We use a controlled invariance approach to design a semi-autonomous lane departure assist system that is guaranteed to keep the vehicle in the lane. The controlled invariant safe set is the set of system states from which an input exists that can keep the vehicle in the lane. First we provide theoretical conditions under which the controlled invariant safe set has a simple characterization that can be quickly computed in real-time. We then use this characterization to derive a feedback strategy that keeps the vehicle in the lane and overrides the driver only if he/she could otherwise force a future lane departure. We also provide a detailed description of the above mentioned conditions, including algorithmic approaches that allow to verify whether these conditions are satisfied.
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