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@@ -18,7 +18,7 @@ favicon = false
 
 Whether learned, simulated, or analytical, approximations of a robot's dynamics can be inaccurate when encountering novel environments. Many approaches have been proposed to quantify the aleatoric uncertainty of such methods, i.e. uncertainty resulting from stochasticity, however these estimates alone are not enough to properly estimate the uncertainty of a model in a novel environment, where the actual dynamics can change. Such changes can induce epistemic uncertainty, i.e. uncertainty due to a lack of information/data. Accounting for *both* epistemic and aleatoric dynamics uncertainty in a theoretically-grounded way remains an open problem. We introduce **L**ocal **U**ncertainty **C**onformal **Ca**libration (LUCCa), a conformal prediction-based approach that calibrates the aleatoric uncertainty estimates provided by dynamics models to generate probabilistically-valid prediction regions of the system's state. We account for both epistemic and aleatoric uncertainty non-asymptotically, without strong assumptions about the form of the true dynamics or how it changes. The calibration is performed locally in the state-action space, leading to uncertainty estimates that are useful for planning. We validate our method by constructing probabilistically-safe plans for a double-integrator under significant changes in dynamics.
 
-{% figure(alt=["LUCCA Diagram"] src=["model_final.png"] dark_invert=[true]) %}
+{% figure(alt=["LUCCA Diagram"] src=["./model_final.png"] dark_invert=[true]) %}
 **Figure.** Schematic of Local Uncertainty Conformal Calibration (LUCCa). Starting from a calibrated prediction region `$\hat{\mathcal N}_{\tau, cal}$`, we propagate the state uncertainty by composing an approximate dynamics model `$\tilde f$` outputting predictive MVNs of the future state with local conformal calibration. We consider approximate dynamics where the input and output distributions are MVNs of the state, but otherwise do not restrict the structure of `$\tilde f$`.
 {% end %}
 
@@ -45,7 +45,7 @@ $$
 
 
 
-{% figure(alt=["Loewner Order Dynamics Propagation"] src=["loewner_order_diagram.png"] dark_invert=[true]) %}
+{% figure(alt=["Loewner Order Dynamics Propagation"] src=["./loewner_order_diagram.png"] dark_invert=[true]) %}
 **Figure.** Schematic of Local Uncertainty Conformal Calibration (LUCCa). Starting from a calibrated prediction region `$\hat{\mathcal N}_{\tau, cal}$`, we propagate the state uncertainty by composing an approximate dynamics model `$\tilde f$` outputting predictive MVNs of the future state with local conformal calibration. We consider approximate dynamics where the input and output distributions are MVNs of the state, but otherwise do not restrict the structure of `$\tilde f$`.
 {% end %}
 
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