Self-Consistent Neural Control: Learning Trajectories for Implicit Equilibrium
Overview
This paper introduces Self-Consistent Neural Control (SCNC), a framework designed to optimize trajectories in physical systems defined by implicit equilibrium. The authors address limitations of adjoint learning, which relies on frozen-tangent approximations that neglect higher-order sensitivity terms. SCNC derives a mathematical bound on gradient error and uses a practical finite-difference approximation to control sensitivity variations. Validated on deformable objects ranging from elastic rods to thin-walled tubes and Slinky-like structures, SCNC demonstrates faster convergence, reduced switching to undesirable equilibrium branches, and a doubling of the stable optimization rate compared to adjoint learning (83.3% vs. 41.7%), with average loss reductions exceeding 1.5 orders of magnitude on complex systems like thin-walled tubes.
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“reducing switching to undesirable equilibrium branches, doubling the stable optimization rate over adjoint learning 83.3% vs. 41.7% and reducing the average loss by more than 1.5 orders of magnitude on thin-walled tubes, where sensitivity variations are pronounced.”
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- arXiv Robotics — research abstractsSignalSelf-Consistent Neural Control: Learning Trajectories for Implicit Equilibrium
This paper introduces Self-Consistent Neural Control (SCNC), a framework designed to optimize trajectories in physical systems defined by implicit equilibrium. The authors address limitations of adjoint learning, which relies on frozen-tangent approximations that neglect higher-order sensitivity terms. SCNC derives a mathematical bound on gradient error and uses a practical finite-difference approximation to control sensitivity variations. Validated on deformable objects ranging from elastic rods to thin-walled tubes and Slinky-like structures, SCNC demonstrates faster convergence, reduced switching to undesirable equilibrium branches, and a doubling of the stable optimization rate compared to adjoint learning (83.3% vs. 41.7%), with average loss reductions exceeding 1.5 orders of magnitude on complex systems like thin-walled tubes.
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