Local Conformal Calibration of Dynamics Uncertainty from Semantic Images

Figure 2: Online component of OCULAR . Given an estimated Gaussian at time t , a desired action a_{t} , and observation o_{t} , we create an approximate next-step Gaussian \tilde{\mathcal{N}}_{t+1} via the approximate model \tilde{f} . The current-time information X_{i}^{raw} is processed, and the learned representation X_{i} passed to the Decision Tree. The resulting leaf node \mathcal{X}_{k} has an associated \hat{q}_{k} which is multiplied by a fixed constant to get \xi_{k} . The approximate uncertainty estimate is then calibrated by scaling its covariance by \xi_{k} and the output is passe

Figure 6: The three tested Isaac Sim environments (based off Rivermark).

Figure 1: Offline component of OCULAR . 1: o_{t} from D_{\mathrm{cal}}^{part} are projected into a planar footprint o^{\prime}_{t} by \varphi . A CAE is trained to reconstruct o^{\prime}_{t} , and the decoder is discarded. 2: All data in D_{\mathrm{cal}} is processed by process ( ) into a learned representation X_{i} , and nonconformity scores R_{i} are computed. 3: a Decision Tree is trained on D_{\mathrm{cal}}^{part} to partition the learned input space \mathcal{X} into regions of approximately constant score. 4: The holdout processed D_{\mathrm{cal}}^{CP} data is fed through the DTree and s

Figure 3: Rollouts in map U of the planar robot (see App. 0.D.1 for all maps). The NoCP gains too much momentum in the low-friction region, leading to collisions. SplitCP ’s single scaling factor makes all its sampled plans highly conservative and in collision, resulting in goal-chasing behavior. LUCCa and OCULAR have comparable performance, slowing down in high-uncertainty regions, and reaching both subgoals safely. Yet, LUCCa requires data specific to each tested map, while our method produces safe plans without any data from the executed environment.

Figure 4: Rollouts in icyMain of Isaac Sim experiment (see App. 0.D.2 for other maps). NoCP and SplitCP gain too much momentum over ice and collide. LUCCa and OCULAR both slow down when OOD, keeping next-state uncertainty manageable and reaching all subgoals without collisions. While LUCCa requires icyMain-specific data, our method plans without any data from icyMain.

Figure 5: Trajectories of OCULAR and baselines in the planar environment, across 30 runs for each map-method combo. The uncalibrated baseline gains too much momentum in the low-friction region, leading to collisions. SplitCP is too conservative, with all its sampled plans being in collision. This results in goal-chasing behavior and an inability to avoid obstacles. LUCCa and OCULAR have comparable performance, slowing down in high-uncertainty regions, and reaching both subgoals without colliding. However, LUCCa uses data specific to each tested map, while our method produces safe plans without