The baby is three months old and when lying on our bed, starts arching…

The baby is three months old and when lying on our bed, starts arching his back and head sideways, pulling it in a circular motion with his little arms. We lie parallel to the bed, but within 10 minutes we're lying perpendicularly. Is this normal? Does he try to turn over? If he grabs onto a pillow or blanket, he ends up lying on his side.