added all videos

Author: luis-marques

content/_index.md

@@ -33,49 +33,100 @@ In this work, we rigorously analyze configuration errors using Lie Groups, exten
 
 <div class="figure-column">
 
-{{ figure(alt=["CLAPS Overview"] src=["./title_figure_manual.png"]) }}
-
+{% figure(alt=["CLAPS Overview"] src=["./title_figure_manual.png"]) %}
+**Figure.** Our proposed algorithm (**CLAPS**) constructs prediction regions `$\mathcal{C}^q$` (in C-Space) that are *marginally guaranteed* to contain the next *unknown system configuration* at a user-set probability `$(1-\alpha)$`. By considering the robot's symmetry, we can construct more *efficient* prediction regions.
+{% end %}
 </div>
 
 </div>
 
 # Problem Statement
 
-**Problem.** Given an approximation `$\tilde f$` of the system's *unknown* stochastic dynamics `$f$`, a goal region `$\mathcal G \subseteq \mathcal S$`, a safe set `$\mathscr C \subseteq \mathcal S$`, a calibration dataset of state transitions `$D_{cal}$` and an acceptable failure-rate `$\alpha \in (0,1)$`, we aim to recursively solve the following stochastic optimization problem with planning horizon `$H \in \mathbb N$`:
-```
-$$
-\begin{alignat}{3}
-&\!\min_{(u_{t},\ldots,u_{t+H-1})}        &\qquad& J(s, u, \mathcal G)\\
-&\text{subject to} &      & Y_{\tau} \sim f(\bar{X}_\tau),\quad & \forall\tau\in\{t, \ldots, t+H-1\}\\
-&               &  & \mathbb P(Y_{\tau} \in \mathscr C) \ge (1-\alpha),\quad & \forall\tau \in \{t,\ldots, t+H-1\} \\
-&               &  & u_{\tau} \in \mathcal U, s_{\tau+1} \in \mathcal S, \quad &\forall\tau\in\{t, \ldots, t+H-1\}
-\end{alignat}
-$$
-```
-&emsp; *Dynamics, (2)*: The real system evolves following the unknown stochastic dynamics `$f$`. We only have access to an approximation `$\tilde f$` and the inference transitions in `$D_{cal}$`.<br>
-&emsp; *Safety, (3)*: Our trajectory should remain probabilistically safe, which we define as requiring it to lie within a safe set `$\mathscr C$` with at least a user-specified probability. This is difficult to guarantee in general for any `$f$` and `$\tilde f$`, since our approximation can be arbitrarily wrong in deployment conditions. <br>
-&emsp;*State and Control Admissibility, (4)*: Both the control inputs and the states must belong to pre-defined sets. <br>
-&emsp;*Objective Function, (1)*: Additionally, we aim to achieve optimality relative to an objective that incorporates `$\mathcal G$` along with the state and control sequences, `$s := (s_{t+1},\ldots, s_{t+H})$` and `$u := (u_{t},\ldots,u_{t+H-1})$`. For example, `$J$` might minimize the expectation of a distance metric to `$\mathcal G$`, control effort, or epistemic-uncertainty along the state-control sequences.
+**Problem.** TBD - sumamrize key assumpt, goals, ...
 
 # CLAPS
 
-Given a dynamics predictor and a small calibration dataset, LUCCa provides probabilistically valid prediction regions for the robot's future states accounting for both aleatoric and epistemic uncertainty. We prove its validity for any finite set of calibration data, predictors outputting a multivariate normal uncertainty, any unknown true dynamics function, and uncharacterized aleatoric perturbations. LUCCa calibrates the uncertainty locally relative to the system's state-action space, leading to prediction regions that are representative of predictive uncertainty and therefore useful for planning. For the first planning step, LUCCa satisfies the safety condition (3) above. For subsequent planning steps, such a guarantee becomes more complex but we show that if the dynamics approximation is linear (actual dynamics are still unconstrained) and we can satisfy additional assumptions on the controller, then LUCCa can satisfy the safety condition (3) for all planning steps (see Appendix `$A$` for a discussion and the proof).
-
+TBD - explain method, include algorithm blocks
 
