Computation of Solution Spaces for Optimization-based Trajectory Planning

The nonlinearity of the vehicle dynamics and the non-convexity of collision avoidance constraints pose major challenges for optimization-based trajectory planning of automated vehicles. Current solutions to these challenges are either tailored to specific traffic scenarios, simplify the vehicle dynamics, are computationally demanding, or may get stuck in local minima. This work presents a novel approach to address the aforementioned shortcomings by identifying collision-free driving corridors that represent spatio-temporal constraints for motion planning using set-based reachability analysis. We derive a suitable formulation of collision avoidance constraints from driving corridors that can be integrated into arbitrary nonlinear programs as well as (successive) convexification procedures. When combining our approach with existing motion planning methods based on continuous optimization, trajectories can be planned in arbitrary traffic situations in a computationally efficient way. We demonstrate the efficacy of our approach using scenarios from the CommonRoad benchmark suite.