Energy-optimal path-planning for quadrotors in forests.

Abstract

Motivated by the threat to the Lebanese forests brought upon by the Pine Processionary Moths, a system-level algorithm is proposed to have aerial drones navigate forest environments and visit each tree in an energy-optimal manner. In fact, the developed path-planning algorithm can be generalized for use to visit and inspect various cylindrically-shaped objects (e.g. power poles, concrete structures, and similar) in an energy-optimal manner. Given a map of the domain, an energy-optimal path is established between all pairs of objects (trees in this case) using optimal control theory to arrive at a hybrid solver of different transcription methods including Legendre-Gauss-Radau (LGR) and Hermite-Simpson (H-S) collocation methods. For cases with very large number of trees, a third-order polynomial estimation is established to map the position coordinates to energy consumption, which results in a significant reduction of computation time. After populating an adjacency matrix from the optimal control solver or polynomial estimation, the problem is defined as a travelling salesman problem (TSP), where the drone is to visit all objects only once, which requires the use of graph theory; Integer Linear Programming (ILP) along with Sub-Tour Elimination Constraints (SEC) are used to develop the general optimal tour. The algorithm is tailored to the needs of the intended application where prior information from previous scans are leveraged to generate a new set of trees, which includes infected trees in addition to ones with a relatively high probability to be infected based on a proposed probability distribution. The tour is further modified as a second tour is going on where a change of status from infected to non-infected, or vice-versa, results in a change in the probability of infection of each tree, which in turn changes the pool of trees required to visit. This abrupt change in tree sets requires a new path that is satisfied by a Fixed-Start-Fixed-End travelling salesman problem, which is solved using a genetic algo