H-PAC Hand: Control-Oriented Modeling and Tendon-Elasticity Compensation for an Underactuated Robotic Hand

Underactuated tendon-driven hands offer compact actuation and passive compliance, but tendon elongation under restoring-spring loading introduces configuration-dependent joint deviations. This paper presents H-PAC, a modular 6-actuator, 15-DoF robotic hand with a control-oriented modeling and implementation framework. A sparse analytical actuator-joint model is derived from the tendon-routing geometry, and a mechanics-based compensation model is developed to account for tendon-elasticity-induced joint errors. The proposed method is implemented in a hierarchical architecture: a host computer performs workspace-constrained posture mapping and compensation, while an ESP32 generates synchronized commands for six position-controlled servos. The same control parameters and execution strategy are used across all tasks without task-specific retuning. Monotonic servo-sweep experiments show that the compensation substantially improves joint-angle prediction. The MAE of the index DIP joint decreases from 1.15 degrees to 0.18 degrees, and all nine evaluated joints achieve an MAE below 0.23 degrees. Representative postures and grasping configurations are further executed using the same control pipeline without external joint or force sensing in the control loop. The results demonstrate a practical approach to improving posture reproducibility in compact underactuated robotic end-effectors.