# A Practical and Effective Layout for a Safe Human-Robot Collaborative Assembly Task
## 4 Results and Discussion  
The effectiveness of the proposed collaborative layout is evaluated in terms of safety and productivity. Concerning the safety, the experimental tests prove that the collision avoidance algorithm can quickly drive the robot through alternative trajectories in order to avoid the human. Figure 9 shows an example of collision avoidance that happens when the robot is placing a\(\rightarrow\)A and the operator is taking B (for a more detailed overview of the entire assembly cycle the reader is referred to the video in \"Supplementary Materials\"). For each frame, the MATLAB calculation environment is reported in the robot base reference frame. In the latter, the robot links are represented as blue lines, together with the nine control points. The optimized skeleton of the human upper body is colored in red and made of 15 significant joints. The robot planned trajectory is also shown as the rectilinear dashed path connecting \(\mathbf{p}_{C}\) to \(\mathbf{p}_{A}\), while the solid line is the trace of the actual collision avoidance trajectory. The robot approaches the collaborative zone from point \(\mathbf{p}_{C}\) and starts following the rectilinear planned path towards \(\mathbf{p}_{A}\), while the human is still applying the glue on the first cube (Frame 1). Then, the operator finishes preparing A (Frame 2) and takes B, while the robot is crossing the relative station, so that the robot reacts backwards to avoid the human hand (Frame 3). As the hand retracts, the robot returns on the planned path (Frames 4 and 5) and reaches \(\mathbf{p}_{A}\), while the human is preparing A+B (Frame 6).  
The collision avoidance trajectory is analyzed in Figure 10. The robot planned trajectory is also shown with the dashed line, together with the strategical points. To give an idea of the repulsive effect, the repulsive velocity vectors acting on the TCP are reported on the actual path at significant samples. The repulsive effect increases nearby \(\mathbf{p}_{B}\), which is the point above station B where the human takes the cube. Here, the actual path bends backwards due to the presence of the human hand. The operator takes the cube within a time interval of 1 s, so the repulsive effect is localized only on a limited portion of the collision avoidance path.  
Figure 8: Scheme of the control strategy. Data and algorithms are reported in different colors to indicate which hardware device they are associated with.  
The possibility to carry out the task with the highest level of collaboration brings significant advantages in terms of task times. At the top of Figure 11, the workflow diagram of the proposed assembly cell is shown. In this case, which represents a responsive collaboration, the human and the robot complete their task in the same time interval, resulting in a mean cycle time of 112 s. The human and robot tasks run in parallel and the robot collaborates while the human executes value added operations, i.e., actions that carry on the assembly process.  
Figure 9: Frames of the collision avoidance during the “Place a\(\rightarrow\)A” stage.  
Figure 11: Workflow diagram of the assembly cycle for responsive and sequential collaborations.  
Figure 10: Collision avoidance trajectory during the “Place a\(\rightarrow\)A” stage.  
that, the robot leaves the collaborative zone and the operator can take B. This generates a first delay of approximately 23 s on the human's task. A second delay of approximately 3 s would be at the end of the \"Prepare A+B\" phase, since the robot has not finished yet the \"Place a\(\mapsto\)A\" stage and is still in the collaborative zone, therefore, the human must wait before he takes C. The mean cycle time, in this case, is 138 s. Comparing the latter result with the previous case, the major result is that the highest level of collaboration optimizes productivity by saving up to the 18% of the cycle time.