Top-down view of a 2-link robot arm reaching one of three candidate targets. In efficient mode the end-effector follows a straight-line (minimum-length) path to the true goal — that path stays nearly equidistant from all three candidates until very late, so a human observer's Bayesian goal estimate stays uncertain almost to the end. In legible mode the trajectory bows through an intermediate waypoint pushed away from the other candidates, at the cost of extra path length — this makes the true goal statistically much more likely than the alternatives, much earlier.
P(target=k | motion so far) ∝ exp(−β · cost(start→now→k))
legibility(t) = mean confidence in true target over t∈[0,1]
legible path = shortest path + λ·exaggeration term
- Exaggeration — how far the legible path bows away from the ambiguous region early on; higher values disambiguate sooner but add path length.
- Human's live guess — a simulated Bayesian observer scoring each candidate target by how well the arm's motion-so-far explains reaching it, normalized into a live confidence readout.
- Legibility score — the time-averaged confidence the observer places in the arm's true (correct) target across the whole reach, from 0 (never sure) to 1 (certain from frame one).
- New trial — randomizes the 3 target positions and the true goal, then keeps a running scatter of path length vs. legibility score for both modes so the trade-off is visible over many trials.
Real-world relevance: on a factory floor or in a surgical robot sharing space with people, a shortest-path trajectory that stays ambiguous can make a human hesitate, freeze, or step into the arm's true path at the worst moment. Deliberately legible motion trades a small amount of extra travel distance for a much earlier, much more confident read of the robot's intent — directly reducing collision risk and building trust.