Safe Trajectory Tracking in Uncertain Environments

In the model predictive control formulations of trajectory tracking problems, infeasible reference trajectories and a priori unknown constraints can lead to cumbersome designs, aggressive tracking, and loss of recursive feasibility. This is the case, for example, in trajectory tracking applications for mobile systems in the presence of constraints that are not fully known a priori. In this article, we propose a new framework called model predictive flexible trajectory tracking control, which relaxes the trajectory tracking requirement. In addition, we accommodate recursive feasibility in the presence of a priori unknown constraints, which might render the reference trajectory infeasible. In the proposed framework, constraint satisfaction is guaranteed at all times while the reference trajectory is tracked as good as constraint satisfaction allows, thus simplifying the controller design and reducing possibly aggressive tracking behavior. The proposed framework is illustrated with three numerical examples.