Solution:

Place points:

The place point is the third point of the pick-and-place trajectory. The coordinate frame is denoted by $T_{\text {base }}^{\text {place }}$.

This represents the final position and orientation of the part being manipulated. The place orientation $R^{\text {place }}$ is selected in such a way that the approach vector $r^3$ is orthogonal to the surface on which the part will come to rest.

The distance place between the place position and the place surface, measured along the approach vector should be identical to the distance between the pick position and the pick surface.

$ \mathrm{d}^{\text {place }}=\mathrm{d}^{\text {pick }}\\ $

1) $d^{\text {place }}=d^{\text {pick }}$

The object is picked up from the work surface and placed exactly touching the work surface.

2) $\mathrm{d}^{\text {place }}\lt\mathrm{d}^{\text {pick }}$

The robot penetrates the object into the work surface when the part is placed, as a result of which the part slides in between the fingers of the grippers.

3) dplace $^{\text {pledpick }}$

The placed part is unsupported when it reaches the destination and the robot opens its fingers and the object or the part falls down because of gravity.

Set-down point:

The last point in the pick-and-place trajectory is the set-down point, denoted by $T_{\text {base }}^{\text {set }}$.

It is a point near the place point that the robot moves to before an attempt is made to place the part. The set-down point is an intermediate point that is inferred from the place point.