Path planning for energy distribution system

Study notes of UAV path planning for energy distribution system.

Wireless power transfer background

Consider a two-stage energy distribution system [1]. 1. UAV interacts with center senosr node(s) 2. Center sensor node(s) interact with other nodes

For inductive power delivery, Ampere's Law and Faraday's Law need to be applied. The flux linkage looks like [2]:

The induced voltage is expressed by:

For acoustic power distribution, there's piezoelectric driver and transducer in each sensor node. Therefore the energy of the storage capacitor E_SC at any time t can be expressed as:

where E_m is the energy consumption from storage capacitor within an unit timestamp, T is the acoustic power transmitted to other nodes within an unit timestamp, R is the acoustic power transmitted from other nodes, I is indevtice power transmitted from the UAV.

Single weighted node clustering and multi-clusters

Therefore, to find the optimal center node, iterative loop is required. This search is bounded by acoustic limits. The choosing criteria should be:

where d(P, P_i) is the distance between node i position and current node position, w_i is the weighing parameter of node i (the energy of storage capacitor). This is because the altitude of UAV will affect the number of charging nodes.

Then for larger planes, multiple clusters will be formed like following figure [3]:

The algorithm is aimed at finding the minimum path.

Dijkstra's algorithm

The method is to find the shortest path between two nodes in weighting system G = {V, E}. Basically, the main concept is marking each node with (length or * as unknown) and separating G into two sets V₁ (node length which is already known) and V₂ (node length which is unknown). Consider the following example - assuming we have 6 nodes and from node a to destination node f:

1. starting node a = 0, b = 3, c = 2, V₁ = {a}, V₂ = {b, c, d, e, f}

2. starting node c, b = 2+5 = 7 > 3 (keep 3 then), e = 2+4 = 6, V₁ = {a, c}, V₂ = {b, d, e, f}

3. starting node b, d = 3+6 = 9 , e = 3+3 = 6, V₁ = {a, c, b}, V₂ = {d, e, f}

4. starting node e, d = 6+5 = 11 > 9 (keep 9 then), f = 6+7 = 13, V₁ = {a, c, b, e}, V₂ = {d, f}

5. starting node d, f = 9+6 = 15 > 13 (keep 13 then), e = 9+5 = 14 > 13 (keep 13 then), V₁ = {a, c, b, e, d}, V₂ = {f}

Then we can get shortest path (a, c, e, f) or (a, b, e, f) and total length is 13.

Implementation

This algorithm will be realized through C++. See Dij_algorithm for more information.

Reference

[1] D. E. Boyle, S. W. Wright, M. E. Kiziroglou, A. Y. S. Pandiyan, and E. M. Yeatman, "Inductive Power Delivery with Acoustic Distribution to Wireless Sensors," in Wireless Power Week, London, UK, 2019.

[2] Abdolkhani, A (2016) Fundamentals of inductively coupled wireless power transfer systems. In Coca, E (ed.), Wireless Power Transfer – Fundamentals and Technologies. Rjieka, Croatia: InTech.

[3] D. E. Boyle, S. W. Wright, M. E. Kiziroglou, A. Y. S. Pandiyan, and E. M. Yeatman, "Optimal energy distribution using clustering algorithm"