Some Applications of Biomimetics and Fractional Calculus in Control and Modeling of (Bio)robotic Systems

Rapid development of biological science and technologies will further improve the active applications of control engineering by advanced biomimetic and biologically inspired research. First of all, it has promoted a biologically inspired control synergy approach that allows the resolution of redundancy of a given robotized system. In particular, the actuator redundancy control problem has been stated and solved by using Pontryagin’s maximum principle, where control synergy was established at the coordination level. Besides, fractional calculus (FC), is a mathematical topic with more than 300 years old history, in recent years there have been extensive research activities related to applications of FC in many areas of science and engineering. Here, they are presented by the advanced algorithms of PID control based on FC, tuned by genetic algorithms, in the position control of robotic system with 3 DOFs driven by DC motors. Also, a chattering-free fractional \( PD^{\alpha } \) sliding-mode controller in the control of a given robotic system has been proposed and realized. The effectiveness of the proposed optimal fractional order controls are demonstrated by the given robot. Finally, it is shown that one can obtain analytical expressions for generalized forces of the magnetorheological damping elements of fractional order which are used for obtaining better model of (bio)robotic systems.

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