## 1 Introduction  
Collaborative robots (cobots) are robots designed to enable the combination of the strength, force, and repeatability of automatic machines with the dexterity and cognitive capacities of humans, allowing them to work together in a shared workspace. It is expected that they will boost the Industry 4.0 revolution and, in particular, the digitalization and the human-centered design of an industrial workspace [1]. However, the physical human-robot interaction (pHRI) required in such a shared workspace introduces novel mechanical risks with respect to \"traditional\" industrial robots [2]. In this regard, the International Organisation for Standardization (ISO) has introduced four methods of operation [2]: i.e., hand guiding, safety-rated monitored stop, speed and separation monitoring, and power and force limiting. Such modalities constitute a framework to define a cobot, proposing proper implementations and evaluations of safety requirements in terms of mechanical risk. Commercially available solutions provide out-of-the-box user interfaces and tunable parameters to allow the integrator to implement these collaborative operation methods [3; 4; 5]. In addition to safety, other important topics that have to be considered when designing and implementing a collaborative workspace are physical and cognitive ergonomics. For the former,we can utilize industry standards, guidelines, and best practices already developed for manual work and modify and apply them to collaborative scenarios [6; 7]. On the contrary, the latter has not yet been fully studied, and guidelines and best practices are not available [8]. It has been demonstrated that the operator's subjective acceptance of pHRI can be increased by means of smooth, i.e., predictable, motions [9; 10; 11; 12]. We therefore formulate a robot motion planning approach to achieve a psychologically less-stressful working environment. Among all motion planning techniques that are available in the literature, trajectory planning through via-points is of particular importance for collaborative robotics. The Technical Specification ISO TS-15066 [13] foresees the hand guiding modality as collaborative operation: even unskilled workers can intuitively program a path by simply moving the robot manually in its workspace and saving step-by-step the needed via-points through an interface. The worker can thus directly define the robot's configuration and avoid the obstacles that may be placed in the reachable workspace. The computation of a safe trajectory along the via-points is then made by the robot controller according to the ISO specifications. Starting from the outcome of the hand-guiding operation and path definition, this work focuses on the problem of designing trajectories that allow guaranteeing both safe and psychologically less stressful movements without overlimiting the robot performance. In the literature, there is a plethora of different techniques for planning a robotic trajectory [14] that focus on the optimization/minimization of, e.g., time, smoothness, energy, and torque. Among these, minimum jerk motion profiles have drawn particular interest in the robotics community for mainly two reasons:  
* There is experimental evidence that suggests that humans adopt minimum jerk movements [15; 16; 17], and thus, these can be perceived as predictable and familiar by a person that interacts with the robot. In [18], the impact of different industrial robot motion profiles was investigated in a cooperative human-robot interaction (HRI) task showing that minimum jerk trajectories significantly reduce the heart rate in humans, thus suggesting an improvement of robot acceptance and a reduction of the psychological stress;
* Minimum-jerk trajectories reduce the induced mechanical vibrations and, thus, wear in the elements of an automatic machine, e.g., robot, as well as the error during the trajectory tracking phase [19; 20; 21; 22; 23; 24].