[2605.03288] Neural Control: Adjoint Learning Through Equilibrium Constraints
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Computer Science > Robotics
arXiv:2605.03288 (cs)
[Submitted on 5 May 2026]
Title:Neural Control: Adjoint Learning Through Equilibrium Constraints
Authors:Dezhong Tong, Jiawen Wang, Hengyi Zhou, Yinglong Shen, Xiaonan Huang, M. Khalid Jawed
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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.
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2605.03288 [cs.RO]
(or arXiv:2605.03288v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2605.03288
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arXiv-issued DOI via DataCite (pending registration)
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From: Dezhong Tong [view email] [v1] Tue, 5 May 2026 02:19:37 UTC (2,752 KB)
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