A Method for Reducing the Complexity of Model Predictive Control in Robotics Applications

This letter describes an approach for parametrizing input and state trajectories in model predictive control. The parametrization is designed to be invariant to time shifts, which enables warm-starting the successive optimization problems and reduces the computational complexity of the online optimization. It is shown that in certain cases (e.g., for linear time-invariant dynamics with input and state constraints) the parametrization leads to inherent stability and the recursive feasibility guarantees without additional terminal set constraints. Due to the fact that the number of decision variables are greatly reduced through the parametrization, the warm-starting capabilities are preserved, and the approach is suitable for applications where the available computational resources (memory and CPU-power) are limited.