Geometric optimal filtering for an articulated n‐trailer vehicle with unknown parameters

In this article, we consider the equations of motion for an articulated n-trailer vehicle with different masses and inertias in the presence of force and torque commands. We design a second-order optimal filter to estimate the pose of the first vehicle and of the trailers exploiting the Lie group structure and the nonholonomic and hooking constraints. We consider the filtering problem from three different perspectives: in the first masses and inertias are time-varying and perfectively known, in the second they are known only in the first part of the maneuver, but they are not updated over time. In the last case masses and inertias are considered within the state vector and therefore estimated by the filter. Depending on the needs in real-life applications (e.g., whether the masses and inertias remain fixed or change during the maneuver and are unknown), the best-performing filter can be used. The sensing system consists of a GPS-like configuration (global positioning system) obtained by using an antenna attached to the leading car.