Constraint Shield for Learned Interaction Dynamics

1. Integration point: use a neural policy $\pi_\phi(o_t)$ to generate a desired action sequence or nominal first action, and place a differentiable or sampling-based MPC safety layer after it. The learned model must predict both task output and safety quantity, such as contact force, torque, temperature, collision margin, or constraint residual. 2. Pseudocode: initialize $s_0$ from the observer; generate $u^{\mathrm{nom}}_{t:t+H-1}$ by rolling out the policy; roll out $F_\theta$ for candidate sequences; solve the nonlinear or quadratic program minimizing tracking error plus $\alpha\|u-u^{\mathrm{nom}}\|^2$ under $\hat F_i\le F_{\mathrm{safe}}-m$ and actuator/state bounds; execute only $u_t$; observe the next state and repeat. Calibrate margin $m$ from a validation-set upper quantile of prediction error. Include constraint-active trajectories during training so the force head is accurate near the boundary. 3. Computed versus estimated: the hard constraint structure comes from the paper; $F_\theta$, $h_\theta$, uncertainty margin $m$, and policy are learned or calibrated. 4. First cheap experiment: use a one-dimensional mass-spring or MuJoCo point-mass pushing task with an unknown stiff wall, train an MLP policy and neural one-step force predictor, then compare the policy alone with horizon-$H=10$ projected MPC. Sweep target speed and wall stiffness. The predicted signature is a sharp crossing for the unconstrained controller when predicted force equals $F_{\mathrm{safe}}$, while the shielded controller's measured violation rate remains below 1% with margin $m$ until infeasibility. Tracking error should show a kink when the constraint becomes active.