The technology involves determining a minimum lateral gap distance between a vehicle configured for autonomous driving and one or more other objects in the vehicle's environment. The minimum lateral gap is used when determining whether to have a driver take over control of certain driving operations. This provides a measure of safety during disengagements or other change of control events. Determining the minimum lateral gap includes calculating a budgeted distance based on a cross-track error for a lateral position of the vehicle, an allowed actual gap distance to an object in the vehicle's environment, and a perception error associated with a location of the object in the vehicle's environment. This determination can be done for a set of possible operating speeds and steering rate limit combinations. The vehicle's control system may notify the driver to take control, for instance with audible, visual and/or haptic notifications.