Crash avoidance and mitigation is still one of the major challenges faced by the autonomous vehicles industry. Path planning in autonomous vehicles is a crucial phase during crash avoidance with other vehicles. It is important for the path planning algorithm to be reactive in uncertain situations which usually arise in urban road scenarios. This study proposes a reactive online path planning strategy for obstacle avoidance and crash mitigation for an imminent collision with another vehicle. A cubic Bezier curve trajectory generation method is used for creating a maneuver around the obstacle vehicle. Relative hitting heading angle is considered to account for the crash severity between two vehicles. Two cases are considered where one is an imminent crash scenario and the other is where an obstacle can be avoided with a minimum safety distance. This obstacle avoidance problem is then converted to an optimization problem where potential crash severity, vehicle kinematic constraints and path smoothness are considered as constraints. The resulting cost function consists of a quadratic convex function and a piecewise defined function. This is further solved using a novel methodology where the piecewise function is included in the inequality constraints, so that the problem can be solved using quadratic programming method. This will also lead to a quick real time implementation. It is shown that the proposed method is able to avoid collisions and also minimizes the crash severity in case of an imminent collision.

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