Avoiding the saturation and resonance effects via simple adaptive control of an electrically driven vehicle using omnidirectional wheels

The task of solving the adaptive control of a partially and imprecisely modeled electrical vehicle driven by three omnidirectional wheels together with the torque and/or power limits of the drives is considered. Instead of the applicationof precise analytical models and sophisticated parameter estimation techniques the vehicle is modeled as a rigid body while the considerable part of the burden carried by it through elastic connection is completely neglected in the controller’s model. Instead of that, a simple kinematically designed,
PID–type trajectory tracking is formulated that is approximated by robust fixed point transformations. It is shown that if the nominal trajectory to be traced does not significantly excite the unknown degree of freedom of the vehicle–burden connection precise and stable control can be achieved by the adaptivity, while the pure PID–type control may excite this degree of freedom and can be corrupted by achieving either the torque or the power limits of the actual drives applied. This statement is substantiated by numerical simulations. The main advantage of the proposed control method is that it operates
with local basin of attraction developed for convergent iterative Cauchy sequences that is easy to design by setting only a few parameters. Its disadvantage is that it cannot guarantee global stability therefore its application must
be preceded by numerical tests. Its use may be especially useful in applications in industrial workshops when modeling the dynamics of the coupled burden technically is very difficult, e.g. when it is a tank partially containing
liquid.