Partitioning contact-state space using the theory of polyhedral convex cones

The assembly plan from observation (APO) system observes a human operator perform an assembly task, analyzes the observations, models the task and generates the programs for the robot to perform the same task. A major component of the APO system is the task recognition module, which models the observed task. The task model in the APO context is defined as a sequence of assembly states of the part being assembled and the actions which cause the transition between the states. The state of the assembled part is based on its freedom, which can be computed from the geometry of the contacts between the part and its environment. This freedom can be represented as a polyhedral convex cone (PCC) in screw space. We show that any contact configuration can be classed into a finite number of contact states. These contact states correspond to typologically distinct intersections of the PCC with a linear subspace T in screw space. The models of any observed task can be represented as a path in a transition graph obtained from these contact states. We illustrate the theory by implementing the APO system for polygonal objects assembled in a plane using rotation and translation.