Conformalized Reachable Sets for Obstacle Avoidance With Spheres

Safe motion planning algorithms are necessary for deploying autonomous robots in unstructured environments. Motion plans must be safe to ensure that the robot does not harm humans or damage any nearby objects. Generating these motion plans in real-time is also important to ensure that the robot can adapt to sudden changes in its environment. Many trajectory optimization methods introduce heuristics that balance safety and real-time performance, potentially increasing the risk of the robot colliding with its environment. This paper addresses this challenge by proposing Conformalized Reachable Sets for Obstacle Avoidance With Spheres (CROWS). CROWS is a novel real-time, receding-horizon trajectory planner that generates probalistically-safe motion plans. Offline, CROWS learns a novel neural network-based representation of a spherebased reachable set that overapproximates the swept volume of the robot’s motion. CROWS then uses conformal prediction to compute a confidence bound that provides a probabilistic safety guarantee on the learned reachable set. At runtime, CROWS performs trajectory optimization to select a trajectory that is probabilstically-guaranteed to be collision-free. We demonstrate that CROWS outperforms a variety of state-of-the-art methods in solving challenging motion planning tasks in cluttered environments while remaining collision-free.

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 SPARROWS1 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.

For citation, please refer to

(Kwon et al., 2024)