Obtained from Esper or Telepathos, the ESP ability allows Kirby to use many psychic abilities. It is also usable as a Mode for Robobot Armor.
Kirby creates a bubble of psychic energy that explodes immediately.
Hold B + Control Pad
Kirby creates a bubble of psychic energy that can move around. The bubble explodes when B is released, after a short period of time, or after hitting an enemy twice.
15 (bubble, explosion)
Hold B for a long time without moving the Control Pad
Kirby creates a massive bubble of psychic energy that deals more damage than PK Shift. Explodes when B is released or after a short amount of time.
23 (bubble), 30 (explosion)
Dash + B (Vanish)
Vanish, then release B (Reappear)
Kirby instantly transports himself forward, causing damage to any enemies he transports near. The longer B is held, the longer Kirby stays invisible and the farther he goes. Holding up/down can make Kirby reappear above or below where he normally does. Pressing backwards makes Kirby go less distance. Using the + Control Pad doesn't work without holding B.
L/R right before getting hit
Kirby teleports quickly to dodge an attack, then creates a small bubble of psychic energy to damage enemies around him.
L/R when getting hit
Kirby teleports immediately to dodge an attack, then creates a large, powerful bubble of psychic energy to damage enemies around him.
The ESP ability appears to be a reference to Ness, a character from both the EarthBound and Super Smash Bros. series. The ability references Ness's psychic powers, particularly PK Shift/PK Electroshift referencing PK Flash, while the ability hat itself is the same as Ness's hat, albeit with the colors swapped. The in-game description even references Ness.
ESP is one of only a few regular Copy Abilities whose English name differs from its Japanese name. The reason it was changed was likely because the term "Esper" is associated with the SNES RPG Final Fantasy VI, while the ability cap is instead a reference to the Mother series.
This discrepancy could also be due to the way Japan pronounces the term "ESP," saying it as one word as opposed to the way the United States pronounces it as an acronym.
This is the only new Copy Ability being introduced in Kirby: Planet Robobot to also have a Mode for the Robobot Armor (which happens to be introduced in the exact same game as the new ESP ability).
When guarding with ESP, a small psychic swirl appears around Kirby. If he is hit during the swirl, he will initiate either PK Evade or PK Insight, depending on the timing.