# Experimental Evaluation of Collision Avoidance Techniques for Collaborative Robots
## 4 Results
### Test Case 3  
In the last case, the obstacle moves on a straight line between two points while the robot takes a fixed position in the middle of the trajectory (Figure 14). The obstacle moves at a speed of 0.11 m/s, higher than the reference speed \(v_{inf}\); thus, the safety radius \(r\) results increased than \(r_{inf}\). When the obstacle reaches the end-effector's region of influence, the algorithm demands a repulsive velocity from the robot that starts to move. Once the obstacle leaves the region of influence, the positioning error is recovered, and the robot returns to its stationary pose. Figure 11: Test case 2, Mode I. The error between simulation and real system. Joint rotations (**left**) and joint speeds (**right**). Figure 12: Test case 2, Mode II. The error between simulation and real system. Joint rotations (**left**) and joint speeds (**right**). Figure 13: Test case 2, Mode III. The error between simulation and real system. Joint rotations (**left**) and joint speeds (**right**). Figures 15-17 show the graphs of joint positions and velocities in the three avoidance modes. Similar considerations to case 2 can be made by analyzing the different responses for the various modes. Figure 14: Test case 3: avoidance of a dynamic obstacle interfering with the end-effector in a fixed position, Mode I. Simulated (**top**) and real (**bottom**) motion of the robot. Figure 15: Test case 3, Mode I. Joint rotations (**left**) and speeds (**right**). Figure 18-20 show the trend of the error between simulations and real data. The absolute error increases, as in the second test case, from the moment the obstacle is perceived but remains below 0.04 rad in position. The average of the error is about 0.005 rad for position and 0.01 rad/s for speed. As a summary of the results obtained by comparison between simulated and experimental data, Table 2 reports maximum and average errors of joint positions and speeds for all the examined cases. Figure 16: Test case 3, Mode II. Joint rotations (**left**) and speeds (**right**). Figure 17: Test case 3, Mode III. Joint rotations (**left**) and speeds (**right**). Figure 18: Test case 3, Mode I. The error between simulation and real system. Joint rotations (**left**) and joint speeds (**right**). The tests described in this chapter were performed after carefully evaluating the coefficients that allow the algorithm to perform optimally. Some of these values, particularly the proportional gains, cannot be determined a priori. These gains were modified by trial and error until a good fit was obtained between simulated and real data; it was also verified that the robot motion was continuous and smooth. However, it should be noted that the absolute error between the simulations and the real case would have been acceptable even with the same parameters used in the simulation. In detail, the values for \(v_{rep}\) and \(\mathbf{k}_{e}\) used in simulation and the real system are listed in Table 3. \begin{table}
\begin{tabular}{l c c c c} \hline  & **Max Position** & **Max Speed Error** & **Average Position** & **Average Speed** \\  & **Error [rad]** & **[rad/s]** & **Error [rad]** & **Error [rad/s]** \\ \hline Test case 1 & 0.008 & 0.008 & 0.003 & 0.003 \\ \hline Test case 2 & 0.13 & 1.50 & 0.02 & 0.10 \\ \hline Test case 3 & 0.04 & 0.08 & 0.005 & 0.01 \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of results: comparison between simulated and real joint data. Figure 19: Test case 3, Mode II. The error between simulation and real system. Joint rotations (**left**) and joint speeds (**right**). \begin{table}
\begin{tabular}{l c c c} \hline  & \(\mathbf{v_{rep}}\) [m/s] & \(\mathbf{k_{ep}}\) [\(\mathbf{s^{-1}}\)] & \(\mathbf{k_{cr}}\) [\(\mathbf{s^{-1}}\)] \\ \hline Simulated & 2 & 10 & 30 \\ \hline Real & 1 & 1 & 0.16 \\ \hline \end{tabular}
\end{table} 
Table 3: Values of the algorithm parameters for the simulation and for the real case. Figure 20: Test case 3, Mode III. The error between simulation and real system. Joint rotations (**left**) and joint speeds (**right**).