Hand-force Calibration

When a six-axis force/torque (F/T) sensor is attached to the robot, calibrate:

• the end-effector gravity, and its center.
• the biases:
  • the rotation between the sensor and robot
  • the robot installation declination
  • the bias of sensor.

1. Model

From the Bias Estimation and Gravity Compensation for Wrist-Mounted Force/Torque Sensor.

The stationary mode or the gravity compensation model:

$$ {}^s\mathbf{F} = {}^s\mathbf{F}_{contact} + {}^s_e\mathbf{R} \cdot {}^e_b\mathbf{R} \cdot \mathbf{F}_b + {}^s\mathbf{F}_0 $$

$$ {}^s\mathbf{T} = {}^s\mathbf{T}_{contact} + ({}^s_g\mathbf{P})^\wedge \cdot {}^s_e\mathbf{R} \cdot {}^e_b\mathbf{R} \cdot \mathbf{F}_b + {}^s\mathbf{T}_0 $$

The calibration model:

$$ {}^s\mathbf{F} = {}^s_e\mathbf{R} \cdot {}^e_b\mathbf{R} \cdot \mathbf{F}_b + {}^s\mathbf{F}_0 $$

$$ {}^s\mathbf{T} = ({}^s_g\mathbf{P})^\wedge \cdot ({}^s\mathbf{F} - {}^s\mathbf{F}_0) + {}^s\mathbf{T}_0 $$

2. Method

• original: in the least-square method, decide the sign of F_b by the robot installation types.
• improvement here: decide the sign of F_b by comparing the total fitting errors.

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Citation

If you use this code or method, please cite the following paper:

@misc{yu2025handforcecalibration,
  author       = {Winkin Yu},
  title        = {Hand-Force Calibration with Bias Force Sign Selection via Total Error Minimization},
  year         = {2025},
  howpublished = {GitHub repository},
  url          = {https://github.com/GeneHit/hand_force_calibration},
  note         = {Original idea implemented in code.}
}