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Representing Robot Geometry as Distance Fields: Applications to Whole-body Manipulation (2307.00533v3)
Published 2 Jul 2023 in cs.RO
Abstract: In this work, we propose a novel approach to represent robot geometry as distance fields (RDF) that extends the principle of signed distance fields (SDFs) to articulated kinematic chains. Our method employs a combination of Bernstein polynomials to encode the signed distance for each robot link with high accuracy and efficiency while ensuring the mathematical continuity and differentiability of SDFs. We further leverage the kinematics chain of the robot to produce the SDF representation in joint space, allowing robust distance queries in arbitrary joint configurations. The proposed RDF representation is differentiable and smooth in both task and joint spaces, enabling its direct integration to optimization problems. Additionally, the 0-level set of the robot corresponds to the robot surface, which can be seamlessly integrated into whole-body manipulation tasks. We conduct various experiments in both simulations and with 7-axis Franka Emika robots, comparing against baseline methods, and demonstrating its effectiveness in collision avoidance and whole-body manipulation tasks. Project page: https://sites.google.com/view/lrdf/home
- M. Quigley, K. Conley, B. Gerkey, J. Faust, T. Foote, J. Leibs, R. Wheeler, A. Y. Ng et al., “Ros: an open-source robot operating system,” in ICRA workshop on open source software, vol. 3, no. 3.2. Kobe, Japan, 2009, p. 5.
- S. Zimmermann, M. Busenhart, S. Huber, R. Poranne, and S. Coros, “Differentiable collision avoidance using collision primitives,” in Proc. IEEE/RSJ Intl Conf. on Intelligent Robots and Systems (IROS). IEEE, 2022, pp. 8086–8093.
- B. Curless and M. Levoy, “A volumetric method for building complex models from range images,” in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, 1996, pp. 303–312.
- J. J. Park, P. Florence, J. Straub, R. Newcombe, and S. Lovegrove, “Deepsdf: Learning continuous signed distance functions for shape representation,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 165–174.
- P. Liu, K. Zhang, D. Tateo, S. Jauhri, J. Peters, and G. Chalvatzaki, “Regularized deep signed distance fields for reactive motion generation,” in Proc. IEEE/RSJ Intl Conf. on Intelligent Robots and Systems (IROS). IEEE, 2022, pp. 6673–6680.
- M. Koptev, N. Figueroa, and A. Billard, “Neural joint space implicit signed distance functions for reactive robot manipulator control,” IEEE Robotics and Automation Letters, vol. 8, no. 2, pp. 480–487, 2022.
- M. Macklin, K. Erleben, M. Müller, N. Chentanez, S. Jeschke, and Z. Corse, “Local optimization for robust signed distance field collision,” Proceedings of the ACM on Computer Graphics and Interactive Techniques, vol. 3, no. 1, pp. 1–17, 2020.
- J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans, “Reconstruction and representation of 3d objects with radial basis functions,” in Proceedings of the 28th annual conference on Computer graphics and interactive techniques, 2001, pp. 67–76.
- J. Ortiz, A. Clegg, J. Dong, E. Sucar, D. Novotny, M. Zollhoefer, and M. Mukadam, “isdf: Real-time neural signed distance fields for robot perception,” arXiv preprint arXiv:2204.02296, 2022.
- S. Izadi, D. Kim, O. Hilliges, D. Molyneaux, R. Newcombe, P. Kohli, J. Shotton, S. Hodges, D. Freeman, A. Davison et al., “Kinectfusion: real-time 3d reconstruction and interaction using a moving depth camera,” in Proceedings of the 24th annual ACM symposium on User interface software and technology, 2011, pp. 559–568.
- M. Breyer, J. J. Chung, L. Ott, R. Siegwart, and J. Nieto, “Volumetric grasping network: Real-time 6 dof grasp detection in clutter,” in Proc. Conference on Robot Learning (CoRL). PMLR, 2021, pp. 1602–1611.
- Z. Jiang, Y. Zhu, M. Svetlik, K. Fang, and Y. Zhu, “Synergies between affordance and geometry: 6-dof grasp detection via implicit representations,” arXiv preprint arXiv:2104.01542, 2021.
