## 1 Introduction
### Safety Standards and HRC Modes  
The International Federation of Robotics has reported an all-time high of 517,385 new industrial robots installed in 2021 in factories around the world, with a growth rate of 31%, increased by 22% compared to 2018 (pre-pandemic record). Until now, the stock of operational robots around the globe has reached 3.5 million units [16]. With the increasing use of robots in industry, standardization and guidelines to ensure the safety of human operators are required [10]. Many standards have been proposed to give guidelines for thesafe use of collaborative robots. The machinery safety is regulated under the Machinery Directive, which covers the scope of collaborative applications [10]. The following reference standards are reported (see Table 1):  
Four categories of safety requirements are defined for collaborative robots in the type C international standards (ISO 10218-1, ISO 10218-2, and ISO TS 15066) [10; 12; 13]:  
* Safety-rated monitored stop (SMS)  
SMS [10; 13] is a collaboration arrangement in which robot motion is stopped before a human operator enters the collaborative workspace to interact and carry out a task with the robotic system. This is the most basic form of collaboration and takes place within a collaborative area, that is, an area of operation shared by the robot and the human. Both parties can work in this area, but not simultaneously, since the robot cannot move if the operator is in the shared space. Therefore, it is ideal for tasks in which the robot primarily works alone and is occasionally interrupted by a human operator. Examples of such tasks include visual inspection or the positioning of heavy components by the robot for the human. * Hand-guiding (HG)  
Another mode of collaboration is known as hand-guiding [10; 13], or \"direct teach\". In this mode, the operator simply moves the robot to teach it significant positions, without the use of intermediate interfaces such as teach pendants. These positions are communicated as commands to the robot system. Throughout this process, the robot arm's weight is compensated such that its position is held. A guiding, hand-operated device is used by the operator to guide the robot's motion. For this advanced form of collaboration, the robot must be equipped with safety-rated monitored stop and speed functionalities. Once the robot has learned the motion and the human operator has left the collaborative area, the robot may execute the program in automatic mode. However, if the operator enters the area, the program is interrupted. When the operator is using the hand-guiding device, the robot operates in a state of safety-rated monitored speed functionality until the operator releases the arm and leaves the collaborative area, allowing the robot to resume automatic operation once again. * Speed and separation monitoring (SSM)  
In SSM [10; 13], the robot operates even when a human is present by means of safety-rated monitoring sensors. Thus, human and robot operations take place simultaneously. To reduce risks, a stipulated protective distance must always be kept between the two parties. If this distance is not kept, the robot operation stops and only resumes once the operator