This paper presents a set of basic problems concerning the control of an underactuated dynamic system. Exemplary system of a planar rigid body with a coupling input force is described. Lie brackets method is used to show accessibility of the system. A tracking problem is solved with computed torque algorithm. The coupling force makes the convergence to zero of all state variables errors impossible. After numerical simulation, stability of the system is mentioned.
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.
This article presents the construction of a prototype three-wheeled vehicle for people with disabilities, approved in the L2e category. The vehicle is equipped with a special tilt mechanism that allows people with disabilities, who cannot balance their body, to return to an upright position after completing a driving maneuver on a curve of the road. The tilt angle of the vehicle depends on its speed and steering angle. When designing the vehicle, the availability and price of spare parts for scooters and motorcycles were taken into account to make the vehicle as cheap as possible.
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