A node-to-node composite graph and pseudo-Boolean modelling: An unmanned aerial vehicle energy application

Abstract

Unmanned aerial vehicles (UAV) have been gaining momentum in recent years because of their vast application areas in the defence and civilian sectors. Their use can result in future missions to be more effective while also be conducted in a safer manner. UAVs, due to their large operational potential may be required to travel over long distances and prespecified way points thus requiring an effective and efficient decision making mechanism which allow the UAV to start and complete its mission. These missions may start and terminate at different or identical topological locations (or nodes). In the current paper a node-to-node graph theory energy costs modelling method is developed and presented. The modelling method requires as a priori the node-to-node energy costs. Furthermore, several propositions were presented to allow for the energy matrix to be perturbable, thus representing possible atmospheric variations which may occur during the UAVs mission. The UAV is modelled using energy graphs which allow a topological optimum to be obtained via suitable optimization algorithms. The energy costs implicitly contain time, propulsion force, and velocity information thus producing realistic results.

Optimality and Reachability - Pseudo Boolean Power Flows for multi-sourced Vehicle Topologies

“…Like stated previously, in [6] it was discussed the problem of obtaining a tour for an agent that is given an assignment to traverse a sequence of way points until it reaches its goal. The solution to the above was approached from two different perspectives.…”

“…Omit from matrix R n the identity matrix (I=that every node is reachable by itself) which then it reduces to matrix R g . The proofs of the reachability matrix and propositions 2 can be found in [6]. Proposition 2 and equation 7 are used to formulate the reachability mission requirement defined below.…”

“…The proof of proposition 4 is derived from the proof of equation 7 included in reference [6]. It follows from proposition 4 that if each agent is assigned with multiple node goals then for all goals, respectively, to be realizable then the elements of interest from the reachable matrix R g (Proposition 2) should be non-zero.…”

“…In [3], [4], [5], [6] and [7] it was discussed an important problem. It was that of obtaining a tour for an agent that is given an assignment to traverse a sequence of way points until it reaches its goal, when the route from i to j and j to i are of different magnitude.…”

“…The problem was first introduced by Minieka in 1979 and received great attention from researchers in the following years. In work [6] and [7] the solution to the above was approached from two different perspectives. The first one was with respect to minimum distance traversed and , secondly, with respect to energy consumed.…”