Four-Bar Mechanism's Proportional-Derivative and Neural Adaptive Control for the Thorax of the Micromechanical Flying Insects

The paper focuses on the dynamics and control of the nondeformable and deformable four-bar mechanism (three of the bars are mobile and one is fixed), this being a subsystem of the micromechanical flying insects' (MFIs) thorax. The control of the mechanism (six-order system described by Lagrange equations) is initially achieved by using a proportional-derivative (PD) control law, a Newton-Raphson type algorithm, and the Lyapunov theory. Because the thorax's dynamics is strongly nonlinear and is characterized by fast time varying coefficients, the PD control law cannot always guarantee small overshoot and angular rates; to overcome this drawback, over the control law PD component we superpose a neural adaptive component which compensate the error of the global nonlinearity's approximation associated to the thorax's dynamics. The two obtained control systems are validated by complex numerical simulations.