Posture regulation for unicycle-like robots with prescribed performance guarantees

This study aims to address the regulation problem for the unicycle model while guaranteeing prescribed performance. Different controllers based either on polar coordinates or time-varying laws are proposed. The main contribution is the combination of the standard control laws that allow to achieve posture regulation for the unicycle, with the prescribed performance control technique that imposes time-varying constraints to the system coordinates. To apply prescribed performance to the unicycle system which is subject to a non-holonomic constraint, the authors design a specific transformation function that is instrumental in the proof of asymptotic convergence with prescribed guaranties.