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

## TL;DR

This paper introduces a trajectory parametrization method for model predictive control in robotics that reduces computational complexity, enables warm-starting, and guarantees stability in certain cases, making it suitable for resource-limited systems.

## Contribution

The proposed parametrization approach simplifies MPC problems, preserves warm-starting, and provides stability guarantees without extra terminal constraints in linear systems.

## Key findings

- Reduces decision variables in MPC problems.
- Enables effective warm-starting of optimization.
- Provides stability guarantees for linear systems.

## Abstract

This article 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 recursive feasibility guarantees without additional terminal set constraints. Due to the fact that the number of decision variables are greatly reduced through the parametrization, while the warm-starting capabilities are preserved, the approach is suitable for applications where the available computational resources (memory and CPU-power) are limited.