*Article* **Compliant Human–Robot Collaboration with Accurate Path-Tracking Ability for a Robot Manipulator**

**Daniel Reyes-Uquillas \*,† and Tesheng Hsiao †**

Department of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan; tshsiao@cn.nctu.edu.tw

**\*** Correspondence: danielreyes.04g@g2.nctu.edu.tw

† These authors contributed equally to this work.

**Abstract:** In this article, we aim to achieve manual guidance of a robot manipulator to perform tasks that require strict path following and would benefit from collaboration with a human to guide the motion. The robot can be used as a tool to increase the accuracy of a human operator while remaining compliant with the human instructions. We propose a dual-loop control structure where the outer admittance control loop allows the robot to be compliant along a path considering the projection of the external force to the tangential-normal-binormal (TNB) frame associated with the path. The inner motion control loop is designed based on a modified sliding mode control (SMC) law. We evaluate the system behavior to forces applied from different directions to the end-effector of a 6-DOF industrial robot in a linear motion test. Next, a second test using a 3D path as a tracking task is conducted, where we specify three interaction types: free motion (FM), force-applied motion (FAM), and combined motion with virtual forces (CVF). Results show that the difference of root mean square error (RMSE) among the cases is less than 0.1 mm, which proves the feasibility of applying this method for various path-tracking applications in compliant human–robot collaboration.

**Keywords:** path tracking; compliance control; human–robot interaction; sliding mode controller; manual guidance
