Beginning a sentence with a participial phrase is usually jarring and awkward. If you don't really know what a participial phrase is, you can often spot one by looking for an -ing verb. You won't find -ing verbs only in participial phrases, but that will be a warning sign, and then you can investigate further. Here's an example:
Pulling open the rusty door, Joe peered into his darkened chamber, poked the candle past the threshold.
"Pulling open the rusty door" is the participial phrase. These tend to be jarring because we read the whole opening phrase (up to the comma) without knowing who is acting. This can be confusing and misleading. We don't know which door this is or what the circumstances are until later in the sentence. Unless you want us to feel jarred and disoriented, or unless the previous sentence sets things up very clearly, this structure is usually a bad idea.
Another issue is that when you use a sentence structure with a participial phrase either preceding or following the main clause, what you are saying is that the action of the -ing verb and the action of the main verb occur simultaneously. Let's take a look at this sentence:
Larry parked the car, walking to sketch select sections of the property that he was particularly interested in.
"Walking to sketch . . ." is the participial phrase. "Larry parked the car" is the main clause (the section with the sentence's subject and predicate). What this sentence means is that Larry parked and walked simultaneously. That's not possible. He must park first, then walk.
Rising to her feet, Jane staggered toward the base of the slope.
"Rising to her feet" is the participial phrase, and "Jane staggered . . ." is the main clause. This sentence is saying that Jane rose and Jane staggered toward the base simultaneously. Again, that's not what she's doing. She must rise first, then stagger.
Here's another example:
Quickly looking around the room, Sam tore down the curtains and pulled the curtain rod from the curtains.
The author here is saying that Sam looked around the room and tore down the curtains simultaneously. But that isn't what the author means. What he means is that Sam looked around the room, saw the curtain rod, and pulled down the curtains to get to the rod (to use it as a weapon). The actions aren't simultaneous, so the author shouldn't use a participial phrase. Instead, one might say,
Sam quickly looked around the room, tore down the curtains, and pulled out the curtain rod.
In this case, I think a stronger separation of the looking and the tearing down would be better, to stress his moment of decision. Shorter sentences would also stress the frantic nature of his actions.
He glanced around the room. The curtain rod. He tore down the curtains, pulled out the rod.
Participial phrases can be great, on rare occasion, to jar and disorient the reader. Just make sure you use them at the right time and in the right way. Writing is all about being aware of what you're doing and making informed decisions in your work.