Neural Control

Abstract

Many physical AI tasks are governed by implicit equilibrium: an agent actuates a subset of degrees of freedom (boundary DoFs), while the remaining free DoFs settle by minimizing a total potential energy. Even seemingly basic tasks such as bending a deformable linear object (DLO) to a target shape can exhibit strongly nonlinear behavior due to multi-stability: the same boundary conditions may yield multiple equilibrium shapes depending on the actuation trajectory. However, learning and control in such systems is brittle because the actuation-to-configuration map is defined only implicitly, and naive backpropagation through iterative equilibrium solvers is memory- and compute-intensive. We propose Neural Control, a boundary-control framework that computes trajectory-dependent, memory-efficient proxy gradients by differentiating equilibrium conditions via an adjoint formulation, avoiding unrolling of solver iterations. To improve robustness over long horizons, we integrate these sensitivities into a receding-horizon MPC scheme that repeatedly re-anchors optimization to realized equilibria and mitigates basin-switching in multi-stable regimes. We evaluate Neural Control in simulation and on physical robots manipulating DLOs, and show improved performance over gradient-free baselines such as SPSA and CEM.

Experiment Results

Task 1 Any points to any points

Task 2 Midpoint trajectory following

Task 3 Final shape control

Reference

If you find our work useful, please cite:

@misc{tong2026neuralcontroladjointlearning,
      title={Neural Control: Adjoint Learning Through Equilibrium Constraints}, 
      author={Dezhong Tong and Jiawen Wang and Hengyi Zhou and Yinglong Shen and Xiaonan Huang and M. Khalid Jawed},
      year={2026},
      eprint={2605.03288},
      archivePrefix={arXiv},
      primaryClass={cs.RO},
      url={https://arxiv.org/abs/2605.03288}, 
}