Robust Control of a Reduced Humanoid Robot Model using Genetic Algorithms and Fractional Calculus

There is an open discussion between those who defend mass distributed models for humanoid robots, and those on favor of simple concentrated models. Even though each of them have its advantages and disadvantages, little research have been conducted analyzing the control performance due to the mismatch between the model and the real robot, and how the simplifications affect the controller’s output. In this paper we address this problem by combining a reduced model of the humanoid robot, which has an easier mathematical formulation and implementation, with a fractional order controller, which is robust to changes in the model parameters. This controller is a generalization of the well-known PID structure obtained from the application of Fractional Calculus to control, as will be discussed in the paper. With this strategy we cancel the main disadvantage of the reduced model, which is the assumption that the robot has a simple mass distribution, and benefit from the robustness of the fractional order controller, which tolerates a less precise model. We model and identify the humanoid robot as a triple inverted pendulum and, using a gain scheduling strategy, we compare the performance of a classical PID with a fractional order controller, tuning the controller parameters with a genetic algorithm.