For many on the autism spectrum, rhythm and repetitive motion are key issues. They tend to soothe the brain and offer comfort. While some perseverative behaviors are not desired, certain rhythm and motion can be helpful, especially those that accompany various sports.
My son Jacob met Josh Davis in 2012 at Western Illinois University, where they both attend college. They shared a homeschool connection, and something else. Jacob's brother is autistic. Josh has Asperger's. Through conversation with Josh, Jacob learned that sports, namely swimming, played an integral part of Josh's positive social and academic development.
Josh was featured in an article in Pantagraph.com in 2008. Here is the link: