Sub-Frame Contact-Onset Estimation in a Self-Calibrated BJT Thermal Pixel Array Using a Four-Frame erfc Template

Area of Science:

• Robotics
• Sensor Technology
• Materials Science

Background:

• Bipolar-junction-transistor (BJT) thermal pixel arrays offer low-cost, force-free tactile sensing for robotic skins.
• Existing BJT arrays suffer from slow frame rates (e.g., 4 Hz, 252 ms interval), limiting contact timing resolution.
• This limitation hinders applications requiring precise contact-aware control.

Purpose of the Study:

• To develop a method for enhancing the sub-frame contact timing resolution of BJT thermal pixel arrays.
• To enable more accurate estimation of contact onset, amplitude, and thermal diffusion parameters.
• To improve the robustness and applicability of tactile sensing in robotics.

Main Methods:

• Proposed a four-frame complementary-error-function (erfc) template based on 1D semi-infinite heat conduction.
• Employed a grid-initialized semi-analytic Levenberg-Marquardt scheme (Path A) for joint parameter estimation.
• Developed a two-layer rejection pipeline for fault detection and performance validation.

Main Results:

• Achieved a per-contact Cramér-Rao lower bound for contact onset offset (τ₁) of 16.2 ms.
• Empirical cross-contact dispersion was measured at 83.5 ms without external timing synchronization.
• The system demonstrated high accuracy in separating valid contacts from hardware faults and generalized to new subjects, achieving an AUC of 0.878 against synthetic disturbances.

Conclusions:

• The proposed erfc template method significantly improves sub-frame contact timing resolution for BJT thermal pixel arrays.
• The technique provides robust estimation of contact parameters and effective fault rejection.
• Further validation with larger cohorts and external timing references is recommended for future work.