**3. Experimental set-up and results**

In this section, the suggested algorithm is evaluated against two static allocation algorithms: 'Equal Bandwidth' and 'Equal Rates'. The equal bandwidth method allocates bandwidth equally among the different streams, while the equal rates method divides the available bandwidth such that the different streams would have equal rates of transmission.

The experimental set-up is composed of two NAO humanoid robots driven in a certain formation. An operator drives the two robots using a force feedback joystick (Microsoft SideWinder Force Feedback 2) and communicates with the robot through a router connected to a PC as shown in **Figure 2**. The operator sends real-time commands to the agents that return back haptic feedback as proximity measures and visual feedback from cameras mounted on each robot. The signal flows within the different components of the system as illustrated in **Figure 3**. The collaborative task that is to be accomplished by the robots is to maintain a certain formation while traversing an environment and avoiding collision with potential obstacles.

**Figure 2.** Experimental set-up.

The formation is characterized by a fixed distance (D = 60 cm) separating the two robots, while maintaining the error in the vertical direction nearly zero. Accurate position of the humanoids is calculated using the aid of the Inertial Unit built in the robots, which is made of 2-axis gyrometers with 5% precision (*angular speed* ∼500°/s) and a 3-axis accelerometer with 1% precision (*acceleration* ∼2G).

**Figure 3.** Teleoperation experimental set-up of humanoid robots.

### **3.1. Testing scenarios**

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the optimization problem and allocating rates.

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**3. Experimental set-up and results**

**Figure 2.** Experimental set-up.

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In the experiments, the aforementioned values of *A, B, M, W* and *Bmax* are adopted while solving

In this section, the suggested algorithm is evaluated against two static allocation algorithms: 'Equal Bandwidth' and 'Equal Rates'. The equal bandwidth method allocates bandwidth equally among the different streams, while the equal rates method divides the available

The experimental set-up is composed of two NAO humanoid robots driven in a certain formation. An operator drives the two robots using a force feedback joystick (Microsoft SideWinder Force Feedback 2) and communicates with the robot through a router connected to a PC as shown in **Figure 2**. The operator sends real-time commands to the agents that return back haptic feedback as proximity measures and visual feedback from cameras mounted on each robot. The signal flows within the different components of the system as illustrated in **Figure 3**. The collaborative task that is to be accomplished by the robots is to maintain a certain formation while traversing an environment and avoiding collision with potential obstacles.

bandwidth such that the different streams would have equal rates of transmission.

### *3.1.1. Scenario 1: path with no obstacles*

The first scenario consists of driving the swarm in the space delimited by dashed lines, shown in **Figure 4**, and reaching the final destination (dashed rectangular region on the right side) with no obstacles in the path. Obviously, with the absence of obstacles, the shortest path in this case is moving from 'Start' to 'End' in a straight line. The operators tend to adopt the shortest path, the straight line in this case, to reach the final destination.

**Figure 4.** Scenario 1—path with no obstacles.

### *3.1.2. Scenario 2: obstacle in front of robot 1*

In the second scenario, an obstacle is detected in front of Robot 1 (dashed square) when driving the formation in the delimited area as shown in **Figure 5**. The operator should steer to the left in order to avoid the collision with the obstacle. The swarm is forced to steer toward the left since by steering in the opposite direction Robot 2 would then exit the delimited path.

**Figure 5.** Scenario 2—obstacle in front of R1.

#### *3.1.3. Scenario 3: obstacle in front of robot 2*

The third scenario features an obstacle in front of Robot 2 (dashed square) when driving the formation in the delimited area. In this case, the operator steers to the left in order to avoid the collision of Robot 2 with the obstacle as shown in **Figure 6**.

**Figure 6.** Scenario 3—obstacle in front of R2.

### **3.2. Testing and results**

*3.1.2. Scenario 2: obstacle in front of robot 1*

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**Figure 5.** Scenario 2—obstacle in front of R1.

**Figure 6.** Scenario 3—obstacle in front of R2.

*3.1.3. Scenario 3: obstacle in front of robot 2*

collision of Robot 2 with the obstacle as shown in **Figure 6**.

In the second scenario, an obstacle is detected in front of Robot 1 (dashed square) when driving the formation in the delimited area as shown in **Figure 5**. The operator should steer to the left in order to avoid the collision with the obstacle. The swarm is forced to steer toward the left since by steering in the opposite direction Robot 2 would then exit the delimited path.

