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In general, the cooperative driving problems for Connected and Automated Vehicles (CAVs) consist of two parts: determine the desired arrival times and motion planning. However, most of the existing works don't take positioning errors into account. To improve the ability of handling the positioning errors, this paper formulates motion planning as an optimization problem and adds collision avoidance constraints into the optimization problem. Then, an analytical solution of the constructed optimization problem is derived so that it can be solved quickly in practice. A series of simulation tests show that this method is superior to a common-used method in terms of safety and energy consumption. As long as the appropriate safety distance is chosen, the proposed method can make CAVs operate safely against a certain degree of positioning errors.