On nonlinear dynamics and control of a robotic arm with chaos

Abstract

In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC) and the optimal linear feedback control (OLFC). The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC) is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC) involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.