Fitting an object into a box


I have got a robotics 3d problem.

I have an object defined by it’s bounding box (AABB with a robot clamp frame) , some set of 3D points of this object can be available.

I want to find the possible solutions of the robot clamp (position and orientation) to fit this object in another bounding box with the robot clamp.

I would like to know in which way IA could help. And how I could proceed ?