TOWARD LEARNING GEOMETRIC EIGEN-LENGTHS CRUCIAL FOR ROBOTIC FITTING TASKS

Abstract

Some extremely low-dimensional yet crucial geometric eigen-lengths often determine whether an object can be fitted in the environment or not. For example, the height of an object is important to measure to check if it can fit between the shelves of a cabinet, while the width of a couch is crucial when trying to move it through a doorway. Humans have materialized such crucial geometric eigen-lengths in common sense since they are very useful in serving as succinct yet effective, highly interpretable, and universal object representations. However, it remains obscure and underexplored if learning systems can be equipped with similar capabilities of automatically discovering such key geometric quantities in doing robotic fitting tasks. In this work, we therefore for the first time formulate and propose a novel learning problem on this question and set up a benchmark suite including the tasks, the data, and the evaluation metrics for studying the problem. We explore potential solutions and demonstrate the feasibility of learning such eigen-lengths from simply observing successful and failed fitting trials. We also attempt geometric grounding for more accurate eigen-length measurement and study the reusability of the learned geometric eigen-lengths across multiple tasks. Our work marks the first exploratory step toward learning crucial geometric eigen-lengths and we hope it can inspire future research in tackling this important yet underexplored problem.

1. INTRODUCTION

Consider a robot tasked with placing many small objects on warehouse shelves, where both the objects and the shelves have diverse geometric configurations. While the robot can simply try to accomplish the task by trial-and-error, to us as humans, it is clear that certain placements should not be attempted because they will obviously fail. For example, we should not attempt to place a tall object on a shelf whose height is too low. We base this judgement on the estimation of a critical geometric eigen-length or measurement, the height of the object and the shelf, whose comparison allows a quick estimate of task feasibility. While object height is an example of important eigen-lengths of an object that is crucial for the above shelf placement task, it is not hard to think of many other types of object eigen-lengths for other fitting tasks. Figure 1 presents some other example tasks together with the presumable geometric eigen-lengths based on human common sense. For example, the geometric eigen-length diameter is important for the task of stacking plates in different sizes (Figure 1 , (a)), while the width and length



Figure 1: Example tasks and the hypothesized crucial geometric measurements by humans.

