Question $3($Artificial Potential Field$)$

Consider the following configuration $($figure below$).$ The robot is at the position $q(t)=|[x(t)],[y(t)]|=\left[\begin{array}{c}5\\ 5\end{array}\right],$ the obstacle at $q_{\text{o}\text{b}\text{s}1}=|[x_{\text{o}\text{b}\text{s}1}],[y_{\text{o}\text{b}\text{s}1}]|=\left[\begin{array}{c}7\\ 8\end{array}\right],q_{\text{o}\text{b}\text{s}2}=|[x_{\text{o}\text{b}\text{s}2}],[y_{\text{o}\text{b}\text{s}2}]|=\left[\begin{array}{c}7\\ 2\end{array}\right]$ and the target at $q_{\text{G}\text{o}\text{a}\text{l}}=|[x_{\text{G}\text{o}\text{a}\text{l}}],[y_{\text{G}\text{o}\text{a}\text{l}}]|=\left[\begin{array}{c}15\\ 5\end{array}\right].$

Calculate $(q,q_{\text{o}\text{b}\text{s}})$ and $(q,q_{\text{G}\text{o}\text{a}\text{l}}).$

Determine and draw $($approximately$)$ the Attractive force and Repulsive forces for the case: ${}_0=4m.$

Deduce the next position $q(t+1)$ of the mobile robot for each case knowing that $===1$;$R_{\text{o}\text{b}\text{s}}=0\mathrm{.}5$;$R_{\text{G}\text{o}\text{a}\text{l}}=0\mathrm{.}2$;$R_{WMR}=0\mathrm{.}1.$