Fast and reliable trajectory planning is a key requirement of autonomous vehicles. In this paper we introduce a novel technique for planning the route of an autonomous vehicle on a straight, traffic-heavy rural road using the SPIN model checker. We show how we can combine SPIN's ability to identify paths violating temporal properties with sensor information from a 3D Unity simulation of an autonomous vehicle, to plan and perform consecutive overtaking manoeuvres. This involves discretising the sensory information and combining multiple sequential SPIN models with a Linear-time Temporal Logic specification to generate an error path. This path provides the autonomous vehicle with an action plan. The entire process is fast (using no precomputed data) and the action plan is tailored for individual scenarios. Our experiments demonstrate that the simulated autonomous vehicle implementing our approach can drive a median of 37 km and overtake a median of 187 vehicles before experiencing a collision - which is usually caused by inaccuracies in the sensory system. We also describe a memoisation approach which helps to mitigate one of the drawbacks of our approach - the cost of model compilation. Our novel approach demonstrates a potentially powerful future tool for efficient trajectory planning for autonomous vehicles.