Now consider ungrasping the object and placing it into the world. An easy case for the user is to press a button and have the object simply fall into the right place. This is accomplished by a basin of attraction which is an attractive potential function defined in a neighborhood of the target pose (position and orientation); see Figure 10.11. The minimum of the potential function is at the target. After the object is released, the object falls into the target pose by moving so that the potential is reduced to its minimum. This behavior is seen in many 2D drawing programs so that the endpoints of line segments conveniently meet. An example of convenient object placement is in the 2011 Minecraft sandbox game by Markus Persson (Notch), in which building blocks simply fall into place. Children have built millions of virtual worlds in this way.
Alternatively, the user may be required to delicately place the object. Perhaps the application involves stacking and balancing objects as high as possible. In this case, the precision requirements would be very high, placing a burden on both the controller tracking system and the user.
Steven M LaValle 2016-12-31