Flatness conservation in the n-trailer system equipped with a sliding kingpin mechanism

Nonlinear systems, which are differentially flat, have several properties that can be useful on designing effective controllers. In this paper we show that the n-trailer system equipped with a sliding kingpin mechanism is a differentially flat system, like its non-sliding kingpin counter part. The sliding kingpin technique is used to eliminate the undesired deviation of the path of each intermediate vehicle from that of the leading one (off-tracking phenomenon). The linearizing outputs of the flat system are the Cartesian coordinates of the middle of the last semi-trailer's axle. The state space and the kinematic equations of the new modified system are derived and the conditions for flatness are examined. The flatness conservation is also checked relatively to several kinds of dynamic sliding feedback control.