Chaotic behaviors of an underactuated system in the trajectory tracking task

Abstract

This contribution presents some nonlinear behaviors of an underactuated mechanical system under the trajectory tracking task. Presented hovercraft model is fully controlled by the computed torque algorithm with the pseudoinverse operation and proportional-derivative feedback. General form of errors dynamic equation gives possibility to analyze their behavior. These errors present irregular behaviors because of the input force limitations. Positive values of highest Lyapunov exponent and Fourier spectrum shape prove chaotic behavior of the system.

Caster Car – underactuated ground vehicle with caster wheels

“…Full state control algorithm keeps All presented results of optimized selective control (Figures 8,10,14) give acceptable good results of position tracking and stable rotation errors with visible 360 degrees jumps. Results of optimized full state control (Figures 9,11,15) give stable behavior of position and rotation errors with more visible deviations. Final comparison of simulation results in terms of values of errors is presented in Table 3 (position error from the initial condition was neglected in calculations of 𝑒 𝑥 maximum).…”

“…Underactuation property limits the range of system accelerations, even with unbounded inputs [6]. As presented in [11] this type of underactuated system is vulnerable to chaotic behaviors in case of trajectory tracking with limited direction of input force. Traditional vehicles have front-driven and rotating wheels and rear fixedaxis wheels.…”