Help with simulating a drone search algorithm by using matlab in 2D ?

hello people !! I am actually trying to recreate a work from this paper : https://ift.tt/2RhnVKh can understand the paper , however my skills in matlab are very basic , i can write functions and execute it in the terminal. I had never worked on simulations. so please suggest me what are the modules i might need to learn to recreate these results in matlab.Approach i believe is thisgenerate theta values from eq 15 , but then i have another problem the equation is of t(theta)not theta(t) so not sure how to generate values of theta with time values.using theta values and eq(13) i need to generate a Archimedes search trajectory.so to recreate the simulation i think i need to generate a graph(cartesian co-ordinate) (C-SPACE) with a rectangular figure which i will designate as ship and it moves at a certain speed.then using the equation given in paper i generate polar co-ordinate which i will convert to cartesan co-ordinate then use that to generate the spiral i graph.when the tip of the spiral touches the moving rectangle i end the simulation.is this the correct approach ? if yes , what are the modules i need to learn from matlab to implement it.*Thank you in advance !! * via /r/drones https://ift.tt/2OVzfza