A retired Georgia Tech professor who claims Uber and Lyft built their multibillion-dollar ride-sharing platforms by infringing his 2004 patent has enlisted the help of law firms in New York and Atlanta known for their prowess in intellectual property disputes.

Stephen Dickerson—a mechanical engineering professor emeritus and inventor whose research focuses on high-performance, computer-controlled motion devices—wants to claw back millions of dollars in what he claims are unpaid licensing fees from Uber and Lyft.