# Compliant Human-Robot Collaboration with Accurate Path-Tracking Ability for a Robot Manipulator
## 1 Introduction
in [20] defined virtual guides as virtual mechanisms using Gaussian mixtures model (GMM) from multiple user demonstrations, which can be refined through incremental training. They proposed to establish a library of multiple virtual guides which can be created, modified and used by the human operator. The performance was experimentally evaluated with a compliant 3-DOF robot and a user study. The algorithms in [4; 20] concentrated on virtual guides construction and how to iteratively modify the nominal path, but there was no treatment of the accuracy of path-tracking. [PERSON] et al. in [21] optimally reshaped the desired robot trajectory using an adaptive neural network controller to effectively complete co-manipulation tasks with a robotic exoskeleton. The experimental validation was demonstrated in a 2-DOF motion case but did not describe extensibility of the method to higher DOFs or to different types of manipulators. In other words, the research effort was to conceive an algorithm that allows the human to modify the desired trajectory using shared control; thus, the contributions focus on the path generation aspect of human-robot collaboration. However, the challenge of accuracy in human-robot interaction by regulating robot motion in the predetermined task direction remains. Previous works on the accuracy aspect for compliant tasks by the use of virtual fixtures include [5; 6; 7], where virtual fixtures were used together with admittance control to allow for compliant path tracking tasks. A vision-based virtual fixture algorithm for cooperative manipulation was designed and implemented in [5], where the authors described how to create hard and soft virtual fixtures for two types of reference targets--point positioning and curve following--as well as the extensions to virtual geometries such as tubes or cones to confine motion to a volume for a cooperative system which uses admittance control. The experimental setup was validated using the \"Steady Hand Robot\" [22] in macroscale and microscale planar tasks. The results showed that the addition of vision-based virtual fixtures assistance increased performance regarding position error and execution time, and that there is a trade-off between performance and user control. However, the experimental validation consisted in using different fixed levels of admittance, but as covered in [23] adaptive admittance control has been proven more effective. Moreover, there is no distinction between the virtual fixture definition and the admittance control parameter tuning. This complicates the definition of the virtual fixtures and directly influences the achievable tracking performance, as shown in their study. In [6], virtual fixtures were used to control the robot for robotic-assisted surgery. The task was defined and projected into a space of orthogonal directions that consisted of preferred directions and non-preferred ones. The authors of [6] explored and compared two types of error compensation--manual and autonomous--to reduce the path-tracking task error. The results showed that manual compensation was not sufficient for correction of all deviations, particularly when a translational virtual fixture was defined and the deviation error for orientation occurred, and vice versa. This was solved with their proposed autonomous compensation method where the user had control of the system along the preferred directions through the forces applied, while the robotic system independently compensated deviations. In [7], a framework for compliant path tracking tasks was proposed. The system used a virtual robot approach to obtain the desired velocities that were treated as the command to the internal position controller. Motion constraints and task space constraints can be defined in this framework. The proposed approach was experimentally evaluated using a 7-DOF KUKA LWR cobot. The results showed that it is easy to define different constraints in the framework by adjusting the properties and parameters in their algorithm.