How can a robot place an item on a cluttered desk?- Group 2

Consider a service robot that needs to place a book on a cluttered desk. If there is enough space on the desk for the book, the robot places the book in this space. Otherwise, the robot rearranges the other items on the desk, to create enough space for the book, and then places the book in this space.
The following video illustrates how a robot rearranges items on a table to be able to swap the red box and the gray tray on a desk, and places the items in empty spaces without any collisions:
https://www.dropbox.com/s/6khnulsrtvxy7ya/geometric_rearrangement_short.mp4?dl=0 .
The objective is to design and develop an intelligent method to solve the placement problem, and to demonstrate it with a dynamic simulation (Gazebo) and/or a physical implementation with a Baxter robot.
The project is recommended for CS, ME, and EE students, with good programming skills.  Most of the project studies will take place in the Cognitive Robotics lab:
https://www.dropbox.com/s/9cv0eslmgfjcq4l/cogrobo-outreach.mp4?dl=0 .