Case studies on passivity-based stabilisation of closed sets

We present a novel control design procedure for the passivity-based stabilisation of closed sets which leverages recent theoretical advances. The procedure involves using part of the control freedom in order to enforce a detectability property, while the remaining part is used for passivity-based stabilisation. The procedure is illustrated in four case studies of path following coordination for one or two kinematic unicycles, and variations of these problems. Among other things, we present a smooth global path following controller making the unicycle converge to an arbitrary closed and strictly convex curve, and a coordinated path following controller for two unicycles.