# Gait Generation using Intrinsically Stable MPC in the Presence of Persistent Disturbances

## TL;DR

This paper enhances an existing model predictive control method for humanoid robots to maintain balance despite persistent disturbances by incorporating a disturbance observer into the control framework.

## Contribution

It introduces a disturbance observer into the Intrinsically Stable MPC to handle persistent disturbances, ensuring stability and balance in humanoid gait generation.

## Key findings

- Validated through MATLAB simulations with LIP model
- Demonstrated in dynamic simulations of NAO humanoid in DART
- Achieved improved balance robustness under disturbances

## Abstract

Maintaining balance while walking is not a simple task for a humanoid robot because of its complex dynamics. The presence of a persistent disturbance makes this task even more challenging, as it can cause a loss of balance and ultimately lead the the robot to a fall. In this paper, we extend our previously proposed Intrinsically Stable MPC (IS-MPC), which guarantees boundedness of the CoM with respect to the ZMP, to the case of persistent disturbances. This is achieved by designing a disturbance observer whose estimate is used to compute a modified stability constraint included in the QP problem formulation. The method is validated by MATLAB simulations for the LIP as well as dynamic simulations for a NAO humanoid in DART.