorithm that combines a data-driven strategy with a forward kinematics function. The proposed approach ensures that predicted joint configurations are well within the robot's constraints.
  arXiv  Detail & Related papers  (2021-02-25T15:39:33Z)
• Nothing But Geometric Constraints: A Model-Free Method for Articulated Object Pose Estimation [89.82169646672872]
  We propose an unsupervised vision-based system to estimate the joint configurations of the robot arm from a sequence of RGB or RGB-D images without knowing the model a priori. We combine a classical geometric formulation with deep learning and extend the use of epipolar multi-rigid-body constraints to solve this task.
  arXiv  Detail & Related papers  (2020-11-30T20:46:48Z)
• An Analysis of SVD for Deep Rotation Estimation [63.97835949897361]
  We present a theoretical analysis that shows SVD is the natural choice for projecting onto the rotation group. Our analysis shows simply replacing existing representations with the SVD orthogonalization procedure obtains state of the art performance in many deep learning applications.
  arXiv  Detail & Related papers  (2020-06-25T17:58:28Z)
• Comparison of Distal Teacher Learning with Numerical and Analytical Methods to Solve Inverse Kinematics for Rigid-Body Mechanisms [67.80123919697971]
  We argue that 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. We analyze solve rate, accuracy, sample efficiency and scalability. With enough training data and relaxed precision requirements, DT has a better solve rate and is faster than state-of-the-art numerical solvers for a 15-DoF mechanism.
  arXiv  Detail & Related papers  (2020-02-29T09:55:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.