[論文レビュー] Analysis of a Cuspidal 6R Robot

Feeß, Alexander, Weiß, Martin|arXiv (Cornell University)|Feb 16, 2026

Robotic Mechanisms and Dynamics被引用数 0

ひとこと要約

The paper analyzes the kinematics of the Transpressor, a cuspidal 6R robot, providing up to 16 inverse kinematic solutions, analytic results for special poses, a numerical solver for the general case, and a singularity-free path between solutions for a class of robots.

ABSTRACT

We present a theoretical and numerical analysis of the kinematics for the "Transpressor", a cuspidal 6R robot. It admits up to 16 inverse kinematics solutions which are described geometrically. For special target poses, we provide the solutions analytically and present a simple numerical solver for the general case. Moreover, an analytical estimate of the Jacobian determinant on a path between two solutions proves cuspidality for a class of robots similar to the transpressor.

研究の動機と目的

• Motivate the study of cuspidal 6R manipulators and their complex inverse kinematics (IKS).
• Develop analytical IK results for special poses and a general numerical IK solver for the Transpressor-like robot.
• Demonstrate the existence of singularity-free transitions between IK solutions for a wide class of configurations.
• Provide insights into cuspidality and Jacobian behavior to aid motion planning and safety in kinematic design.

提案手法

• Model the robot using DH parameters and a simplified KUKA Transpressor-like 6R chain.
• Divide the problem by reducing the IKS to the initial 3R chain to compute p5 and circle S on the plane A.
• Discretize the circle S and numerically solve the 3R IK on each point to enumerate IK solutions.
• Provide analytical IK solutions for poses with vertical z_E-axis and poses on the z1-axis.
• Analyze the Jacobian determinant to establish conditions for singularity-free paths between IK solutions.

実験結果

リサーチクエスチョン

• RQ1 How many inverse kinematic solutions can the considered 6R cuspidal robot have (0, 4, 8, 12 or 16)?
• RQ2 Can there exist singularity-free transitions between different IK solutions for the same end-effector pose?
• RQ3 What analytic IK forms exist for special target poses (vertical z_E-axis, z1-axis poses), and how many solutions do they yield?
• RQ4 Under what DH-parameter regimes can cuspidality be guaranteed or demonstrated?
• RQ5 How can a numerical IK solver be constructed to reliably find all solutions for the general case?

主な発見

• The 6R cuspidal robot can have up to 16 inverse kinematic solutions for a given pose (ignoring joint limits).
• Analytical IK solutions exist for poses with vertical z_E-axis and for poses on the z1-axis, yielding up to 16 solutions in those cases.
• A general numerical approach discretizes a circle in the plane A and solves the initial 3R IK at sample points to enumerate solutions.
• A singularity-free change of solution is possible for a wide class of solution pairs, demonstrated via Jacobian determinant analysis and a concrete example; solutions can be grouped into classes with non-changing determinant signs, enabling monotone, singularity-free paths within a class.
• The paper provides sufficient analytical and numerical mechanisms to establish cuspidality and to plan motion without encountering singularities over many IK solutions for the class of robots studied.