PDE solution to UAV/UGV trajectory planning problem by spatio-temporal estimation during wildfires

Unmanned Aerial Vehicles(UAVs)and Unmanned Ground Vehicles(UGVs)have been used in research and development community due to their strong potential in high-risk missions.One of the most important civilian implementations of UAV/UGV cooperative path planning is delivering medical or emergency supplies during disasters such as wildfires,the focus of this paper.However,wildfires themselves pose risk to the UAVs/UGVs and their paths should be planned to avert the risk as well as complete the mission.In this paper,wildfire growth is simulated using a coupled Partial Differential Equation(PDE)model,widely used in literature for modeling wildfires,in a grid environment with added process and measurement noise.Using principles of Proper Orthogonal Decomposition(POD),and with an appropriate choice of decomposition modes,a low-dimensional equivalent fire growth model is obtained for the deployment of the space-time Kalman Filtering(KF)paradigm for estimation of wildfires using simulated data.The KF paradigm is then used to estimate and predict the propagation of wildfire based on local data obtained from a camera mounted on the UAV.This information is then used to obtain a safe path for the UGV that needs to travel from an initial location to the final position while the UAV’s path is planned to gather information on wildfire.Path planning of both UAV and UGV is carried out using a PDE based method that allows incorporation of threats due to wildfire and other obstacles in the form of risk function.The results from numerical simulation are presented to validate the proposed estimation and path planning methods.

A numerical implementation of the length-scale independent phase field method

The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework.It replaced the discrete representation of crack by diffusive damage and solved it based on a minimization of the global energy storage functional.As a result,no crack tracking topology is needed,and complex crack shapes can be captures without user intervention.However,it is also reported to have an inconsistency between the predicted fracture toughness and the material strength.Recently,a novel energetic degradation function was proposed in literature to handle this issue.This research does some further modifications to the global energy storage functional so that Newton's method can be directly used to solve the energy minimization.With the new energy form,direct implementation of the length-scale independent phase field method into finite element packages like LS-DYNA becomes possible.This paper presents the framework and details of implementing the length-scale independent phase field method into LS-DYNA through a user-defined element and material subroutine.Several numerical examples are presented to compare with the experiment crack shape.Most importantly,this paper is one of the first ones to quantitatively predict accurate force response compared to experiments.These examples verify the accuracy of the new energy form and implementation.