Heading-Sensorless Autonomous Vehicles: Luenberger-Based Linear MPC for Tracking and Safe Obstacle Avoidance

Following a trajectory and avoiding obstacles are two closely linked control tasks for an autonomous vehicle. Classical reactive controllers are tuned for one operating range, do not look ahead and have no built-in way to keep a minimum distance from an obstacle. This paper presents a Linear Time-Invariant Model Predictive Control (LTI-MPC) scheme combined with a Luenberger observer for the kinematic bicycle model. The model is linearised once around $(0,0,0,v_{\mathrm{nom}})$ and written in deviation coordinates so that the drift term of the predictor is exact. The observer, tuned with the discrete-time algebraic Riccati equation, rebuilds the heading from the noisy DGPS-RTK position and odometry speed, so no heading sensor is needed. Static obstacles are handled by a local re-planner with a designed clearance, and a closed-form rule links its blending length to the maximum reference heading. Tested in a closed loop with observer and measurement noise on five scenarios, the LTI-MPC reaches a tracking RMSE of 0.018 m at 4 m/s on a sinusoidal path; achieves, in simulation, a clearance of 0.98–0.99 m from the obstacle (the reference is designed for 1.0 m, the requirement is 0.5 m); and is the only controller among PID-type, Stanley and MPC whose accuracy degrades smoothly from 2 to 8 m/s with a single tuning. The observer converges within $1^{\circ }$ in 0.24 s. A sweep of constant-radius turns shows that the linearisation stays accurate at up to ${30}^{\circ }$ of heading change.