Survey on Automated LEGO Assembly Construction

LEGO has been very popular toy in the world because it is attractive and fun to play with and stimulates one's creativity by providing means to conveniently assemble a variety of interesting shapes using the limited types of given bricks. However, it is hard for the beginners to design and assemble complex models they desire to make without instructions. Building a LEGO assembly manually usually requires a significant amount of trial-anderror. LEGO company therefore presented the LEGO construction problem in 1998 and in 2001. The problem statement is "Given any 3D body, how can it be built from LEGO bricks?" In this paper we will investigate the current research efforts to address the LEGO construction problem. We will review the problem definition, formulation, and a variety of approaches to solve the problem. We will discuss the data representations for input 3D polygonal models and the LEGO assembly structures, cost functions that will guide the search for the optimal solution, and various solution methods