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Intelligent Control for Underactuated Robot Based on Optimization Technic

Abstract

This study aims to understand the complexity and control balancing in the upright position of a three-link underactuated robot system. The Robogymnast is one of the important types of three-link systems mimicking human acrobatics; it composes three joints and three links (arm, torso, and leg, respectively) powered by two geared DC motors.
A mathematical model for the robot derived using Euler-Lagrange equations. Since the system is a nonlinear multi-link mechanism requiring a complex mathematical model considering information accuracy. It presents more challenges modeling the Robogymnast and dealing with control motion problems. The Euler-Lagrange formula and Artificial Neural Network (ANN) model are used to model the nonlinear Robogymnast system. The comparison results show that the dynamic model obtained by the ANN is significantly better than the model derived from the Euler-Lagrange formula because the ANN model accepted the initial deviation of absolute angle for each link up to 3 degrees. In contrast, the dynamic model derived from the Euler-Lagrange formula accepted 1 degree and becomes unstable at 3 degrees.

Firstly, a Discrete Linear Quadratic Regulator (DLQR) controller is used to balance the gymnastic robot in the upright position. The construction of DLQR depends on the selection of the weight matrices.
Secondly, to find optimum values of the weighting matrices; a swarm optimization technique called Whale Optimization Algorithm (WOA) is applied to adjust the weighting matrices. As well as, another optimization technique is used to find the optimum values of weighing matrices, this technique is called Aquila Optimization (AO). The evaluation of the best technique has been implemented. The WOA-based DLQR controller achieves the best result according to the transient response of the relative angles but consumes higher voltage from the two motors compared to the AO-based DLQR controller. The first, second, and third links reached a steady state after 1.825 seconds with a minimum deviation (-0.5° and -1.5° for the first and second links, respectively, and no deviation for the third link). Moreover, the control voltage of the first motor consumed 7.12V, and the second motor consumed 2V to achieve the desired response, which is less than the limited voltage (12V).
Thirdly, a Fuzzy Logic Controller (FLC) was designed to achieve online tuning to stabilize and balance the system. The result of the FLC showed that the system consumed more settling time than WOA-based DLQR to be stable in an inverted position. Therefore, a hybrid controller combining FLC with WOA-based DLQR was proposed to achieve online tuning with less settling time for the relative angular position (1.5 seconds) and acceptable deviation of the links from the upright balancing point (-1.15° and -3.4° for the first and second links respectively, and no deviation for the third link). The first motor consumed 6.7 volts of control effort, but the second motor consumed only -1.5 volts; this was considered satisfactory voltage to bring the Robogymnast to an inverted position and stabilize it in the upright balancing point within a suitable duration.
Finally, the comparison among the previous methods demonstrated that the hybrid system achieves online tuning with a satisfactory response to stabilize the gymnastic robot vertically. The comparison with previous research demonstrates that the FLC with the WOA-based DLQR method achieves the best transient response regarding overshoot, settling time, and less control effort than the other methods.