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.
Figures & tables
Fig. 1: Overview and DOF mapping of H-PAC Hand. (a) Human hand annotated with anatomical DOFs (MCP/PIP/DIP, MP/IP, and CMC). (b) The H-PAC Hand with 15 joint DOFs q1−q15 : four long digits each with MCP/PIP/DIP flexion–extension, and the thumb with IP/MP flexion–extension and CMC abduction–adduction.
Fig. 2: Tendon routing and analytic modeling for four fingers. Four-finger figure-eight routing from full extension to an intermediate flexion: straight segments Lk , joint pulleys of radius Ri , cables connected to the servo hubs (purple), the passive ”cable-spring” return path (green), parameters related to the closed-form geometric expression of the MCP joint ( α , d1 , d2 ), and joint angles qMCP , qPIP , qDIP . qi,ref (where i={DIP,PIP,MCP} ) denotes the structural geometric limits of the independent finger module for analytical derivation, while the actual operational range limits are constrained by the palm housing to prevent excessive flexion.
Fig. 3: Tendon routing and analytic modeling for thumb. The thumb uses figure-eight tendon routing for coupled MP/IP flexion, parameterized by αth , d1,th , and d2,th , with joint angles qMP and qIP . The structural limits qi,ref ( i={IP,MP} ) are defined analogously to the four-finger model. Servo-6 drives the CMC joint, with its output axis coaxial to the CMC joint axis and the servo horn directly rigidly attached to the CMC joint.
Finger Joint
Joint Label
Admissible Workspace [qmin,qmax] (rad)
Thumb IP
q1
[0.00,0.99]
Thumb MP
q2
[0.00,1.25]
Index DIP
q3
[0.00,1.31]
Index PIP
q4
[0.00,1.61]
Index MCP
q5
[0.00,1.27]
Middle DIP
q6
[0.00,1.28]
TABLE I: Admissible workspace of each finger joint of H-PAC. A monotonic servo sweep dedicated to workspace determination is used to obtain [qmin,qmax] .
Fig. 4: Comparative analysis of joint angle residuals under uncompensated and compensated control. This figure illustrates the relationship between the angle residuals and the servo control angles for target joints across the five fingers. Red circles represent the original uncompensated residuals (Residual_ideal) and green squares denote the residuals after mechanics-based compensation (Residual_comp). All subplots are standardized with a Y-axis range from −2.0 to +2.0 degrees to facilitate a direct comparison of performance.
Fig. 5: Mean Absolute Error (MAE) comparison of joint angles for five fingers of H-PAC Hand under uncompensated and compensated conditions. The red bars represent the MAE between real joint angles and ideal joint angles (without compensation), while the green bars denote the MAE between real joint angles and compensation joint angles (with compensation). The fingers include the thumb (with MP and IP joints) and four fingers (each with MCP, PIP and DIP joints). The MAE is calculated in the unit of degrees ( ∘ ).
Fig. 6: Representative posture and grasping demonstrations of the H-PAC Hand. Left: Hand gestures, including precise thumb-to-finger opposition (thumb opposing the index, middle, and ring fingers respectively), representative multi-finger combinations and digit gestures 1-8. Right: An extended set of 16 representative grasps under the same controller, covering diverse contact topologies (enveloping, lateral, and tip pinches) and tool morphologies (rod-like, ring-like, and press-type). All results from the same control stack (analytic mapping + mechanics-based compensation), without external joint or force sensing in the control loop.
Tendon-driven underactuated hands excel in adaptive grasping but often suffer from kinematic unpredictability and highly non-linear force transmission. This ambiguity limits their ability to perform precise free-motion shaping and deliver reliable payloads for complex manipulation tasks. To address this, we introduce the PHANTOM Hand (Hybrid Precision-Augmented Compliance): a modular, 1:1 human-scale system featuring 6 actuators and 15 degrees of freedom (DoFs). We propose a unified framework that bridges the gap between precise analytic shaping and robust compliant grasping. By deriving a sparse mapping from physical geometry and integrating a mechanics-based compensation model, we effectively suppress kinematic drift caused by spring counter-tension and tendon elasticity. This approach achieves sub-degree kinematic reproducibility for free-motion planning while retaining the inherent mechanical compliance required for stable physical interaction. Experimental validation confirms the system's capabilities through (1) kinematic analysis verifying sub-degree global accuracy across the workspace; (2) static expressibility tests demonstrating complex hand gestures; (3) diverse grasping experiments covering power, precision, and tool-use categories; and (4) quantitative fingertip force characterization. The results demonstrate that the PHANTOM hand successfully combines analytic kinematic precision with continuous, predictable force output, significantly expanding the payload and dexterity of underactuated hands. To drive the development of the underactuated manipulation ecosystem, all hardware designs and control scripts are fully open-sourced for community engagement.
Teng Yan, Jiongxu Chen, Qixiang Hua +4
The Hong Kong University of Science and Technology (Guangzhou)
This paper presents the SoftHand Model-W: a 3D-printed, underactuated, anthropomorphic robot hand based on the Pisa/IIT SoftHand, with an integrated antagonistic tendon mechanism and 2 degree-of-freedom tendon-driven wrist. These four degrees-of-acuation provide active flexion and extension to the five fingers, and active flexion/extension and radial/ulnar deviation of the palm through the wrist, while preserving the synergistic and self-adaptive features of such SoftHands. A carpal tunnel-inspired tendon routing allows remote motor placement in the forearm, reducing distal inertia and maintaining a compact form factor. The SoftHand-W is mounted on a 6-axis robot arm and tested with two reorientation tasks requiring coordination between the hand and arm's pose: cube stacking and in-plane disc rotation. Results comparing task time, arm joint travel, and configuration changes with and without wrist actuation show that adding the wrist reduces compensatory and reconfiguration movements of the arm for a quicker task-completion time. Moreover, the wrist enables pick-and-place operations that would be impossible otherwise. Overall, the SoftHand Model-W demonstrates how proximal degrees of freedom are key to achieving versatile, human-like manipulation in real world robotic applications, with a compact design enabling deployment in research and assistive settings.
Dhillon B. Merritt, Christopher J. Ford, Haoran Li +4
All authors are with the School of Engineering Mathematics and Technology, and Bristol Robotics Laboratory, University of Bristol, Bristol, BS8 1UB, U.K.
Robotic hands vary widely in anatomical fidelity and mechanical complexity, and these structural choices influence the coordination of joint motions and the difficulty of controlling the system. A unified framework is presented in which the kinematic and actuation stages are analysed separately and in composition, through the conditioning of the task Jacobian, the actuation matrix, and their product. It is applied to two hands representing opposing design philosophies, the Shadow Dexterous Hand and the Anatomically Correct, Biomechatronic Hand, along four morphological aspects: joint axis geometry, actuator-to-DOF ratio, coupling architecture, and authority distribution. All parameters are derived from the hands' canonical digital representations. Anatomical fidelity carries no uniform advantage: oblique axes improve thumb conditioning but leave the long fingers worse conditioned than the orthogonal-axis design, while the branching tendon network improves the effective control mapping at every long finger and worsens it significantly at the thumb, where actuator authority is concentrated on thumb opposition. Predictions derived from these metrics are evaluated against reinforcement learning experiments using PPO, DDPG+HER, and TQC+HER, across three different tasks.
Zalán Tari, Eszter Birtalan, Péter Polcz +1
Pázmány Péter Catholic University, Faculty of Information Technology and Bionics, Budapest, Hungary