# Joint Communication-Motion Planning in Networked Robotic Systems
## 2 Conventional Relay-Assisted Robot System
### Task Execution: Act
#### 2.4.2 Results  
We consider a workspace of a \(50\) m \(\times\)\(25\) m region, and the remote base station is located at a fixed position \(x_{d}=(10,0)\). We adopt the \(802.11\) g protocol and the corresponding bandwidth \(B=20\)MHz. Moreover, \(\beta\) is often obtained from empirical measurements, here we set \(\beta=3.68\). Furthermore, the noise power spectral density \(N_{0}\) is set to \(-100\) dBm/Hz. For the end-to-end PER upper bound, we use an accepted value \(0.01\), and adopt the transmission-mode index \(n=2\)[15]. The motion parameters are measured for a Pioneer 3 DX robot as follows: \(\kappa_{1}=7.4\), \(\kappa_{2}=0.29\) and \(v_{\rm max}=1\)[17].  
We assume the trajectory of the sensing robot travels along a straight line from \(x_{\rm s,1}=(0,20)\) to \(x_{s,9}=(40,20)\). The JCMP-optimized trajectories of the relay robot at different data sampling rates are shown by the square lines in Figure 3. In each time step, the relay robot aims at moving to the position where the total energy cost is minimal.  
If we only take the communication quality into account for motion planning, namely, adopting the non-JCMP philosophy that just optimizes communication performance, during each period of time \(T\), the optimal position of the relay robot is located on the straight line between the base station and the sensing robot, as shown by Figure 3a and serve it as our benchmark. As we increase the data sampling rate of the sensing robot with several separate values, \(\eta_{\rm s}=1\), \(5\), \(10\) Mbit/s. The results demonstrate that at a lower data sampling rate, the relay robot may prefer staying at the same place to moving, as shown in Figure 3. At a higher data sampling rate, e.g., \(\eta_{\rm s}=10\) Mbit/s, it is preferred that the relay robot moves to the position with better wireless communication quality instead of staying at the same place, and gets closer to the trajectory of the benchmark. The reason is that when the data sampling rate increases, the weight of the communication terms in the objective function of (8) increases. In order to minimize the total energy consumption of the system, the optimization algorithm tends to minimize those terms with larger weights.  
Figure 3: _Cont_.  
We compare the total energy consumption of the JCMP with that of the benchmark during the whole period, and the results are shown in Figure 4. The data sampling rates evaluated are from \(\eta_{\rm s}=\)100 kbit/s to 12 Mbit/s. When the motion energy of the sensing robot is not considered, the corresponding total energy consumption of the JCMP to the benchmark ranges from 89.16% to 2.01%, and this ratio is defined as the energy saving of the JCMP. On the other hand, considering that the motion of the sensing robot cannot be optimized, when the constant motion energy of the sensing robot is included, the corresponding total energy saving ratio will decrease. Based on the results of Figure 4, we may conclude that at relatively low data sampling rates, the JCMP is capable of saving more energy than the benchmark, which only optimizes the communication energy. At high data sampling rates, e.g., \(\eta_{\rm s}=12\)Mbit/s, the communication term becomes the dominant component in the objective function, and hence the solution may get closer to that of the CAMP benchmark.  
Figure 4: Energy saving ratio for different data sampling rates.