The third scenario features an obstacle in front of Robot 2 (dashed square) when driving the formation in the delimited area. In this case, the operator steers to the left in order to avoid the In order to evaluate the suggested algorithms, for each scenario, teleoperators drove the swarm under the Equal Bandwidth, Equal Rates and Optimized Bandwidth method. In each trial, the following performance parameters are collected: the completion time in *seconds*, the average speed of each robot in cm/s, the average deviation of each robot from the shortest path (Esp1 and Esp2) in , the average error in the formation in the horizontal and vertical directions (*Δx* and *Δy*) in *cm*, the maximum errors in both directions as well as the average bandwidth in Mbps consumed. The first static algorithm divides the available bandwidth equally among the 6 communication channels, whereas the second applied algorithm allocates equal rates to all communication channels. The computed rates for each channel for the static algorithms are reported in **Table 1**. It is worth noting that since the image frame size is much greater than the other data exchanged, allocating that equal bandwidth to all communication channels reduces the cameras' frame rate to around 1 Hz, while allocating equal rates to all communication channels increases frame rates to 1.5 fps; however, it drops the rates of all other data exchanged by a factor of five.


**Table 1.** Computed rates (in Hz) of both static algorithms.

The path in front of the formation can be visualized by the cameras located on the forehead of each robot. Robots R1 and R2 navigate inside a delimited path while avoiding obstacles to reach the final destination. Moreover, a force feedback that corresponds to the distance to obstacles in front of the formation is calculated based on values measured by the ultrasonic sensors mounted on each robot. In order to evaluate the suggested algorithm, four teleoperators drove the formation under the three allocation methods in the three defined scenarios for a total number of runs equal to 36. Under each scenario, the bandwidth methods were *randomly* selected for each driver. Additionally, two training runs were performed by each user in order to get familiar with the task performed and experiment the haptic and visual feedback before executing the official runs. Results for the three mentioned scenarios are recorded in **Ta‐ bles 2**–**4**. Runs, which included visible slippage by the robots, were repeated in order not to bias the results.

Referring to **Table 2**, at an average bandwidth consumption less than that of both static algorithms, dynamic optimized bandwidth allocation method results in a better performance in the first scenario. With a reduction in bandwidth consumption of around 70 Kbps, the operator performs better when using the proposed dynamic algorithm than when applying the static ones. With the dynamic bandwidth algorithm, the average trial duration is 1.9 s less than the best static allocation method. Moreover, the driving performance improved signifi‐ cantly, since the parameters measuring the average error with respect to the shortest path improved in addition to the average speed of both robots. The instantaneous error to the shortest path has decreased by around 0.15 cm for both robots, while the average speed of both robots is around 0.35 cm/s higher. As for the parameters reflecting the quality of the executed collaborative task, we remark that the dynamic algorithm performs better than both static methods. The average errors in the horizontal and vertical directions are smaller as well as the maximum error is in both directions. For instance, the average horizontal error decreased by 10% for around 0.05 cm, while the average vertical error decreased by 40% (0.19 cm). It is worth noting that for most parameters the proposed method has a lower standard deviation indi‐ cating a more consistent performance.


**Table 2.** Results of Scenario 1 at 1.4 Mbps.

In Scenario 2, the advantage of dynamic bandwidth allocation is also demonstrated by the collected results in **Table 3**. With a reduction in bandwidth consumption of around 70 Kbps, the operators perform better when using the proposed dynamic algorithm than when applying the static ones. With the dynamic bandwidth algorithm, the average trial duration is 3.7 s less than the best static allocation. Moreover, the driving performance improves significantly, since the parameters measuring the average error with respect to the shortest path improve in addition to the average speed of both robots. The instantaneous error to the shortest path decreased by around 0.4 cm, while the average speed of both robots is around 0.35 cm/s higher. Additionally, the maximum errors in the horizontal and vertical directions decreased by around 0.35 cm. It is worth noting here that the runs performed with 'Equal Rates' method lead to a better average horizontal and vertical error; however, with this method, high peaks of errors are reached in both directions that almost reach the tolerated bounds of 2.5 and 5 cm.

The rates of visual feedback of robots R1 and R2 during Scenario 3 for the different adopted bandwidth algorithms are presented in **Figure 7**. Additionally, the rates of haptic feedback of robots R1 and R2 and the collaboration and commands rate during Scenario 3 for the different bandwidth algorithms are presented in **Figures 8** and **9**, respectively.

Furthermore, we examine the percentage of runs in which the suggested algorithm outper‐ forms the two static algorithms for each performance parameter in all scenarios. In other words, we count the number of times a user performed better according to a parameter when adopting the dynamic algorithm versus when driving with each of the static algorithms. Percentage of best performance for task duration, average speed of each robot (Speed R1, Speed R2), error of each robot with respect to the shortest path (Esp1 and Esp2) and maximum alignment and separation errors in the formation are recorded in **Table 5**. From the collected results, it can be seen that operators perform better with the dynamic allocation algorithm than the static algorithms at a minimum of 67% of the runs (Esp1 and Esp2 with Equal Bandwidth and Max horizontal/vertical error with Equal Rates). The suggested algorithm reaches a success rate of 92% for the speed R1 with respect to 'Equal Rates' static allocation.


