VR Teleoperation Trainer: The Power Law of Practice

Training Setup

Task difficulty 3 / 5

Feedback modality

Session

Trial #1 · reaching…

Completion time

— s

Hit rate (last 20)

—%

Skill retention

100%

How it works

Each VR drill sends the arm from its current end-effector position to a new target within its reach envelope. Trial time and reach error are drawn from the power law of practice (Newell & Rosenbloom, 1981):

T(n)     = T∞ + (T₁ − T∞) · n^(−c)
σ(n)     = σ∞ + (σ₁ − σ∞) · n^(−c)

where n is the trainee's effective trial count, T₁/σ₁ are first-attempt time and error spread (set by difficulty), T∞/σ∞ are the skilled asymptote, and c is the learning-rate exponent — both set by feedback modality (haptic feedback learns fastest and plateaus lowest). Each attempt's actual landing point is offset from the target by a folded-normal error of magnitude σ(n); it counts as a hit when that offset is inside the target's tolerance ring.

The 2-link arm reaches the (possibly missed) point via closed-form planar inverse kinematics:

d  = |target|,  clamped to [|L₁−L₂|, L₁+L₂]
θ₂ = atan2(√(1−k²), k),  k = (d² − L₁² − L₂²) / (2 L₁ L₂)
θ₁ = atan2(ty,tx) − atan2(L₂sinθ₂, L₁+L₂cosθ₂)

Skip a day applies an Ebbinghaus-style forgetting step, n ← max(1, n·e^(−1/S)) with memory strength S growing with training received — so a well-trained arm forgets little, a novice one regresses close to trial one.

Hit Miss Current target

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