The first step to control the humanoid motion its own stabilization. To perform this stabilization, we pretend to implement a discrete LQR (Linear Quadratic Regulator), which implement a gain matrix in a control close loop. The control system will operate at a sampling rate that is limited by the frequency of communication between the controller (PC / matlab) and robot (real or virtual). In the first approach, we consider that the contact point between the feet and the floor is a rotational joint without sensors or actuators. Thus, the point of contact with the ground only has 1 DoF, to control the stability of the robot is required only the pitch signal from the IMU.

**Applied Methodology:**

In our approach we will identify the model like a 3 link suspended pendulum to achieved the dynamic of the real model (3 link inverted pendulum) rotating the poles (characteristic of the dynamic system). After to obtain the dynamic of the 3 link inverted pendulum, should be possible to implement a LQR to stabilise the system.

For more detailed information about the methodology to implement the LQR in a 3 link inverted pendulum from the suspended model, see the report here.

**Simulations and results:**

The simulations was implemented with a frame rate of 200Hz (0.005s).

In our approach we try to obtain the model through the MatLab Identification Toolbox (we use an ARX model) and with the classic dynamic rules.

The detailed information about the obtain data, the methods and first obtain models for the real robot and the EZPhisics, see the report here.