True object
Belief estimate (ghost)
Belief cloud
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A robot arm has to pick up an object whose exact pose it never directly observes — only a noisy sensor reading, visualized here as a scattered belief cloud around a ghost estimate. Three controllers face the same randomized trials: a naive controller that trusts the single mean estimate and grasps tightly, a robust controller that widens its gripper to cover most of the uncertainty in one shot, and an information-gathering controller that spends a moment probing the scene by touch before committing to a precise final grasp. Switch modes, adjust the sensor noise, and run trials to see how success rate trades off against time-to-grasp.