The advancement of autonomous robotics is pivotal for the future of space operations, particularly in the domain of on-orbit servicing. A critical component of such intelligent systems is the end-effector. A dexterous robotic hand, capable of performing complex manipulation tasks with human-like adaptability, offers significant advantages over traditional specialized tools. It promises greater versatility for tasks such as satellite maintenance, module assembly, and scientific experimentation, potentially reducing the need for extravehicular activity by astronauts. This paper presents the comprehensive design and implementation of a control system for a tendon-driven, five-fingered dexterous robotic hand developed specifically for the demanding environment of space.
The fundamental challenge in designing a space-qualified dexterous robotic hand lies in balancing high performance with robustness and reliability. Two primary architectural paradigms exist: internally-actuated hands, where motors and controllers are integrated into the fingers and palm, and tendon-driven (externally-actuated) hands. While internally-actuated designs offer high control precision and low hysteresis, they often result in bulky, heavy fingers with significant technical complexity and cost. In contrast, a tendon-driven dexterous robotic hand relocates the major actuators and transmission systems to the forearm. This approach dramatically reduces the size, weight, and inertia of the fingers, enabling superior agility. Furthermore, it allows for the use of more powerful motors and offers inherent safety through mechanical compliance. To minimize the number of actuators while maintaining full control over multiple degrees of freedom (DoF), an “N+1” tendon routing strategy is commonly employed, where N+1 tendons control N joints. However, this design introduces inherent coupling between the joint space and the tendon space, necessitating sophisticated mapping and control strategies to achieve precise motion. Additionally, tendon-driven systems are susceptible to effects like friction, backlash, and differential tensioning, which can lead to control hysteresis and asynchronous finger motion, critically undermining stable grasping.
To address these challenges, this work details a hierarchical, real-time control system engineered for a 12-DoF, tendon-driven space dexterous robotic hand. The mechanical design features five anthropomorphic fingers: a 4-DoF thumb, 3-DoF index and middle fingers, and 1-DoF ring and little fingers (which are coupled in an underactuated manner), all driven by 16 independent motors via tendon networks. The core contributions of this paper are: (1) a robust hardware architecture centered on a high-performance multi-axis motion controller; (2) a modular, real-time software framework based on RTX (Real-Time eXtension) shared memory for efficient data exchange and task integration; (3) the derivation of explicit joint-space to tendon-space decoupling matrices for precise kinematic control; and (4) a novel real-time, multi-finger coordinated motion control algorithm that ensures synchronous finger arrival at target positions while mitigating the negative effects of tendon-driven delay.
Hardware Architecture of the Control System
The hardware system is designed with a clear hierarchical structure to ensure precise, flexible, and intelligent operation. It integrates sensing, computation, and actuation into a cohesive pipeline, as summarized in Table 1.
| Component | Model/Type | Primary Function |
|---|---|---|
| Master Input | Data Glove | Captures human operator’s hand pose for teleoperation. |
| Host Computer | Industrial PC | Runs high-level software for UI, task planning, and data processing. |
| Multi-Axis Controller | ELMO Gold Maestro (GMAS) | Central real-time controller; executes synchronized motion profiles for all axes via EtherCAT. |
| Motor Drives | ELMO Gold Solo Whistle | Drive brushless DC motors; provide low-level current/torque control and encoder feedback. |
| Actuators | Maxon EC13 Brushless DC Motors | Provide mechanical power for tendon winding/unwinding. |
| Position Sensor | Hall Effect Sensors + Magnets | Measure absolute joint angles for closed-loop position control. |
| Data Acquisition | High-Resolution ADC Card | Digitizes analog signals from Hall effect sensors. |
The host computer serves as the central command node, hosting the man-machine interface and high-level planning algorithms. Motion commands are sent via Modbus/TCP to the GMAS multi-axis controller. The GMAS controller is the cornerstone of real-time performance, capable of synchronously controlling up to 96 axes over an EtherCAT network. This is essential for the coordinated motion of the 16 motors driving the dexterous robotic hand. Each motor is paired with a high-performance drive that interfaces directly with the motor’s embedded encoder (providing high-resolution motor shaft feedback) and manages the power stage. For critical joint-level position feedback, each finger joint is equipped with a Hall effect sensor and a paired magnet. As the joint rotates, the changing magnetic field produces an analog voltage signal, which is digitized by a dedicated data acquisition card. This absolute joint angle measurement is fundamental for overcoming the limitations of motor-side-only control in a tendon-driven system.
