Consider the following two$-$link planar RR manipulator.

The manipulator begins at the starting configuration $q_s($solid lines$)$ and must follow a path to the final configuration $q_f($dash$-$dot lines$)$ while avoiding collision with the obstacle $($red$,$ single dot$),$ as illustrated below. Artificial potential forces must be determined to automate path generation from $q_s$ to $q_f.$

$o_1(q_s)=\left[\begin{array}{c}0\end{array}\right]$

$8,o_2(q_s)=\left[\begin{array}{c}6\end{array}\right]$

$8$

$90$

Obstacle $=\left[\begin{array}{c}7\end{array}\right]$

$1$

Note the following.

Note the following.

DH origin and obstacle locations in the workspace are indicated in the figure,

${}_0=10$ to determine the sphere of influence for the obstacle,

${}_1={}_2=5,$

${}_1={}_2=500,$

$d,$ and

the obstacle may be analyzed as a single point in the workspace.

$(4$ pts$)$ Evaluate the attractive artificial potential force$($s$)$ acting at origin $1,o_1(q_s).$

$(2$ pts$)$ Evaluate and specify whether origin $1,o_1(q_s),$ and origin $2,o_2(q_s),$ are within the obstacle's sphere of influence.

$(4$ pts$)$ Evaluate the repulsive artificial potential force$($s$)$ acting at origin $1,o_1(q_s).$

Consider the following two$-$link planar RR manipulator.

The manipulator begins at the starting configuration $q_s($solid lines$)$ and must follow a path to the final configuration $q_f($dash$-$dot lines$)$ while avoiding collision with the obstacle $($red$,$ single dot$),$ as illustrated below. Artificial potential forces must be determined to automate path generation from $q_s$ to $q_f.$

$o_1(q_s)=\left[\begin{array}{c}0\end{array}\right]$

$8,o_2(q_s)=\left[\begin{array}{c}6\end{array}\right]$

$8$

$90$

Obstacle $=\left[\begin{array}{c}7\end{array}\right]$

$1$

Note the following.