The preimage planning framework (or LMT framework, named after its developers, Lozano-Pérez, Mason, and Taylor) was developed as a general way to perform manipulation planning under uncertainty [311,659]. Although the concepts apply to general configuration spaces, they will be covered here for the case in which and is polygonal. This is a common assumption throughout most of the work done within this framework. This could correspond to a simplified model of a robot hand that translates in , while possibly carrying a part. A popular illustrative task is the peg-in-hole problem, in which the part is a peg that must be inserted into a hole that is slightly larger. This operation is frequently performed as manufacturing robots assemble products. Using the configuration space representation of Section 4.3.2, the robot becomes a point moving in among polygonal obstacles.
The distinctive features of the models used in preimage planning are as follows: