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In this paper, we consider several control strategies to minimize off-tracking and rearward amplification of a multi-axle steering system with a tractor and three full trailers. A five-degree-of-freedom linear yaw-plane model is used to describe the vehicle dynamics. A tyre model describing the lateral tyre forces as a linear function of sideslip angles is incorporated in the yaw model. Given any arbitrary tractor track desired realtime by the driver, automated control inputs are the steering angles of front axles of the trailers. A minimum rearward amplification ratio (RWA), as a surrogate for minimum off-tracking, has been used as the control criterion for medium to high speeds to arrive at an optimal Linear Quadratic Regulator (LQR) controller. Robustness of the optimal controller with respect to tyre-parameter perturbations is then examined. Based on the simulation results, we find that, active steering at all trailers gives the lowest RWA. To achieve acceptable levels of RWA and off-tracking, at least two of the three trailers must be actively steered. Among the three two-trailer-steering possibilities, actively steering trailers 1 and 2 is optimal and results in the lowest RWA with offtracking practically eliminated. The optimal LQR controller is remarkably robust with respect to tyre-parameter variations.

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First the effectiveness of command steering of trailers in reducing off-tracking during a 90u turn for a truck with three trailers is examined. In command steering, front trailer axles are steered proportionately to the articulation angles between the tractor and corresponding trailers. Then, based on insights gained, the approach of an optimal linear quadratic regulator (LQR) controller to minimize off-tracking indirectly, by minimizing rearward amplification, is used. The simulation results demonstrate that command steering is very effective only for low speeds, although it also reduces the turn radius during a 90u turn. Command-steering-based LQR control is, however, very effective for all speeds.

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