Fuzzy control strategy for acrobots combining model-free and model-based control

Abstract

This paper describes a fuzzy control strategy for the control of an acrobot. The strategy combines model-free and model-based fuzzy control. The model-free fuzzy controller designed for the upswing ensures that the energy of the acrobot increases with each swing. The control law for the torque is derived directly from the energy of the acrobot. The model-based fuzzy controller, which is based on a Takagi-Sugeno fuzzy model for balancing, employs the concept of parallel distributed compensation. The stability of the fuzzy control system for balance control is guaranteed by a common symmetric positive matrix, which satisfies linear matrix inequalities and is found by a convex optimization technique.

New Results of Energy-Based Swing-up Control for a Rotational Pendulum

“…It has been widely used in control experiments to verify the effectiveness of various control design methods, see, e.g., [2]. It, together with the cart-pole system in [3], the Pendubot in [4], [5], the Acrobot in [6], [7], has been studied as one of typical examples of underactuated mechanical systems which have fewer actuators than the degrees of freedom.…”

Model-based fuzzy control application to a self-balancing two-wheeled inverted pendulum

“…For example, the Pendubot (see [2], [7] and [8]) and the trailers (see [15] and [17]). In other words, the fuzzy control has been widely and successfully applied to a lot of nonlinear control processes.…”

A small spiking neural network with LQR control applied to the acrobot

“…The area of acrobot swing-up control is quite advanced with many other existing successful techniques in addition to those mentioned previously, including sigmoid NN function approximation for reinforcement learning [4,20], evolving a non-feedback vector of torque values [12], a fuzzy controller used to increase the acrobot's energy [13], output zeroing based on angular momentum and rotation angle of center-of-mass [17]. Although the primary focus of this study is the application of SNNs as control models for complex robotic platforms, it has given some specific insights into the techniques which may be used to improve acrobot swing-up solutions.…”