Challenges of Trajectory Planning with Integrator Models on Curved Roads

Abstract In the context of trajectory planning for autonomous vehicles, a widely used vehicle model relies on linear integrator dynamics. We consider planning with this model type, with a focus on the requirement to account for curved road topologies. As our analysis reveals, this generally gives rise to non-convex, coupled constraints on the vehicle’s states and inputs, which impedes computationally efficient planning. We propose a method to resolve this issue by modification of the non-convex constraints. This modification is based on inner approximations of sub-level sets of nonlinear functions, which are obtained by quantifier elimination. The efficacy of the method is demonstrated in two example scenarios.