Distributed Trajectory Optimization and Fixed-Time Tracking Control of a Group of Connected Vehicles

This paper investigates a distributed trajectory optimization and trajectory tracking control problem for a collection of vehicles. A two-layered framework is established for distributed trajectory optimization and fixed-time tracking control. The trajectory optimization problem is solved using distributed convex optimization based on spacing errors minimization, resulting in an algorithm to provide the optimal trajectory for all following vehicles. The lower layer plays the role of tracking the designated trajectory and robustly guarantee zero steady-state spacing errors for the vehicular platoon. The controller is derived based on the tracking error system in the context of fixed-time stability and terminal sliding mode control theory. The methodology can guarantee the internal stability and string stability, as demonstrated by numerical simulations.