How to Build a High-Performance UR5 Inverse Kinematics Solver with IK-Geo

Summary

Hiring? I'm a robotics Ph.D. open to full-time or consulting roles. Contact me. How to Build a High-Performance UR5 Inverse Kinematics Solver With IK-Geo August 27, 2025 Inverse kinematics (IK) is a fundamental problem for robot arms: What joint angles achieve a desired hand pose? UR5e robot following a straight line with all 8 IK solutions. The best choice of IK solution may depend on joint limits, singularities, collision avoidance, or dynamic performance. IK remains a challenge for many practitioners using UR-style robots in industry and research, but we will show how to write a high-performance IK solver based on IK-Geo: Fastest and most accurate IK solver in our testing with independently verified performance: >40x faster than IKFast, ~200x faster if only returning one solution, and errors on the order of machine epsilon (\(10^{-16}\)). Returns all solutions, allowing for optimal choices based on joint limits, singularities, obstacles, and dynamic performance. Returns singular solutions, enabling smooth robot motion by avoiding transitions to joint-level control. Easy to implement, debug, and modify. Available in MATLAB, C++, Rust, and Python. The speed, accuracy, and reliability unlock new capabilities for real-time control, path planning, simulation, and analysis. This tutorial builds on one part of the methods I developed in IK-Geo: Unified robot inverse kinematics using subproblem decomposition, where I introduced an IK method that finds all solutions for any 6-DOF revolute robot. Want to skip the derivation and see the code? Check out the single-file MATLAB implementation. Introduction The UR5 and newer UR5e, part of the UR series, are collaborative robot arms from Universal Robots. Robots with similar kinematics are also made by Standard Bots, Techman Robot/Omron, and Dobot. UR-style robots like the UR5 have three parallel joint axes (2, 3, 4) and two pairs of intersecting joint axes (1, 2) and (5, 6). Rendering of a UR5 collaborative robot arm: one of th...