Robots that play chess, provide directions, go out for groceries—these are the helpful robots on display at this year’s CES tech trade show in Las Vegas. And while they don’t resemble humans, exactly, many are designed to accomplish their tasks with digital eyes, turning heads, waving arms and grabbing hands.

“We’re on the cusp of a robotic moment,” said J.P. Gownder, a robotics-focused senior analyst and vice president at the Forrester research firm. Not only are robots developing physical skills necessary to carry out domestic...