GCS method for autonomous vehicle motion planning beats nonlinear control speed

Motion planning for autonomous vehicles typically pits high-fidelity nonlinear optimal control against faster but less accurate geometric methods. Now, researchers Matheus Wagner and Antônio Augusto Fröhlich from the Federal University of Santa Catarina demonstrate that optimization over Graphs of Convex Sets (GCS) can bridge this gap. Their approach divides free space into convex regions connected as a directed graph, handling nonconvex obstacles through discrete connectivity choices while keeping trajectory constraints convex within each region. Vehicle motion is modeled using Bézier curves for spatial paths and a polynomial time-scaling function, with a simplified dynamic bicycle model (small-slip, linear tires) that enforces dynamic feasibility through convex constraints on trajectory derivatives.

Tested on CommonRoad scenarios including static obstacle avoidance and lane changes, the GCS-based planner produced collision-free, dynamically consistent trajectories that closely matched those from a full nonlinear discrete-time optimal control solver. Crucially, the GCS method showed significantly lower computational cost and was far less sensitive to initial guesses—a practical advantage for real-time deployment. The paper's findings suggest GCS offers a structured convex approximation that captures dominant geometric and dynamic effects, making it a promising alternative for real-world autonomous driving systems where speed and reliability are paramount.