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This paper presents a method for estimating how the driver of a vehicle can use steering, braking or acceleration to avoid a collision with a moving object. In the method, the motion of the object can be described with an arbitrary motion model and polygons are used to describe its expected extension. The key idea is to parameterize the motion of the vehicle such that an analytical solution can be derived for estimating the set of manoeuvres that the driver can use to avoid the object at discrete times. The union of the solutions for all times is used to estimate how a collision can be avoided during the complete prediction horizon. Additionally, a decision-making algorithm is proposed that decides when to initiate autonomous braking to avoid or mitigate a potential collision. A collision avoidance by braking system, based on the proposed method and algorithm, has been evaluated on simulated traffic scenarios at intersections. It is shown that a vehicle equipped with such a system can potentially reduce the impact velocity with up to 40 km/h in left turn across path situations.