 {% figure(alt=["CLAPS Method Diagram"] src=["./method_diagram3v2.png"] dark_invert=[true]) %}
 **Figure.** **C**onformal **L**ie-Group **A**ction **P**rediction **S**ets (Offline) A dataset of state transitions is used jointly with an approximate dynamical model to derive a rigorous symmetry-aware probabilistic error bound on the configuration predictions. During deployment, our algorithm takes in a desired action `$u_{des}$` and computes a *calibrated C-Space prediction region* `$\mathcal{C}^q$` that is marginally guaranteed to contain the true configuration resulting from executing `$u_{des}$`.
 {% end %}
 
-
-# C-Space Visualizations
-
-Configuration space (C-space) representations are fundamental to understanding robot motion planning. These visualizations show how the robot's configuration space changes under different scenarios.
-
-{{ figure(src = ["./cspace_videos/Isaac_Jetbot_over_confident_0300_3D_rotation.mp4", "./cspace_videos/Isaac_Jetbot_over_confident_0301_3D_rotation.mp4"], alt = ["C-space visualization - scenario 0300", "C-space visualization - scenario 0301"], dark_background=[true]) }}
-
-# Robot Demonstrations
-
-{{ figure(alt=["LUCCa in Action", "Baseline Comparison"] src=["./mbot_videos/mbot_clip1.mp4", "./mbot_videos/mbot_clip2.mp4"] subcaption=["**LUCCa in Action** - Robot navigating with calibrated uncertainty estimates", "**Baseline Comparison** - Traditional approach without conformal calibration"]) }}
+# Experiments
+TBD - explain
+
+## JetBot Experiments (Simulation)
+
+put table, explain c-space below
+
+{{ figure(src = ["./cspace_videos/Isaac_Jetbot_over_confident_0300_3D_rotation.mp4", "./cspace_videos/Isaac_Jetbot_over_confident_0330_3D_rotation.mp4","./cspace_videos/Isaac_Jetbot_over_confident_0336_3D_rotation.mp4"], alt = ["C-space visualization - scenario 0300", "C-space visualization - scenario 0301"], dark_background=[true]) }}
+
+## MBot Experiments (Hardware)
+
+epxlain
+
+{{ figure(alt=["LUCCa in Action", "Baseline Comparison"] src=["./mbot_videos/mbot_clip1.mp4", "./mbot_videos/mbot_clip2.mp4", "./mbot_videos/mbot_clip3.mp4"] subcaption=["**LUCCa in Action** - Robot navigating with calibrated uncertainty estimates", "**Baseline Comparison** - Traditional approach without conformal calibration"]) }}
+
+explain
+
+put runtime in words.
+
+<figure class="single-video-figure">
+    <div class="single-video-wrapper">
+        <iframe
+            src="https://www.youtube.com/embed/hyddmrzfx7Y"
+            title="MBot Hardware Demonstration"
+            frameborder="0"
+            allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share"
+            allowfullscreen>
+        </iframe>
+    </div>
+</figure>
+
+<style>
+.single-video-figure {
+    max-width: 1000px;
+    margin: 2rem auto;
+    display: flex;
+    flex-direction: column;
+    align-items: center;
+}
+
+.single-video-wrapper {
+    position: relative;
+    width: 100%;
+    height: 0;
+    padding-bottom: 56.25%; /* 16:9 aspect ratio */
+    border: 2px solid #e9ecef;
+    box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
+    overflow: hidden;
+}
+
+.single-video-wrapper iframe {
+    position: absolute;
+    top: 0;
+    left: 0;
+    width: 100%;
+    height: 100%;
+}
+
+.single-video-figure figcaption {
+    padding: 1rem;
+    background: #f8f9fa;
+    border-top: 1px solid #e9ecef;
+    text-align: center;
+    font-size: 0.9rem;
+    line-height: 1.4;
+    width: 100%;
+    max-width: 1000px;
+}
+
+@media screen and (max-width: 768px) {
+    .single-video-figure {
+        margin: 1rem auto;
+    }
+}
+</style>
 
 # BibTeX <small><small>(cite this!)</small></small>