Design and stability analysis of a lane following controller

This paper considers the design and stability analysis of a steering controller. The objective of the controller is to steer a ground vehicle along a reference line located in the middle of the lane to be followed. We define an arbitrary look-ahead point located on the local longitudinal axis of the vehicle. The distance between the look-ahead point and the reference line is called the look-ahead offset. During perfect lane tracking, the ratio of the steer angle to the look-ahead offset is independent of the curve radius under reasonable approximations. That ratio is computed in terms of the vehicle speed and various vehicle parameters. Then, a constant controller is designed to achieve that ratio at steady state. The controller is a continuous function of the vehicle speed. The only information processed by the controller is the look-ahead offset, which can be measured using a radar-based or a vision-based sensor. Using Routh-Hurwitz analysis, we analytically prove that the closed-loop system is stable. Given any range of longitudinal speeds, there exists a sufficiently large look-ahead distance ensuring the closed-loop stability for all speeds in that speed range. For a particular set of parameter variations, it is also shown that choosing the look-ahead distance large enough guarantees the robustness of closed-loop stability, Various simulation results demonstrating the performance of the controller are included.