Walking stability control system on humanoid when turning based on LQR method

When a humanoid robot turns, the centre of mass of the robot moves with its body. This rotation causes an unwanted moment on the sole and causes the robot to become unbalanced. If the projection of the centre of mass on the foot of the humanoid robot moves beyond the supporting leg's limit, then that moment can cause the robot to fall. Therefore, we need a control system to optimize the movement of the centre of mass in a humanoid robot. In this study, we use the Linear Quadratic Regulator (LQR) method to handle this. The inverted-pendulum mathematical model is used as a control system response approach to the robot. The position of the centre of mass of the robot is obtained by reading the position of 12 servos on foot and using forward-kinematics. The current position of the centre of mass of the robot is corrected by the desired centre of mass resulting from the walking pattern. The results of these corrections serve as input controls to stabilize the robot. The result of the control is the torque which must be produced by the robot actuator. The torque is converted to the angle and angular velocity of the pitch and roll on the robot's ankle. Inverse kinematics is used to calculate the angle of each foot servo and make the walking motion according to the walking pattern (both straight and turning). The results showed humanoid robots when turning can reduce overshoot in the system and speed up the system response time compared to the system response without LQR control.