# Compliant Human-Robot Collaboration with Accurate Path-Tracking Ability for a Robot Manipulator
## 1 Introduction
However, all parameters were tuned heuristically and specifically for the evaluated task. The authors of [24] presented a hybrid position-force control oriented to surface treatment tasks, e.g., sanding, deburring, polishing, etc. They used sliding mode concepts for the robot force control to maintain the orientation of the tool always perpendicular to the surface and to obtain the desired tool pressure on the surface. The lower-priority tracking controller was designed to follow the desired trajectory where deviations to satisfy safety constraints are allowed. Finally, redundancy resolution was also included to keep the manipulator near its home configuration for safety purposes. The method showed increased robustness and low computational cost, and experimental validation of the approach using a 7R manipulator proved its applicability and effectiveness. The common drawbacks of the cited works are that, in many cases, the accuracy aspect of path tracking when compliance is combined for co-manipulation tasks was not explored. Besides, the experimental setup often relies on robots designed to be inherently suitable for manipulation tasks. Furthermore, kinematic constraints such as singularities, joint limits, task space limits, etc., if considered, are part of the virtual fixture definition and therefore task dependent. As a result, the task must be carefully planned to avoid these kinematic constraints, which imposes restrictions on the task definition. Given these recent references in the field and considering their contributions and stated drawbacks, we believe the topic of path tracking is highly relevant to human-robot collaboration applications, and the study of the associated design strategies is of great importance and value. In this paper, we aim to achieve compliance of a robot manipulator along a predefined path, giving the robot the ability to move forward or backward depending on the direction of an external force applied to the end effector while tracking the path. Figure 1 illustrates this objective, where a desired path is shown and in the case of an external force is applied, the robot is compliant only along the path tangential direction, and not compliant along the normal direction. To accomplish this goal, we propose a dual-loop control structure, including an inner motion control loop and an outer admittance control loop. A modified sliding mode controller (SMC) is designed for the inner motion control, which guarantees desirable state tracking performance and robustness while significantly suppresses chattering. In the outer admittance loop, we define the compliance control problem in the tangential-normal-binormal (TNB) frame associated with the path to find the projection of the external force in the tangential direction and develop an atemporal path generation strategy by parameterizing the path with respect to the arc length to move along the path as desired by the user. Furthermore, an adaptive admittance law that has been experimentally verified in [23] is exploited to allow a timely, intuitive, and simple communication between the human and robot. In addition, the proposed adaptive admittance law considers the most common kinematics constraints that can appear in manual guidance interaction and adapts the admittance parameters appropriately based on the objectives of safety, accuracy, and comfort. In this approach, kinematic constraints are not task dependent and instead are configuration dependent, which means that they can be reused in multiple applications. Furthermore, these constraints are treated simultaneously, considering smooth transitions among them. Combining the TNB frame projection and adaptive admittance law, the outer admittance control loop realizes a safe and intuitive human-robot collaboration along a predefined path while the robust inner motion control loop guarantees that the robot follows the path accurately.