Rigidity-Conditioned Active-Sensing Policy

Integrate this at the reward and auxiliary-loss interface of an actor-critic or PPO policy. The actor receives UAV positions, noisy target hypotheses or a particle set of target hypotheses, and recent measurements; it outputs headings or velocity commands. A differentiable simulator predicts the next positions and the corresponding range, bearing, or time-difference-of-arrival sensing graph. Construct one rigidity-matrix row for every selected sensor-target or sensor-sensor relation, compute the singular values with torch.linalg.svdvals, and add beta * log(sigma_r + epsilon) to the reward. If target uncertainty is represented by particles, compute the score for each particle and use the minimum or a soft minimum, -tau*logsumexp(-rho/tau), so the policy cannot exploit only one optimistic hypothesis. To reduce cost, use a fixed-size edge subset E_t containing longest-baseline, nearest, and highest-quality links; this is the pruning idea, while the full matrix is retained for evaluation. The paper-derived quantities are the rigidity construction and smallest-nonzero-singular-value criterion. Estimate empirically the gauge rank r, sensor noise, and reward coefficient beta; for a known 2-D localization setup, explicitly project out known translation and rotation nullspaces or calibrate r from noiseless configurations. First run a cheap experiment with 4--8 simulated UAVs, a moving target, range/bearing noise, and random initial target error. Compare PPO with task reward alone, PPO plus determinant/FIM reward, and PPO plus rigidity reward. Measure localization error, time to enter the 50 m radius, and the singular spectrum. The quantitative prediction is a sharp degradation boundary: episodes with rho(R_t) near zero should have substantially larger localization error, while conditioning improves monotonically as rho rises. With pruning, the rank and score should remain within 10--20% of the full matrix while SVD computation decreases roughly in proportion to the number of retained edges. Sweep policy actions to estimate the minimum score threshold rho_c at which the 80% success requirement is crossed; the rigidity method predicts this transition should be more stable under target-estimate bias than an FIM-only policy.