Algorithm 2: Dynamic navigation algorithms for calorific heat maps Environmental Interaction and Mathematical Representation (outline)

1. Input: $\mathit{n}\mathit{a}\mathit{t}\mathit{u}\mathit{r}\mathit{a}\mathit{l} \mathit{l}\mathit{a}\mathit{n}\mathit{g}\mathit{u}\mathit{a}\mathit{g}\mathit{e} \mathit{r}\mathit{e}\mathit{p}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n} \mathit{t}\mathit{a}\mathit{s}\mathit{k}$ $\mathcal{L}$

2. Breakdown of tasks:

3.     $\left({\mathcal{l}}_{\mathbf{1}},{\mathcal{l}}_{\mathbf{2}},\dots ,{\mathcal{l}}_{\mathit{n}}\right)$

4. The problem is reduced to the optimization equation

5. ${\mathbf{m}\mathbf{i}\mathbf{n}}_{{\mathit{\tau }}_{\mathit{i}}^{\mathbf{r}}}\{{\mathcal{F}}_{\mathit{t}\mathit{a}\mathit{s}\mathit{k}}\left({\mathbf{T}}_{\mathit{i}},{\mathcal{l}}_{\mathit{i}}\right)+{\mathcal{F}}_{\mathit{c}\mathit{o}\mathit{n}\mathit{t}\mathit{r}\mathit{o}\mathit{l}}\left({\mathit{\tau }}_{\mathit{i}}^{\mathbf{r}}\right)\} \mathbf{subject} \mathbf{to} \mathcal{C}\left({\mathbf{T}}_{\mathit{i}}\right)$

6. Constructing a mathematical representation of ${\mathcal{F}}_{\mathit{t}\mathit{a}\mathit{s}\mathit{k}}$

7.     ${\mathcal{F}}_{\mathit{t}\mathit{a}\mathit{s}\mathit{k}}=-\sum _{\mathit{j}=\mathbf{1}}^{\left|{\mathit{\tau }}_{\mathit{i}}^{\mathbf{e}}\right|}\mathbf{V}\left({\mathit{p}}_{\mathit{j}}^{\mathbf{e}}\right), \mathbf{w}\mathbf{h}\mathbf{e}\mathbf{r}\mathbf{e} {\mathit{p}}_{\mathit{j}}^{\mathbf{e}}\in {\mathbb{N}}^{\mathbf{2}}$

8. Construct a two-dimensional space: $\mathbf{V}\in {\mathbb{R}}^{\mathit{w}\times \mathit{h}}$

9. Constructing calorific heat maps:

10.    ${\mathbf{V}}_{\mathit{i}}^{\mathit{t}}=\mathbf{h}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{m}\mathbf{a}\mathbf{p}\left({\mathbf{o}}^{\mathit{t}},{\mathcal{l}}_{\mathit{i}}\right)$

11. Define a high calorific value path:

12.     $\mathit{R}\left(\mathit{P}\right)=\sum _{\mathit{i}=\mathbf{1}}^{\mathit{k}}\mathit{H}\left({\mathit{v}}_{\mathit{i}}\right)$//We define the heat value of a path as the sum of the heat values of all nodes on the path.

13. Path generation:

14.    ${\mathit{v}}_{\mathit{i}}=\mathit{a}\mathit{r}\mathit{g}{\mathit{m}\mathit{a}\mathit{x}}_{\mathit{v}\in \mathit{N}\left({\mathit{v}}_{\mathit{i}-\mathbf{1}}\right)}\mathit{H}\left(\mathit{v}\right)$//$\mathit{N}\left({\mathit{v}}_{\mathit{i}-\mathbf{1}}\right)$ denotes the set of neighbouring nodes of node ${\mathit{v}}_{\mathit{i}-\mathbf{1}}$

15. Output: $\mathit{P}=\{{\mathit{v}}_{\mathbf{1}},{\mathit{v}}_{\mathbf{2}},\dots ,{\mathit{v}}_{\mathit{k}}\}$             //Path with the highest calorific value