Geometric optimization frameworks for safe, real-time trajectory generation

_{Written by Yuwei Wu, PhD Student in Electrical and Systems Engineering}

_{Caption for featured figure: Top: Iterative optimization of the polytopes, ellipsoids, and associated normals. Bottom: Deployment of a single polytope generation from sensor data over increasing temporal windows.}

For autonomous quadrotor flight in cluttered and unknown environments, a fundamental challenge is generating collision-free flight regions directly from onboard sensor data while meeting the stringent latency requirements of agile flight. Existing methods for convex free-space generation often perform substantial redundant computation by processing obstacle measurements that do not ultimately define the feasible region. As a result, they can become computational bottlenecks in high-speed replanning. Meanwhile, many learning-based end-to-end planning approaches lack explicit geometric safety guarantees.

Yuwei Wu, Dexter Ong, and Prof. Vijay Kumar at the University of Pennsylvania’s GRASP Laboratory, in collaboration with Yichen Zhao from IVALab at the Georgia Institute of Technology, developed geometric optimization frameworks for safe, real-time trajectory generation that preserve the formal safety guarantees of optimization-based planning while significantly improving computational efficiency. The resulting work, “STAR-Filter: Efficient Convex Free-Space Approximation via Starshaped Set Filtering in Noisy Environments,” was accepted to the 17th World Symposium on the Algorithmic Foundations of Robotics (WAFR) 2026.

The generation of collision-free spaces can be formulated as an iterative optimization of the shape and placement of these convex regions. Building on this foundation, they introduce STAR-Filter, a lightweight geometric filtering framework that identifies the subset of obstacle measurements that actively constrain the local free-space approximation. By eliminating irrelevant obstacle points before convex region construction, STAR-Filter significantly reduces computational overhead while maintaining robustness to noisy onboard sensing and preserving geometric safety guarantees.

This work contributes to the state of the art in onboard motion planning by enabling faster, more scalable, and more reliable generation of safe flight corridors for aggressive quadrotor flight in cluttered environments.

The full technical details are available in the original paper: https://arxiv.org/pdf/2604.26626