MIT Department of Electrical Engineering & Computer Science

Decidability of Robot Positioning Tasks Using Stereo Vision Systems

Joao P. Hespanha
Yale University

Wednesday, March 4, 1998
2:00 PM (refreshments 1:45)
RLE Conference Room, Room 36-428
EECS Special Seminar

Abstract

The virtue of feedback control is that it can be used to make a controlled process accomplish a prescribed task, despite noise and process, sensor, and actuator modeling errors. Vision systems admit imprecise models because they are difficult to calibrate. Thus, within the context of robot positioning tasks, it is natural to ask if one can precisely accomplish a given task, when imprecisely modeled cameras are used as feedback sensors. This motivates the basic question addressed in this talk:

When is it possible to decide if a prescribed robot positioning task has been accomplished using images acquired by an imprecisely modeled stereo vision system?

To make precise what the issue is, we formalize the concept of a "positioning task" and then introduce the notion of a "decidable positioning task." By a positioning task is meant the objective of bringing the pose of a robot to a specified "target" in the robot's workspace. The pose of the robot and the target are each determined by a list of point features simultaneously observed by an imprecisely modeled stereo vision system. Formally, a positioning task is then represented by an equation of the form T(f)=0, where T is a task function and f a list of observed robot and target point features. A positioning task is then said to be decidable if it is possible to determine whether or not T(f)=0 on the basis of an observed image of f. We show that for a projective two-camera system with known epipolar geometry, a positioning task is decidable just in case the task function T is a suitably defined projective invariant.