# Compliant Human-Robot Collaboration with Accurate Path-Tracking Ability for a Robot Manipulator
## 1 Introduction  
Guidance constraints are a type of active constraints/virtual fixtures, which have been studied in the field of physical human-robot interaction (pHRI) by many researchers [1, 2, 3, 4, 5, 6, 7]. From the work of [PERSON] [1], the concept of perceptual overlay to increase task performance has been explored in different types of human-machine manipulation systems, such as telennipulators and cooperative manipulators [3]. These virtual fixtures are often used to guide the movement of the robot towards desired targets while avoiding obstacles and preventing the robot from entering predefined forbidden regions. Although reference paths for the robot are generated in some applications, the accuracy of path following is not the focus of these techniques. Instead, compliant behavior of the robot that allows deviation of the path is the main concern of most pHRI studies. However, accurate path tracking and compliant behavior are not necessarily antinomies. They can be delicately tailored to meet the requirements for dedicated purposes and achieve better performance. For example, rehabilitation patients can benefit greatly from practicing with equipment that is capable of following a path while still being compliant along the path, because it allows the patient to closely track an optimal path predefined by medical experts, and progress in different levels of assistance, which has been shown to improve rehabilitation progress [8, 9, 10]. Another important application is in industrial assembly tasks. Many efforts have been reported in this area towards efficient human-robot collaboration [11, 12, 13, 14, 15]. The authors of [13] presented a force-overshoot-free controller for high-accuracy assembly tasks using an industrial robot. Furthermore, in [14] a collaborative task for a homokineticjoint assembly is performed using admittance control. In [15], a method for robotic fixture-less approach of large flexible panels assembly using compliance force control is presented and evaluated with an industrial robot. The aim of these approaches is to relieve the operator from having to manipulate heavy components during the assembly and instead being able to focus only with the dexterous part of the assembly. Moreover, an important factor is that in high-precision assembly tasks static fixtures are necessary to keep in place the parts being joined and task performance depends on these fixtures. These tasks could benefit from a compliant path-tracking system. Furthermore, other direct application of path tracking in human-robot collaboration is for educational and physical training purposes where the robot system can be used as a tool to teach complex tasks that are best learned by hand-in-hand demonstration. Examples include practicing calligraphy, assisted hand-motor skills development, and so on [16; 17]. In this sense, the robot system acts as the coach and the user is guided to follow an optimal path that perfectly accomplishes the task while obtaining different levels of assistance to trace the path, from completely passive to completely active. Based on these analyses, we found that in many manual guidance applications, it is beneficial for the robot to follow a path while being compliant along the path. Consequently, the goal of this paper is to investigate the related techniques. Path-tracking is an important feature of most robotic systems. From manipulators to mobile platforms, the ability to follow a path with high accuracy has been investigated by many researchers [2; 18; 19]. Moreover, path-tracking in compliant human-robot collaboration has been the topic of recent studies. In [4], virtual fixtures were created and modified through an iterative method based on kinesthetic teaching and Akima splines. The approach was evaluated in a simulated sanding task using a 3-DOF collaborative robot and a user study which showed that virtual guide assistance improves the performance of co-manipulation tasks. Later, [PERSON] et al.