Parameter-Regression MPC (PaReMPC): Experiments and Extensions of a Broadly Adaptive Approach for SISO Robotic Applications

Model learning combined with model predictive control (MPC) can be an effective control approach for adapting to a wide range of unknown system dynamics or changes thereof. Specifically, we take a parameter regression approach to maximize the adaptation rate during control operation. Here we present this approach as Parameter Regression MPC (PaReMPC) with an N-integrator plant model and demonstrate the approach in two hardware experiments. First, in a loaded motor experiment, PaReMPC achieved high-fidelity tracking within 0.5 seconds, and second, stabilized a ball-balancing robot—both with poor initial parameters. However, this learn-as-you-go approach is inherently greedy and creates an unstable feedback loop with the controller, particularly when nonminimum phase zeros are present. In numerical experiments, we benchmark the ability of PaReMPC to adapt to a range of SISO LTI systems against scenario tree dual control methods (i.e., ST-SMPC) which infer probabilities of candidate modes. In addition, we combine PaReMPC with scenario trees to create a novel ST-PaReMPC approach. Our numerical simulations found that PaReMPC attains the lowest-cost performance in cases of low-noise or non-changing dynamics, but the novel ST-PaReMPC performs best with high noise and changing system dynamics.