# A Fast and Stable Omnidirectional Walking Engine for the Nao Humanoid Robot

## TL;DR

This paper introduces a fast, stable, and parametric omnidirectional walking engine for the Nao humanoid robot, utilizing an abstract dynamics model and LQG control, validated through simulations achieving high walking speeds.

## Contribution

It presents a novel framework combining an abstract dynamics model with an LQG controller and optimization for parametric tuning, enhancing walking speed and stability.

## Key findings

- Achieved 80.5cm/s maximum forward velocity.
- Framework provides fast and reliable omnidirectional walking.
- Validated effectiveness through RoboCup simulation experiments.

## Abstract

This paper proposes a framework designed to generate a closed-loop walking engine for a humanoid robot. In particular, the core of this framework is an abstract dynamics model which is composed of two masses that represent the lower and the upper body of a humanoid robot. Moreover, according to the proposed dynamics model, the low-level controller is formulated as a Linear-Quadratic-Gaussian (LQG) controller that is able to robustly track the desired trajectories. Besides, this framework is fully parametric which allows using an optimization algorithm to find the optimum parameters. To examine the performance of the proposed framework, a set of simulation using a simulated Nao robot in the RoboCup 3D simulation environment has been carried out. Simulation results show that the proposed framework is capable of providing fast and reliable omnidirectional walking. After optimizing the parameters using genetic algorithm (GA), the maximum forward walking velocity that we have achieved was $80.5cm/s$.