Learning Polynomial Representations of Physical Objects with Application to Certifying Correct Packing Configurations
This work addresses the challenge of certifying object packing in robotics and manufacturing, though it is incremental as it builds on existing SOS methods.
The paper tackles the problem of representing physical objects from point cloud data using polynomial sublevel sets, enabling certification of correct packing configurations without overlaps, with results demonstrated through SOS programming.
This paper introduces a novel approach for learning polynomial representations of physical objects. Given a point cloud data set associated with a physical object, we solve a one-class classification problem to bound the data points by a polynomial sublevel set while harnessing Sum-of-Squares (SOS) programming to enforce prior shape knowledge constraints. By representing objects as polynomial sublevel sets we further show it is possible to construct a secondary SOS program to certify whether objects are packed correctly, that is object boundaries do not overlap and are inside some container set. While not employing reinforcement learning (RL) in this work, our proposed secondary SOS program does provide a potential surrogate reward function for RL algorithms, autonomously rewarding agents that propose object rotations and translations that correctly pack objects within a given container set.