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When automobiles are at the threat of collisions, steering usually needs shorter longitudinal distance than braking for collision avoidance, especially under the condition of high speed or low adhesion. Thus, more collision accidents can be avoided in the same situation. The steering assistance is in need since the operation is hard for drivers. And considering the dynamic characteristics of vehicles in those maneuvers, the real-time and the accuracy of the assisted algorithms is essential. In view of the above problems, this paper first takes lateral acceleration of the vehicle as the constraint, aiming at the collision avoidance situation of the straight lane and the stable driving inside the curve, and trajectory of the collision avoidance is derived by a quintic polynomial.