NTH

Rapid Learning of Dexterous In-Hand Pen Writing through Real-Time Jacobian Estimation

AuthorsKai Stewart, Yasunori Toshimitsu, Robert K. Katzschmann

September 13, 2026 3 min read
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The one-line take

A robot hand learns to write with a grasped pen in seconds by estimating how its movements affect the pen in real time, without simulation or demonstrations.

Key results

18
Initialization time

Excitation phase before writing begins

0.64
ORCA pooled mean error

In-plane tracking error in mm across 38 runs

31
Long-horizon run

Minutes writing all 26 letters without recalibration

0.17
Shadow Hand RMSE

Pen-tip tracking RMSE in MuJoCo simulation, in mm

1.48
Wuji Hand 2 RMSE

Pen-tip tracking RMSE in MuJoCo simulation, in mm

What the paper found

This paper presents a lightweight method for dexterous in-hand pen writing that learns the hand–pen relationship directly on the robot instead of relying on an analytic contact model, simulation training, or precollected demonstrations. A webcam tracks an ArUco pen marker at roughly 15 Hz, while a recursive least-squares, Kalman-style estimator continuously updates a command-space task Jacobian. After an 18 s excitation phase, a damped pseudoinverse controller converts desired pen-tip motion into joint commands, and a Jacobian nullspace term stabilizes the grip. On the 17-DoF tendon-driven ORCA hand, ten finger joints alone traced arbitrary single-stroke shapes, the alphabet, and writing on paper, achieving a pooled in-plane error of 0.64 ± 0.10 mm across 38 runs. Continuous Jacobian adaptation prevented long-term drift during a 31-minute run covering all 26 letters, while removing grip regularization caused four failures in ten trials. The same formulation also transferred in MuJoCo simulation to two different hands: Shadow Hand reached 0.17 mm RMSE and Wuji Hand 2 reached 1.48 mm, without hand-specific analytic Jacobians. The main limitation is that the physical controller regulates only planar motion; uncontrolled out-of-plane drift of about 2–3 mm requires compliant or curved paper, and the deliberately slow writing speed remains far below human performance. The result suggests that rapid embodied adaptation can replace compute- and data-heavy reinforcement learning or imitation learning for some contact-rich manipulation tasks.

Original abstract

Dexterous in-hand manipulation of a grasped object with an anthropomorphic hand is an unsolved frontier for robot dexterity. The contact-richness and highly dynamic nature of object-hand interactions tend to require extensive modeling or data-collection efforts for learning-based approaches. Modern simulators used for reinforcement learning (RL) cannot fully replicate the required contact complexity, while collecting dexterous demonstrations for imitation learning (IL) remains an open problem. In this research, we present an embodied control approach based on real-time task Jacobian estimation of the combined hand and object system on the physical robot. Using only the CPU on a laptop, the proposed controller begins in-hand pen writing after approximately 18 s of initialization and continues to adapt online, without an analytic hand--object kinematic/contact model, simulation training, or precollected task demonstrations. We demonstrate that the same estimator/controller formulation works on three anthropomorphic robotic hand systems (one physical, two simulated) to show human-like, in-hand articulation of a grasped pen by an embodiment-independent formulation. Sub-millimeter in-plane precision (mean 0.6 mm across runs) is achieved across letters and shapes written in the air and on paper on a physical robot. To our knowledge, this is the first demonstration of an anthropomorphic hand writing arbitrary single-stroke trajectories with a grasped pen through purely in-hand motion, and it showcases an alternative to compute- and data-heavy approaches such as RL and IL for achieving dexterous manipulation through computationally simple and data-efficient algorithms.

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