- M. Danielczuk, A. Mousavian, C. Eppner, and D. Fox, “Object rearrangement using learned implicit collision functions,” in Proc. IEEE Intl Conf. on Robotics and Automation (ICRA). IEEE, 2021, pp. 6010–6017.
- T. Liu, Z. Liu, Z. Jiao, Y. Zhu, and S.-C. Zhu, “Synthesizing diverse and physically stable grasps with arbitrary hand structures using differentiable force closure estimator,” IEEE Robotics and Automation Letters, vol. 7, no. 1, pp. 470–477, 2021.
- D. Driess, J.-S. Ha, M. Toussaint, and R. Tedrake, “Learning models as functionals of signed-distance fields for manipulation planning,” in Proc. Conference on Robot Learning (CoRL). PMLR, 2022, pp. 245–255.
- J. Schulman, Y. Duan, J. Ho, A. Lee, I. Awwal, H. Bradlow, J. Pan, S. Patil, K. Goldberg, and P. Abbeel, “Motion planning with sequential convex optimization and convex collision checking,” The International Journal of Robotics Research, vol. 33, no. 9, pp. 1251–1270, 2014.
- M. Mukadam, J. Dong, X. Yan, F. Dellaert, and B. Boots, “Continuous-time gaussian process motion planning via probabilistic inference,” The International Journal of Robotics Research, vol. 37, no. 11, pp. 1319–1340, 2018.
- N. Ratliff, M. Zucker, J. A. Bagnell, and S. Srinivasa, “Chomp: Gradient optimization techniques for efficient motion planning,” in Proc. IEEE Intl Conf. on Robotics and Automation (ICRA). IEEE, 2009, pp. 489–494.
- T. Schmidt, R. A. Newcombe, and D. Fox, “Dart: Dense articulated real-time tracking.” in Robotics: Science and systems, vol. 2, no. 1. Berkeley, CA, 2014, pp. 1–9.
- G. Sutanto, I. R. Fernández, P. Englert, R. K. Ramachandran, and G. Sukhatme, “Learning equality constraints for motion planning on manifolds,” in Proc. Conference on Robot Learning (CoRL). PMLR, 2021, pp. 2292–2305.
- V. Vasilopoulos, S. Garg, P. Piacenza, J. Huh, and V. Isler, “Ramp: Hierarchical reactive motion planning for manipulation tasks using implicit signed distance functions,” arXiv preprint arXiv:2305.10534, 2023.
- J. Michaux, Q. Chen, Y. Kwon, and R. Vasudevan, “Reachability-based trajectory design with neural implicit safety constraints,” arXiv preprint arXiv:2302.07352, 2023.
- B. Liu, G. Jiang, F. Zhao, and X. Mei, “Collision-free motion generation based on stochastic optimization and composite signed distance field networks of articulated robot,” arXiv preprint arXiv:2306.04130, 2023.
- J. Denavit and R. S. Hartenberg, “A kinematic notation for lower-pair mechanisms based on matrices,” 1955.
- A. J. Ijspeert, J. Nakanishi, H. Hoffmann, P. Pastor, and S. Schaal, “Dynamical movement primitives: Learning attractor models formotor behaviors,” Neural Computation, vol. 25, no. 2, pp. 328–373, 2013.
- A. Paraschos, C. Daniel, J. R. Peters, and G. Neumann, “Probabilistic movement primitives,” in Advances in Neural Information Processing Systems (NeurIPS), C. J. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger, Eds., vol. 26. Curran Associates, Inc., 2013.
- S. Calinon, “Mixture models for the analysis, edition, and synthesis of continuous time series,” in Mixture Models and Applications, N. Bouguila and W. Fan, Eds. Springer, Cham, 2019, pp. 39–57.
- W. W. Hager, “Updating the inverse of a matrix,” SIAM Review, vol. 31, no. 2, pp. 221–239, 1989.
- A. I. Boyko, M. P. Matrosov, I. V. Oseledets, D. Tsetserukou, and G. Ferrer, “Tt-tsdf: Memory-efficient tsdf with low-rank tensor train decomposition,” in Proc. IEEE/RSJ Intl Conf. on Intelligent Robots and Systems (IROS). IEEE, 2020, pp. 10 116–10 121.
- J. Haviland and P. Corke, “Manipulator differential kinematics: Part 2: Acceleration and advanced applications,” IEEE Robotics & Automation Magazine, 2023.
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