Can you use the simple present tense in sentences with participial phrases?

[hardworker]

I found some examples of participial phrases from the websites, http://www.softschools.com and http://www.k12reader.com. I am going to write them down next.

present participles

(1) Arriving late, Mary sat in the back row.
(2) Sweeping across the night sky, the bats hunted their prey.
(3) Dreaming of being a doctor, the girl decided to take an extra science class.

past participles

(4) Exhausted after a long day, Ben took a nap on the couch.
(5) Excited about dinner, Henry ran the whole way home.
(6) Frightened by the loud fireworks, the dog hid under the couch.

In the sentences above, I highlighted the verbs in the simple past tense. Is it grammatically wrong to use the simple present instead of the simple past? Please explain my question. I appreciate your help and time. Thanks.

[Alan]

Yes, you certainly can.
However, it is much more common in past tense narratives, hence the examples.