this is a path planning problem using an artificial potential fieldTable TP$1$: Obstacle parameters.

Furthermore, the initial drone position is $(5,5)$ and the location of the desired target point is $(70,50).$

Your task is to complete the code template provided and to show that a feasible path can be generated using the artificial potential function method. The drone

equations of motion can be represented by a simple double$-$integrator model in $2$ dimensions $(x,y).$ Assume the vehicle has a mass of $5kg.$

The Potential functions should take the following form,

Attractive: $,U_a=\frac{1}{2}{K}_a{}_a^2$

Repulsive: $U_r=\{\begin{array}{cc}0,& >{}_0\\ \frac{1}{2}{K}_r({}_r-{}_0{)}^2,& {}_0\end{array}$

where ${}_a=\sqrt[\phantom{2}]{(x-x_a{)}^2+(y-y_a{)}^2}$ and ${}_r=\sqrt[\phantom{2}]{(x-x_{\text{o}\text{b}\text{s}}{)}^2+(y-y_{\text{o}\text{b}\text{s}}{)}^2}.$

When developing the appropriate APF control law, you should also include an additional force proportional to the drone velocity as follows,

$F_{x_v}=-K_v{v}_x,F_{y_v}=-K_v{v}_y$