Towards Robustification of Incremental Model Predictive Control Deploying an Adaptive Tube Technique

Abstract:
In this paper, we propose an adaptive tube-based incremental model predictive controller (TIMPC) for a robot manipulator. First, a nominal incremental model predictive controller (IMPC) is designed. The continuous-time nonlinear system model is reconstructed as an incremental system using the time-delay estimation (TDE) methodology. It eliminates the need for an explicit mathematical model. The nominal IMPC is developed based on this approximated incremental system neglecting the discretization and TDE errors, which result in constraint violations. To enhance robustness against these errors, we introduce a tube-based MPC scheme, where a robust add-on term is designed, and constraints are tightened by the minimal robust positive invariant (mRPI) set. Various mRPI sets are calculated offline according to different disturbance bound levels. Then, an adaptive set is employed to adjust the disturbance bound level in the proceeding. It avoids the conservativeness of using one general set while avoiding the complicated online set computation. The proposed adaptive TIMPC is evaluated through real-time experiments on a 3-DoF robot manipulator, demonstrating its effectiveness in terms of tracking performance and ensuring state constraints satisfaction.