Story, first published: The Magazine of Fantasy and Science Fiction, March 1960
Rather than be reprogrammed, a six-hundred-year-old robot, Richard Daniel, disguises himself as human and stows away on a starship. When the starship takes off and goes into hyperspace, Richard is on the outside of the ship. Simak gives a marvelous description of Richard's thoughts and sensations in hyperspace - in most science-fiction stories, the occupants are inside and protected.
When Richard arrives on a planet run by robots, he "sees" a diagram of the spaceship, indicating that something is seriously wrong. Before he can issue any warning, the spaceship blows up. When another robot tries to kill him, he "sees" a diagram of the robot and turns him off. Richard has acquired these new abilities, apparently from his trip through hyperspace. He stows away again on a ship bound for the planet Arcadia, a pastoral paradise and duplicate of Earth. On the journey, Richard wonders why he, a robot, has been granted the gift of paranormal ability instead of a human being. Arcadia needs Richard - to cure a sick child, to fix a broken appliance, or perhaps to teach the people his special talents. ...
Richard has avoided all the traps of Earth to gain his freedom except the last - true to his kind, he must use his gift for the service of humanity.
Ewald, Robert J.: When the Fires Burn High and the Wind is from the North, p.68-69