A model-based velocity controller for chaotization of flexible joint robot manipulators

Abstract

This article presents a model-based velocity controller able to induce a chaotic motion on n-degrees of freedom flexible joint robot manipulators. The proposed controller allows the velocity link vector of a robot manipulator to track an arbitrary, chaotic reference vector field. A rigorous theoretical analysis based on Lyapunov's theory is used to prove the asymptotic stability of the tracking error signals when using the proposed controller, which implies that a chaotic motion is induced to the robotic system. Experimental results are provided using a flexible joint robot manipulator of two degrees of freedom. Finally, by using Poincaré maps and Lyapunov exponents, it is shown that the behavior exhibited by the robot joint positions is chaotic.

Nonlinear Feedback Synthesis and Control of Periodic, Quasiperiodic, Chaotic and Hyper-Chaotic Oscillations in Mechanical Systems

“…Buscarino et al [43] have developed a chaotic electro-mechanical autonomous oscillator that can generate chaotic oscillation and experimentally verified it. Moreno-Valenzuela et al have proposed an adaptive neural network scheme [44] and a model-based velocity controller [45] to produce chaotic motion in a robotic manipulator and verified the results experimentally in a two degrees-of-freedom robot. Natiq et al [46] have reported a novel three-dimensional chaotic system with different characteristics, where the system can exhibit different kinds of chaotic attractors coexisting with different equilibrium states depending upon initial conditions and system parameters.…”

“…Wang et al [23] studied a four-dimensional hyperchaotic system by adding a nonlinear controller to the Lorenz chaotic system and found that the new system's behaviour could be convergent, divergent, periodic, chaotic and hyperchaotic depending upon the parameters selected. There are many applications of chaos; for example, secure communications [24], sonar sensors [25], motion planning for mobile robots [26], line spectra reduction of waterborne noise for underwater vehicles [27], washing machines, dishwashers, chaotic compaction, chaotic mixer and chaotic grinding [28], kerosene fan heater and air conditioners for air circulation [29], robotic manipulator [30], fluid mixing [31], random number generation [32], etc. Choi [33] proposed a chaotic oscillator that produces varieties of musical signals and can be used by musicians for musical performance and composing.…”

Saturated control without velocity measurements for planar robots with flexible joints

“…Table III contains the details of the system parameters. These values were taken from the Quanser 2 DOF serial flexible joint robot arm datasheet and from [9]. The experiments reported in Section III were carried out using the Matlab/Simulink interface, where…”

Dynamic Response and Chaotic Behavior of a Controllable Flexible Robot

“…Based on previous theoretical studies, Moysis et al [27] proposed an improved HyperJerk system, with a hyperbolic sine function as the only nonlinear term, and studied the path to chaos, antimonotonicity, crisis and coexistence attractors, etc. Miranda-Colorado et al [28] proposed a hybrid speed controller for flexible joint robots, which can induce chaotic motion on the manipulators of flexible joint robots with multiple degrees of freedom. Based on Lyapunov theory, the asymptotic stability of the tracking error signal is verified when the controller is used.…”