Many physical AI tasks require sequential implicit computation: at each step, boundary controls are applied, and the resulting configuration is obtained by solving an equilibrium problem. This setting arises naturally in deformable object manipulation, where even bending a deformable linear object (DLO) to a target shape can be nonlinear and multistable: identical boundary conditions may produce different configurations depending on actuation history. Unlike explicit transition models, the control-to-configuration relation is implicit and history-dependent, making long-horizon learning and control brittle; backpropagating through iterative solves is also memory- and compute-intensive. We propose Neural Control, a boundary-control framework that propagates gradients through branch-dependent sequences of equilibrium solves rather than a single fixed point. Neural Control computes trajectory-dependent proxy gradients by differentiating equilibrium conditions with an adjoint formulation, avoiding solver unrolling while keeping forward rollouts on converged equilibria. Combined with receding-horizon continuation, Neural Control re-anchors optimization to realized equilibria and mitigates basin switching. We validate Neural Control on simulated and real DLO manipulation, compare against SPSA and iCEM, and demonstrate applicability to a learned DEQ-style implicit equilibrium model.
The manipulation of Deformable Linear Objects (DLOs) such as cables poses a significant challenge for automation due to their infinite degrees of freedom and non-linear dynamics. In this paper we present a machine learning based optimal control approach for the manipulation of DLOs. This approach is divided into two main components: modeling and control. For modeling the dynamics of the DLO, we propose a learning based approach using a bidirectional Long Short-Term Memory (biLSTM) network. The biLSTM network is trained on synthetic data generated by the MuJoCo physics engine. For manipulating the DLO, a model predictive control strategy that employs Model Predictive Path Integral (MPPI) control is selected. The proposed approach is evaluated through simulation and experiments. The results demonstrate the effectiveness of the proposed method in achieving accurate and efficient manipulation of DLOs.
We present a neuro-inspired framework for embodied planning and control. Building on three principles that enable fast and highly effective goal-directed behavior in the mammalian brain - paired forward/inverse internal models, open-loop multi-step motor commands, and sequential, hierarchical organization of action - our Inverter framework uses learned components, trained end-to-end through Inverse Learning (IL) and supplemented where natural by analytic or algorithmic modules; we formalize IL and delineate it from supervised, reinforcement, and imitation learning. IL bridges Reinforcement Learning (RL)-style amortization, which runs in a single forward pass but emits only one action at a time, and Optimal Control (OC)-style sequence planning over whole trajectories, but with iterative test-time computation. Single Inverters or hierarchical n=2 Inverter stacks match or improve on offline-RL and diffusion-planner baselines on all 3 maze2d and 6 antmaze D4RL variants by an average of +24.2% (range -1.9% to +78.2%), at one-to-two orders of magnitude less inference compute time. Distinctively, optimizing through the Forward Model (FoM) over the entire T-step action sequence - rather than per step - lets Inverters produce smooth, goal-coherent, trajectory-wide structure and reach control policies closer to the analytic optimum than the policy underlying the training data itself. We also identify a failure mode of IL: FoM hacking under narrow training-data coverage, which we mitigate by using random training data with broader coverage. As an application example, a Pulse Inverter synthesizes arbitrary single-qubit quantum gates with fidelity matching the standard iterative numerical baseline (GRAPE), at more than 1000x lower per-gate compute time. In summary, we conclude that IL enables a versatile class of world-interfaces, especially for latency- and resource-critical embodied AI.
We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function Vψ whose positive-definiteness follows from a Cholesky parameterization, a residual Soft Actor--Critic policy that adds bounded torque corrections to the analytic baseline, and a physics-informed neural network that estimates unmodeled dynamics. A closed-form safety filter, derived from the single affine constraint V˙ψ+αVψ≤0, projects every policy output onto the safe set without requiring an online QP solver. We prove: global feasibility of the filter under a drift-decay condition on the control-degeneracy set; exponential stability under exact shielding, with a robust extension whose margin depends on the PINN approximation error; almost-sure convergence of the three-timescale policy--certificate--multiplier updates to a KKT point; and a PAC generalization bound for the certificate over compacts. On a 2-DOF manipulator with nonlinear friction and variable payload, the learned certificate accounts for most of the empirical gain: tracking error drops by 41% on nominal friction and 24% on aggressive friction at the centroid of the training distribution. A 7-DOF scalability study on a Franka Emika Panda confirms clean convergence of the full pipeline at industrial scale, identifies the conditions under which gains over exact model-based baselines should and should not be expected, and documents a warm-start pathology of the learned certificate that has practical implications for deployment.