Physics-Embedded Neural ODEs for Learning Antagonistic Pneumatic Artificial Muscle Dynamics

Soft pneumatic actuators offer inherent compliance and safe interaction but remain difficult to model and control because of their highly nonlinear, distributed dynamics. We present a control-oriented data-driven modeling and control framework that decomposes actuator behavior into a nonlinear static equilibrium model and a linear residual dynamics model identified using Extended Dynamic Mode Decomposition with control (EDMDc). This representation enables feedforward compensation, task-space feedback control, and local closed-loop stability analysis through an augmented linear model. Experiments achieve approximately 1 mm root mean square error (RMSE) during low-speed (approximately 10 mm/s) trajectory tracking and below 10 mm RMSE at higher speeds (approximately 100 mm/s). The framework further achieves stable tracking of highly dynamic user-generated references with peak accelerations exceeding 25 m/s^2 while simultaneously performing real-time obstacle avoidance. Finally, the proposed stability analysis is experimentally validated by accurately predicting stable, marginal, and unstable operating regimes. These results demonstrate that structured, control-oriented learning provides an accurate and practical framework for soft actuator control.

Hybrid manipulators combine motorized rigid joints with pressure-actuated origami segments. Published arms of this kind are controlled with decoupled per-DOF loops, and the cost of this approximation has not been quantified, because the coupled model needed to measure it has not been built. This paper derives such a model for a chain of $N$ alternating revolute joints and Kresling origami segments, including pneumatic chamber dynamics and crease hysteresis. Using the model, we measure the coupling directly and show that its strength varies joint by joint, and that decoupled control loses precisely on the strongly coupled joints while remaining competitive on the one nearly decoupled joint. Coupled model-based controllers track $2.5\times$ tighter than a decoupled PID baseline at lower torque. However, the model predictive controller (MPC) is too slow for real time, and model-free reinforcement learning stalls far below acceptable success rates on a strict settling metric. We therefore distill the MPC into a small neural policy with behavior cloning and DAgger. The distilled policy settles 93-94$\%$ of goals with zero collisions, within a few points of its teacher, and runs inside the 5 ms control step where the MPC does not. Where the teacher itself fails, we trace the failure to a limit cycle with the bellows' lightly damped mode, and we remove it by selecting goal postures holdable at low pressure.

Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons. We propose MPINeuralODE, which combines a soft physics-informed residual with a Multiple-Initial-Condition (MIC) multiple-shooting curriculum whose ingredients are structurally complementary: the physics term anchors the vector-field magnitude on the support that MIC enlarges. We evaluate along three axes: out-of-sample error, long-horizon stability, and Hamiltonian drift, which together expose whether the learned dynamics recover the underlying vector field. On Lotka-Volterra, MPINeuralODE achieves the lowest out-of-sample and long-horizon MSE among data-driven methods, with a 24% reduction over the baseline Neural ODE, while essentially matching the PINN ablation on Hamiltonian drift.