Departmental Papers (ESE)


Assembly problems require that a robot with fewer actuated degrees of freedom manipulate an environment containing a greater number of unactuated degrees of freedom. From the perspective of control theory, these problems hold considerable interest because they are characterized by the presence of non-holonomic constraints that preclude the possibility of feedback stabilization. In this sense they necessitate the introduction of a hierarchical controller. This paper explores these issues in the simple instance when all of the pieces to be assembled are constrained to lie on a line. A hierarchical controller is devised for this problem and is shown to be correct: the closed loop system achieves any desired final assembly from all initial configurations that lie in its connected component in configuration space; the generated sequence of motions never causes collisions between two pieces. Further examination of this approach interprets the controller's mediation of conflicting subgoals as promoting an M-player game amongst the pieces to be assembled.

Document Type

Journal Article

Subject Area

GRASP, Kodlab

Date of this Version

January 1994


Reprinted from Robotica, Volume 12, February 2004, pages 137-155.


autonomous assembly, robots, hierarchical controller, closed loop system



Date Posted: 10 April 2008

This document has been peer reviewed.