Vehicle Motion Planning With Joint Cartesian-Frenet MPC

The Frenet frame is commonly used in motion planning for its superiority of reshaping nonconvex curving boundaries and decoupling lateral and longitudinal behaviors. Nevertheless, such frame is not friendly for describing vehicle-related characteristics such as body shape and classical dynamic models. By contrast, the Cartesian frame facilitates straightforward modeling of vehicle dynamics, but confronts nonconvex constraints on curving lanes. For purpose of combining the complementary superiority of both frames, this letter proposes a joint Cartesian-Frenet MPC planning method based on a locally linear intermediary connection which is updated along with solving iterations. The augmented Cartesian-Frenet state space is constrained by a Cartesian vehicle control model that stands for tracking feasibility, a set of Frenet road constraints that account for driving safety, and a Cartesian-Frenet transformation that connects both frames. The final optimization is solved iteratively, where each iteration formulates into a quadratic programming problem with help of the apriori trajectory solved by the previous iteration. A comparative simulation and a 5-month-long real-vehicle test prove that the proposed method can produce a feasible and smooth trajectory within a safe area efficiently in complex real-world scenarios.