**Table 3.** Once more, the results collected during the experiments performed in Scenario 3 have shown the advantages of the suggested dynamic allocation method as depicted in **Table 4**. The parameters measuring the quality of the collaborative task and the driving performance show real improvements. It is worth noting that in Scenario 3, the average task duration with the dynamic bandwidth method is equal to the average duration with equal bandwidth method. However, three of the four drivers have performed better with the suggested algorithm than with static bandwidth allocation. Only one user performed the trial with a total duration of 53 s. This trial biased the calculated average, which was reflected by the standard deviation value.Results of Scenario 2 at 1.4 Mbps.


**Table 4.** Results of Scenario 3 at 1.4 Mbps.

shortest path has decreased by around 0.15 cm for both robots, while the average speed of both robots is around 0.35 cm/s higher. As for the parameters reflecting the quality of the executed collaborative task, we remark that the dynamic algorithm performs better than both static methods. The average errors in the horizontal and vertical directions are smaller as well as the maximum error is in both directions. For instance, the average horizontal error decreased by 10% for around 0.05 cm, while the average vertical error decreased by 40% (0.19 cm). It is worth noting that for most parameters the proposed method has a lower standard deviation indi‐

cating a more consistent performance.

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**Table 2.** Results of Scenario 1 at 1.4 Mbps.

**Duration (s)**

**Speed R1 (cm/s)**

**Equal bandwidth** Average 35.2 4.53 4.73 0.52 0.53 0.75 0.48 2.63 3.95 1.40

**Equal rates** Average 34.2 4.71 4.91 0.43 0.47 0.54 0.59 1.99 2.92 1.40

**Optimized rates** Average 32.3 5.04 5.27 0.37 0.41 0.49 0.29 1.32 1.33 1.33

In Scenario 2, the advantage of dynamic bandwidth allocation is also demonstrated by the collected results in **Table 3**. With a reduction in bandwidth consumption of around 70 Kbps, the operators perform better when using the proposed dynamic algorithm than when applying the static ones. With the dynamic bandwidth algorithm, the average trial duration is 3.7 s less than the best static allocation. Moreover, the driving performance improves significantly, since the parameters measuring the average error with respect to the shortest path improve in addition to the average speed of both robots. The instantaneous error to the shortest path decreased by around 0.4 cm, while the average speed of both robots is around 0.35 cm/s higher. Additionally, the maximum errors in the horizontal and vertical directions decreased by around 0.35 cm. It is worth noting here that the runs performed with 'Equal Rates' method lead to a better average horizontal and vertical error; however, with this method, high peaks of errors are reached in both directions that almost reach the tolerated bounds of 2.5 and 5 cm.

The rates of visual feedback of robots R1 and R2 during Scenario 3 for the different adopted bandwidth algorithms are presented in **Figure 7**. Additionally, the rates of haptic feedback of robots R1 and R2 and the collaboration and commands rate during Scenario 3 for the different

Furthermore, we examine the percentage of runs in which the suggested algorithm outper‐ forms the two static algorithms for each performance parameter in all scenarios. In other

bandwidth algorithms are presented in **Figures 8** and **9**, respectively.

**Speed R2 (cm/s)**

**Esp1 (cm)**

Std Dev 1.13 0.17 0.23 0.15 0.19 0.56 0.23 1.28 1.30 0.00

Std Dev 5.26 0.77 0.77 0.09 0.10 0.37 0.18 1.25 1.21 0.00

Std Dev 4.39 0.45 0.45 0.05 0.05 0.34 0.18 0.79 0.69 0.0015

**Esp2 (cm)**

**Avg horiz error (cm)**

**Avg vert error (cm)**

**Max horiz error (cm)**

**Max vert error (cm)**

**Average bandwidth (Mbps)**

**Figure 7.** Visual rates of R1 & R2 in Scenario 3.

**Figure 8.** Haptic rates of R1 & R2 in Scenario 3.

Finally, the advantages of the proposed dynamic bandwidth optimization and management scheme over legacy bandwidth management schemes are clearly expressed in the results in terms of performance improvement and conserving network resources. Since the proposed algorithm is scalable and not limited to a single task, the improvement in performance is greatly realized in critical situations, where the collaborative task requires high levels of accuracy especially in cases involving human safety.

**Figure 9.** Collaboration & commands rates in Scenario 3.


**Table 5.** Percentage of best performance.

### **4. Conclusions**

**Figure 7.** Visual rates of R1 & R2 in Scenario 3.

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**Figure 8.** Haptic rates of R1 & R2 in Scenario 3.

Finally, the advantages of the proposed dynamic bandwidth optimization and management scheme over legacy bandwidth management schemes are clearly expressed in the results in terms of performance improvement and conserving network resources. Since the proposed In this work, dynamic optimized bandwidth management in teleoperated collaborative robotics is tackled. The focus was on managing all communication channels, where actuation commands, system state and sensory data are exchanged. This was achieved by monitoring the interesting events occurring in the robots' environment and the changes in quality of collaboration among them. Effective completion of the collaborative task with lower band‐ width consumption and better performance was accomplished proving that the proposed method could be the basis of a framework for developing more complex algorithms applied to highly complex systems.
