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Learning Polynomial Representations of Physical Objects with Application to Certifying Correct Packing Configurations (2312.06791v1)

Published 11 Dec 2023 in math.OC and cs.LG

Abstract: 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.

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References (51)
  1. Learning dynamical systems with side information. In Learning for Dynamics and Control, pages 718–727. PMLR, 2020.
  2. A complete characterization of the gap between convexity and sos-convexity. SIAM Journal on Optimization, 23(2):811–833, 2013.
  3. Geometry of 3d environments and sum of squares polynomials. arXiv preprint arXiv:1611.07369, 2016.
  4. Analysis of online shopping and home delivery in the uk. 2017.
  5. Mosek ApS. Mosek optimization toolbox for matlab. User’s Guide and Reference Manual, Version, 4:1, 2019.
  6. Shape-aware surface reconstruction from sparse 3d point-clouds. Medical image analysis, 38:77–89, 2017.
  7. Convex analysis and optimization, volume 1. Athena Scientific, 2003.
  8. Topology-aware surface reconstruction for point clouds. In Computer Graphics Forum, volume 39, pages 197–207. Wiley Online Library, 2020.
  9. Packaging waste from e-commerce: consumers’ awareness and concern. In Sustainable Waste Management: Policies and Case Studies: 7th IconSWM—ISWMAW 2017, Volume 1, pages 27–41. Springer, 2020.
  10. A sum-of-squares-based procedure to approximate the pontryagin difference of basic semi-algebraic sets. Automatica, 135:109783, 2022.
  11. Simple approximations of semialgebraic sets and their applications to control. Automatica, 78:110–118, 2017.
  12. A deep reinforcement learning algorithm for the rectangular strip packing problem. Plos one, 18(3):e0282598, 2023.
  13. Optimal packing and covering in the plane are np-complete. Information processing letters, 12(3):133–137, 1981.
  14. James Guthrie. Inner and outer approximations of star-convex semialgebraic sets. IEEE Control Systems Letters, 7:61–66, 2022.
  15. Closed-form minkowski sum approximations for efficient optimization-based collision avoidance. In 2022 American Control Conference (ACC), pages 3857–3864. IEEE, 2022.
  16. Polynomial optimization in geometric modeling, 2023.
  17. E Hopper and B Turton. A genetic algorithm for a 2d industrial packing problem. Computers & Industrial Engineering, 37(1-2):375–378, 1999.
  18. Planning irregular object packing via hierarchical reinforcement learning. IEEE Robotics and Automation Letters, 8(1):81–88, 2022a.
  19. Global optimization method for finding dense packings of equal circles in a circle. European Journal of Operational Research, 210(3):474–481, 2011.
  20. Surface reconstruction from point clouds: A survey and a benchmark. arXiv preprint arXiv:2205.02413, 2022b.
  21. Morgan Jones. Sublevel set approximation in the hausdorff and volume metric with application to path planning and obstacle avoidance. arXiv:2303.06778, 2023.
  22. Using sos for optimal semialgebraic representation of sets: Finding minimal representations of limit cycles, chaotic attractors and unions. In 2019 American Control Conference (ACC), pages 2084–2091. IEEE, 2019.
  23. Is online shopping packaging waste a threat to the environment? Economics Letters, 214:110398, 2022. ISSN 0165-1765. https://doi.org/10.1016/j.econlet.2022.110398. URL https://www.sciencedirect.com/science/article/pii/S0165176522000684.
  24. When to trust ai: Advances and challenges for certification of neural networks. arXiv preprint arXiv:2309.11196, 2023.
  25. Semidefinite programming and integer programming. Handbooks in Operations Research and Management Science, 12:393–514, 2005.
  26. John M Lee. Smooth manifolds. Springer, 2012.
  27. Optimizing two-dimensional irregular packing: A hybrid approach of genetic algorithm and linear programming. Applied Sciences, 13(22):12474, 2023.
  28. Johan Lofberg. Yalmip: A toolbox for modeling and optimization in matlab. In 2004 IEEE international conference on robotics and automation (IEEE Cat. No. 04CH37508), pages 284–289. IEEE, 2004.
  29. Surface reconstruction from point clouds by learning predictive context priors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6326–6337, 2022.
  30. Sparse identification of nonlinear dynamics with side information (sindy-si). arXiv preprint arXiv:2310.04227, 2023.
  31. Tractable fitting with convex polynomials via sum-of-squares. In Proceedings of the 44th IEEE Conference on Decision and Control, pages 1672–1677. IEEE, 2005.
  32. Sum-of-squares geometry processing. ACM Transactions on Graphics (TOG), 40(6):1–13, 2021.
  33. Position paper: Reducing amazon’s packaging waste using multimodal deep learning. 2021.
  34. Convolutional occupancy models for dense packing of complex, novel objects. arXiv preprint arXiv:2308.00091, 2023.
  35. Assembly task execution using visual 3d surface reconstruction: An integrated approach to parts mating. Robotics and Computer-Integrated Manufacturing, 81:102519, 2023.
  36. Sdf-pack: Towards compact bin packing with signed-distance-field minimization. arXiv preprint arXiv:2307.07356, 2023.
  37. A systematic grey-box modeling methodology via data reconciliation and sos constrained regression. Processes, 7(3):170, 2019.
  38. Mihai Putinar. Positive polynomials on compact semi-algebraic sets. Indiana University Mathematics Journal, 42(3):969–984, 1993.
  39. Solving 3d packing problem using transformer network and reinforcement learning. Expert Systems with Applications, 214:119153, 2023.
  40. A lightweight surface reconstruction method for online 3d scanning point cloud data oriented toward 3d printing. Mathematical Problems in Engineering, 2018, 2018.
  41. 3d scene reconstruction and digitization method for mixed reality systems. Programming and Computer Software, 49(3):151–160, 2023.
  42. How to certify machine learning based safety-critical systems? a systematic literature review. Automated Software Engineering, 29(2):38, 2022.
  43. A deep reinforcement learning hyper-heuristic with feature fusion for online packing problems. Expert Systems with Applications, page 120568, 2023.
  44. Polynomial level-set methods for nonlinear dynamical systems analysis. In Proc. Allerton Conf. on Communication, Control, and Computing, Allerton, IL. Citeseer, 2005.
  45. How do you manage online delivery package waste? IEEE Engineering Management Review, 48(2):184–192, 2020.
  46. Category-level shape estimation for densely cluttered objects. arXiv preprint arXiv:2302.11983, 2023.
  47. Towards reliable robot packing system based on deep reinforcement learning. Advanced Engineering Informatics, 57:102028, 2023.
  48. Heuristics integrated deep reinforcement learning for online 3d bin packing. IEEE Transactions on Automation Science and Engineering, 2023.
  49. Packerbot: Variable-sized product packing with heuristic deep reinforcement learning. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 5002–5008. IEEE, 2021.
  50. Learning physically realizable skills for online packing of general 3d shapes. ACM Transactions on Graphics, 42(5):1–21, 2023.
  51. Optimizing 3d irregular object packing from 3d scans using metaheuristics. Advanced Engineering Informatics, 47:101234, 2021.

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