Which Object Fits Best? Solving Matrix Completion Tasks with a Humanoid Robot

Matrix completion tasks commonly appear on intelligence tests. Each task consists of a grid of objects, with one missing, and a set of candidate objects. The job of the test taker is to pick the candidate object that best fits in the empty square in the matrix. In this paper we explore methods for a robot to solve matrix completion tasks that are posed using real objects instead of pictures of objects. Using several different ways to measure distances between objects, the robot detected patterns in each task and used them to select the best candidate object. When using all the information gathered from all sensory modalities and behaviors, and when using the best method for measuring the perceptual distances between objects, the robot was able to achieve 99.44% accuracy over the posed tasks. This shows that the general framework described in this paper is useful for solving matrix completion tasks.