Oscillation preventing closed-loop controllers via genetic algorithm for biped walking on flat and inclined surfaces

In this study, a closed-loop controller is designed to overcome the dynamical insufficiency of the 3D Linear Inverted Pendulum Model (LIPM) via the Genetic Algorithm (GA). The main idea is to still use the 3D LIPM with a closed-loop controller because of its ease at modeling. While suppressing the dynamical flaws only the legs are used, in other words a robot is used which does not have any upper body elements to have a more modular robot. For this purpose, a biped is modeled with the 3D LIPM which is one of the most famous modeling methods of humanoid robots for the ease of modeling and fast calculations during the trajectory planning. After obtaining the simple model, Model Predictive Control (MPC) is applied to the 3D LIPM to find the reference trajectories for the biped while satisfying the Zero Moment Point (ZMP) criteria. The found reference trajectories applied to the full dynamical model on Matlab Simulink and the real biped in the laboratory at Istanbul Technical University. From the simulation results on the flat and inclined surfaces and real-time experiments on a flat surface some dynamical flaws are observed due to the simple modeling. To overcome these flaws a Proportional-Integral (PI) controller is designed, and the optimal value of the controller gains are found by the GA. The results assert that the designed controller can overcome the observed flaws and makes biped move more stable, smoother, and move without steady-state error.