Dynamic Control of Virtual Fixtures Under Arbitrary Differentiable Geometric Constraints with a Disturbance Observer

As human-robot collaboration becomes prevalent in dynamic environments, implementing virtual fixture (VF) with high precision during physical human-robot interaction faces critical challenges. While VF methods constrain robot motions to predefined geometries well, the current approaches face two fundamental problems: an inability to handle general geometric constraints and sensitivity to dynamic disturbances in unstructured environments. To address these issues, we propose a novel dynamics-based control framework that intrinsically embeds virtual constraints into the robot’s task space coordinates. By establishing a differential geometric mapping between constraint functions and task coordinates, the method systematically constructs constraint Jacobian matrices, enabling unified implementation of arbitrary twice-differentiable constraints without case-specific derivations. By integrating a disturbance observer within the framework, the method handles external disturbances and dynamic uncertainties, enhancing its stability and control accuracy. Experimental results on a 7-DoF Franka Emika Research robot show that the proposed method achieves submillimeter end-effector constraint accuracy, with a maximum error of 0.96 mm. The evaluation was performed under high-speed human-robot interactions, with an average human-guided linear end-effector speed of approximately 100 mm/s. Consistent performance was maintained across multiple VF types, including planar, linear, circular, and sinusoidal constraints. A stability analysis confirms its input-to-state stability, ensuring robust performance under moderate disturbances. This work introduces a unified dynamics-based VF control framework capable of handling general differentiable constraints with high precision and robustness.