Visual inertial odometry (VIO) is widely used for the state estimation of multicopters, but it may function poorly in environments with few visual features or in overly aggressive flights. In this work, we propose a perception-aware collision avoidance trajectory planner for multicopters, that may be used with any feature-based VIO algorithm. Our approach is able to fly the vehicle to a goal position at fast speed, avoiding obstacles in an unknown stationary environment while achieving good VIO state estimation accuracy. The proposed planner samples a group of minimum jerk trajectories and finds collision-free trajectories among them, which are then evaluated based on their speed to the goal and perception quality. Both the motion blur of features and their locations are considered for the perception quality. Our novel consideration of the motion blur of features enables automatic adaptation of the trajectory's aggressiveness under environments with different light levels. The best trajectory from the evaluation is tracked by the vehicle and is updated in a receding horizon manner when new images are received from the camera. Only generic assumptions about the VIO are made, so that the planner may be used with various existing systems. The proposed method can run in real-time on a small embedded computer on board. We validated the effectiveness of our proposed approach through experiments in both indoor and outdoor environments. Compared to a perception-agnostic planner, the proposed planner kept more features in the camera's view and made the flight less aggressive, making the VIO more accurate. It also reduced VIO failures, which occurred for the perception-agnostic planner but not for the proposed planner. The ability of the proposed planner to fly through dense obstacles was also validated. The experiment video can be found at https://youtu.be/qO3LZIrpwtQ.