1 Introduction
2 Introduction to mobility models
3 Group mobility model for coherent and cooperative network
3.1 Network system and workspace definition
3.2 Network system objects definition
3.3 Group mobility model formulation
4 Algorithm for motion trajectory calculation
4.1 Reference distance estimation
4.2 Displacement calculation
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Step 1: Calculate in the time step t k the new position of the reference point \(\mathbf {c}^{i}_{(k+1)}\), solving the optimization problem for the estimated value of the reference distance \(\hat {d}_{g,(k+1)}^{i}\), and under the assumption that all points from the set \(P^{i}_{(k)}\) are fixed:$$\begin{array}{@{}rcl@{}} && {} \min_{\mathbf{c}^{i}_{(k+1)}}\left[\sum_{G_{g}^{i} \in S_{G,(k)}^{i}}U_{g,(k)}^{i}\left(d_{g,(k+1)}^{i}\right) = \sum_{G_{g}^{i} \in S_{G,(k)}^{i}} \epsilon^{i}_{g,(k)}\right.\\ &&\quad\quad\left.\left(\frac{\hat{d}_{g,(k+1)}^{i}}{\left\|\mathbf{c}^{i}_{(k+1)} - \mathbf{c}^{i}_{g,(k)}\right\|} -1 \right)^{2}\right], \end{array} $$(27)$$ \forall_{O_{j},j = 1,\ldots,M} \quad \mathbf{c}^{i}_{(k+1)} \cap Vol\left(P^{j}_{(k)}\right) = \emptyset, $$(28)$$ \Delta t \cdot v^{i}_{max} \geq \left\|\mathbf{c}^{i}_{(k+1)} - \mathbf{c}^{i}_{(k)}\right\|. $$(29)×The results of calculations are presented in Fig. 7.×
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Step 2: Calculate in the time step t k the displacement for all points from the set \(P^{i}_{(k)}\), solving the optimization problem for the estimated value of the reference distance \(\hat {d}_{g,(k+1)}^{i}\), and under the assumption that the point \(\mathbf {c}^{i}_{(k+1)}\) calculated in step 1 is fixed:$$ \min_{P^{i}_{(k+1)}}\left[\sum_{\mathbf{p}^{i}_{a},\mathbf{p}^{i}_{b} \in P^{i},a\neq b}\left(\bar{r}_{a,b}^{i} - \left\|\mathbf{p}^{i}_{a,(k+1)} - \mathbf{p}^{i}_{b,(k+1)}\right\| \right)^{2} \right], $$(30)$$ \forall_{O_{j},j = 1,\ldots,M} \quad Vol\left(P^{i}_{(k+1)}\right) \cap Vol\left(P^{j}_{(k)}\right) = \emptyset. $$(31)The results of calculations are presented in Fig. 8.×
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Step 3: Recalculate the position of \(\mathbf {c}^{i}_{(k+1)}\) to satisfy the constraint on a solid body, and under the assumption that all points from the set \(P^{i}_{(k+1)}\) calculated in step 2 are fixed:$$ \min_{c^{i}_{(k+1)}}\left[\sum_{\mathbf{p}^{i}_{a} \in P^{i},\mathbf{c}^{i} \in P^{i}}\left(\bar{r}_{0,a}^{i} - \left\|\mathbf{p}^{i}_{a,(k+1)} - \mathbf{c}^{i}_{(k+1)}\right\| \right)^{2} \right], $$(32)$$ \forall_{O_{j},j = 1,\ldots,M} \quad \mathbf{c}^{i}_{(k+1)} \cap Vol\left(P^{j}_{(k)}\right) = \emptyset, $$(33)The results of calculations are presented in Fig. 9.×
5 Motion pattern computing for coherent network
6 Case study results
6.1 The design of coherent network
6.2 Re-establishing the communication infrastructure
6.3 Emergency situation awareness
Time | Average node degree | Average inter-node distance | Sum of energy |
---|---|---|---|
0 | 21.0 | 9.45 | 5936.73 |
20 | 16.0 | 17.71 | 799.14 |
40 | 12.0 | 19.13 | 398.37 |
60 | 8.64 | 19.66 | 189.07 |
80 | 7.55 | 20.46 | 133.55 |
100 | 7.09 | 20.44 | 131.64 |
120 | 6.73 | 21.23 | 119.97 |
140 | 5.55 | 20.65 | 106.94 |
160 | 6.0 | 20.86 | 113.98 |
180 | 5.55 | 20.83 | 111.57 |
200 | 5.27 | 21.16 | 96.83 |