Explicit Tracking Nonlinear MPC with Obstacle Avoidance Features^*

This work proposes a finite-horizon optimal control approach for set-point tracking using an Explicit Nonlinear Model Predictive Control (ENMPC) framework with integrated obstacle avoidance. A partitioning method is employed to evaluate the feasibility domain in the presence of obstacles. An approximate nonlinear multiparametric programming algorithm provides solutions as piecewise linear functions of the parameters, enabling efficient online implementation via piecewise linear state feedback without real-time optimization. Obstacle avoidance is ensured through control barrier functions and artificial variables, maintaining feasibility under varying references. A numerical example demonstrates the method on a differential mobile robot that tracks a reference while avoiding obstacles in its admissible space.