Differentially Flat Model Predictive Trajectory Tracking for Mobile Robots

This work presents a model-predictive, trajectory-following strategy for mobile robot navigation. Given a path to be followed, a trajectory can be formed using numerous techniques ranging from interpolation to smoothing. A trajectory-tracking controller can then be employed. Smoothing the path over its entirety while considering vehicle motion constraints is computationally prohibitive while interpolation techniques may be insufficiently smooth to avoid undesirable transient effects when there are sharp changes in path direction. Thus, a model predictive control (MPC) technique is employed to smooth the trajectory for a small amount of time in front of the current position of the vehicle. The model used within the predictive controller is a differential flat representation of the robot dynamics. This enables quadratic programming techniques to be employed for the rapid creation of the nonlinear robot trajectory. The differentially flat state resulting from the MPC is passed to a trajectory tracking controller capable of tracking a differentially flat trajectory. Thus, the MPC essentially iteratively reshapes the trajectory to account for the motion constraints of the vehicle. Simulation examples are provided to demonstrate the ability of the receding horizon framework to respect vehicle dynamics while creating a reference trajectory that compensates for a non-smooth desired path.