The efficient computation of uncertainty spaces for sensor-based robot planning

This paper describes methods for propogating systems of constrained variables, which may represent geometric uncertainties, sensing errors, disturbance forces, or other variations, through equations describing coordinate transformations in the task domain and for projecting the resulting large linear system onto a lower-dimensional space representing specific variations of interest for a particular problem. We have implemented a system based on these methods. We describe the mathematical representation, briefly describe two projection algorithms; and present a number of examples applying our implementation to robot task planning problems.