Future self-driving cars and current ones with advanced driver assistance systems are expected to interact with other traffic participants, which often are multiple other vehicles. To facilitate the motion planning of the autonomously controlled vehicle in collision avoidance, individual object vehicles with closeness in positions and velocities can be grouped as a single extended moving object. However, due to uncertainties from sensor imperfections and environmental disturbances, the collision avoidance conditions are often expressed as difficult to resolve probabilistic constraints in the motion planning problem. In this paper, we propose a constraint tightening method to transform the probabilistic collision avoidance condition for a vehicle group or an extended object into a deterministic form. This is done via a conservative closed-form transformation of the bivariate integral in the collision probability density function and subsequent computable approximation with logistic functions. Detailed numerical experiments are included to illustrate the workings and the performance of the proposed approach. This method can be incorporated in existing motion planning methods.