A Study of Action-Sequence Diffusion for Open-Loop Control under Dry Friction and Stiction
Resumo
Diffusion models have recently emerged as expressive generative priors for planning and control. This paper studies Action Diffusion, an action-sequence diffusion formulation used as an open-loop proposal distribution for a point-mass system with dry friction and stiction. In this benchmark, motion starts only when the applied input exceeds a static-friction threshold, so effective controls occupy a small and temporally structured subset of the action-sequence space. A compact conditional 1D U-Net generates bounded control sequences conditioned on initial and target states. We compare it with uniform random shooting, random shooting from the same structured dataset prior, and the Cross-Entropy Method (CEM). Results show that Action Diffusion reduces terminal error and stuck steps, especially in low-sample regimes. These results indicate that conditional diffusion provides an effective mechanism for generating temporally coherent control sequences that overcome stiction by conditioning and recombining structured control primitives from the training prior for state-to-state open-loop control.
Referências
Armstrong-Hélouvry, B., Dupont, P., and Canudas de Wit, C. (1994). A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica, 30(7):1083–1138.
Canudas de Wit, C., Olsson, H., Åström, K. J., and Lischinsky, P. (1995). A new model for control of systems with friction. IEEE Transactions on Automatic Control, 40(3):419–425.
Chi, C., Xu, Z., Feng, S., Cousineau, E., Du, Y., Burchfiel, B., Tedrake, R., and Song, S. (2023). Diffusion policy: Visuomotor policy learning via action diffusion. In Robotics: Science and Systems.
Ho, J., Jain, A., and Abbeel, P. (2020). Denoising diffusion probabilistic models. In Advances in Neural Information Processing Systems, volume 33, pages 6840–6851.
Ho, J. and Salimans, T. (2022). Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598.
Janner, M., Du, Y., Tenenbaum, J. B., and Levine, S. (2022). Planning with diffusion for flexible behavior synthesis. In Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pages 9902–9915.
Kemmer, B., Simões, R., Ivamoto, V., and Lima, C. (2023). Performance analysis of generative adversarial networks and diffusion models. In Proceedings of the Brazilian Conference on Intelligent Systems (BRACIS). Springer.
Levine, S., Kumar, A., Tucker, G., and Fu, J. (2020). Offline reinforcement learning: Tutorial, review, and perspectives. arXiv preprint arXiv:2005.01643.
Machado, B. M. and Antonelo, E. A. (2025). Investigating diffusion models for offline behavior cloning in autonomous driving scenarios. In 2025 Brazilian Conference on Robotics (CROS), volume 1, pages 1–6. IEEE.
Olsson, H., Åström, K. J., Canudas de Wit, C., Gäfvert, M., and Lischinsky, P. (1998). Friction models and friction compensation. European Journal of Control, 4(3):176–195.
Rubinstein, R. Y. (1999). The cross-entropy method for combinatorial and continuous optimization. Methodology and Computing in Applied Probability, 1(2):127–190.
Song, J., Meng, C., and Ermon, S. (2021). Denoising diffusion implicit models. In International Conference on Learning Representations.
Williams, G., Drews, P., Goldfain, B., Rehg, J., and Theodorou, E. (2017). Information-theoretic model predictive control: Theory and applications to autonomous driving. In ICRA.
