Adaptation and Probing Under Hidden Dynamics: Evidence from Planar Pushing

Information about hidden dynamics can improve manipulation. Whether a dedicated probe adds to what ordinary task interaction already reveals is a separate question. We study this question in a controlled Push-T variant with an unobserved effective support-friction coefficient that spans more than a decade. Using diffusion policies with a shared backbone and training data, we compare true-parameter access, online estimation from task histories, history conditioning and per-tier specialists, and we measure the room left for a probe as the paired difference between a controller that knows the parameter from its first action and the same controller estimating it along the way. On held-out initial states, true-parameter access improves success by 5.5 percentage points on the evaluated training tiers and by 35.0 points at μ = 2.00, above the training range; the gain appears as closer approaches to the goal at low friction and as completed episodes at high friction. An estimator trained on ordinary task histories locates the friction within 64 steps, and a policy fed its estimate recovers the success-rate gain within the training range (recovered fraction 1.02 [0.76, 1.35]) and 58% of it at μ = 2.00. Parameter-input interventions change the amplitude of the first commanded action chunk and the timing of contact, and an incorrect value impairs success more than masking the input. The controller with the true parameter and the controller with the online estimate differ by 0.1 success points on the training tiers, with an interval that includes zero. These results establish ordinary task interaction as a strong adaptation baseline, and they set the reference against which dedicated probing should be evaluated: a controller that adapts during execution.