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-title:  "CROWS"
+title: CROWS <figure><img src="assets/front_figure.png" alt="ICON"width="20"></figure> 
 date:   2024-09-16 09:00:00 -0400
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   Conformalized Reachable Sets for Obstacle Avoidance With Spheres
@@ -84,6 +84,8 @@ Safe motion planning algorithms are necessary for deploying autonomous robots in
 
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 <!-- # Contributions -->
 To address this challenge, this paper proposes Conformalized Reachable Sets for Obstacle Avoidance With Spheres (CROWS), a neural network-based safety representation that can be efficiently integrated into a trajectory optimization algorithm. CROWS extends SPARROWS<sup>[1](https://roahmlab.github.io/sparrows/)</sup>  by learning an overapproximation of the swept volume (i.e. reachable set) of a serial robot manipulator that is composed entirely of spheres. Prior to planning, a neural network is trained to approximate the sphere-based reachable set. Then, CROWS applies conformal prediction to compute a confidence bound that provides a probabilistic safety guarantee. Finally, CROWS uses the conformalized reachable set and its learned gradient to solve an optimization problem to generate probabilistically-safe trajectories online.
 
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 # [Related Projects](#related-projects)
 
 * [Safe Planning for Articulated Robots Using Reachability-based Obstacle Avoidance With Spheres](https://roahmlab.github.io/sparrows/)