Tsinghua University's parametric IK solver for 7-DoF NERO Arm runs <0.1ms in ROS2

A new paper from Tsinghua University presents a parametric inverse kinematics (IK) solver for 7-DoF redundant robot arms, specifically applied to the NERO Arm. Traditional numerical IK methods (e.g., Jacobian damped least squares) are slow (ms–10 ms), prone to convergence failures, and require complex null-space projection for redundancy control. The proposed method leverages the S-R-S (Spherical-Shoulder-Revolute Elbow-Spherical Wrist) configuration of the NERO arm, parameterizing the redundant degree of freedom using a single elbow angle (ψ). This allows for a closed-form analytical solution that computes all joint angles directly from the target end-effector pose and the chosen elbow angle. The algorithm first extracts shoulder (S), wrist (W), and elbow joint θ₄ using the law of cosines. It then computes the elbow point E from ψ and solves q₁–q₃ and q₅–q₇ analytically.

The key innovation is the active feasible-region control: before selecting ψ, the solver computes the range of elbow angles that satisfy all joint limits. A weighted quadratic objective function then optimizes ψ within this range for criteria like joint-limit avoidance or elbow posture preference. This approach eliminates the risk of limit violations and ensures a globally optimal solution without iterations. The entire solve completes in under 0.1 ms, making it suitable for high-frequency real-time control loops in ROS2. The implementation includes an ik_solver.py library and a ROS2 node (ik_joint_state_publisher.py) that publishes joint states. For developers, this means deterministic, fast IK for 7-DoF arms with direct null-space control, enabling smoother trajectory generation, obstacle avoidance, and safer operation in collaborative robotics applications.