Modular Software Architecture Based on RTX Shared Memory
The software system is partitioned into host (PC) software and target (GMAS controller) software. The host software adopts a modular architecture centered around a shared memory space, enabling efficient, deterministic communication between independent functional modules. This design prioritizes scalability, clarity, and high transmission efficiency, which are vital for the complex, real-time operation of a dexterous robotic hand.
Real-Time Shared Memory Core
The shared memory segment, created using IntervalZero’s RTX, acts as the central data hub. RTX extends the Windows kernel to provide a hard real-time subsystem, ensuring predictable, low-latency execution. It enhances traditional synchronization primitives to minimize priority inversion, guaranteeing safe and concurrent access to the shared memory by multiple modules. All critical data—including sensor readings, command setpoints, and system status—is written to and read from this shared space.
Host Software Modules
The host software comprises several independent modules that interact solely through the shared memory, as outlined in Table 2.
| Module | Primary Function |
|---|---|
| Man-Machine Interface (MMI) | Graphical user interface for operator command input and system status monitoring (e.g., motor positions, errors). |
| Virtual Display Module | Renders a 3D simulation of the dexterous robotic hand using Open Inventor for real-time visualization and offline task simulation. |
| Data Glove Module | Acquires joint angle data from the teleoperation glove and writes it to shared memory. |
| Data Acquisition Module | Reads digitized joint angles from the ADC card and writes them to shared memory. |
| Motor Control Module | The core real-time process. Reads commanded positions/velocities from shared memory and sends them to the GMAS controller via Modbus/TCP. Also reads back actual motor positions from the controller. |
This decoupled architecture ensures that non-critical modules (like the GUI) cannot interfere with the timing of critical real-time processes (like the motor control loop). The Motor Control Module typically runs on the RTX real-time subsystem for maximum determinism.
Target Software
The software on the GMAS controller is responsible for executing the synchronized multi-axis motion profiles. It receives high-level commands (e.g., target positions and velocities for each motor) from the host and employs its internal trajectory planner and PID filters to generate precise current commands for each drive over the EtherCAT network, ensuring all motors of the dexterous robotic hand move in a coordinated fashion.
Motion Control: From Joint Space to Tendon Space
Accurate control of a tendon-driven dexterous robotic hand requires solving the mapping between desired joint motions and the required tendon displacements. This involves deriving the coupling matrices inherent in the “N+1” tendon routing.
Joint-Tendon Kinematic Mapping
The tendon displacement vector $\Delta \mathbf{l}$ is related to the joint angular displacement vector $\Delta \boldsymbol{\theta}$ by a transpose of the routing matrix $\mathbf{R}$, which incorporates the pulley radii at each joint:
$$
\Delta \mathbf{l} = \mathbf{R}^T \Delta \boldsymbol{\theta}
$$
We derive this explicitly for the different finger types of the dexterous robotic hand.
1. Index/Middle Finger (3-DoF, 4 Tendons): These fingers have abduction/adduction (joint 1), metacarpophalangeal – MCP (joint 2), and proximal interphalangeal – PIP (joint 3) joints. Tendons 1 and 2 actuate the base, while tendons 3 and 4 actuate the intermediate joint, with coupling across joints.
$$
\Delta \mathbf{l}_{im} = \mathbf{R}_{im}^T \Delta \boldsymbol{\theta}_{im}
$$
$$
\begin{bmatrix}
\Delta l_{im1} \\
\Delta l_{im2} \\
\Delta l_{im3} \\
\Delta l_{im4}
\end{bmatrix}
=
\begin{bmatrix}
r_{im11} & r_{im21} & 0 \\
r_{im12} & -r_{im22} & 0 \\
-r_{im13} & r_{im23} & r_{im33} \\
-r_{im14} & -r_{im24} & -r_{im34}
\end{bmatrix}
\begin{bmatrix}
\Delta \theta_{im1} \\
\Delta \theta_{im2} \\
\Delta \theta_{im3}
\end{bmatrix}
$$
Here, $r_{imij}$ denotes the radius of tendon $j$ at joint $i$ of the finger.
2. Thumb (4-DoF, 5 Tendons): The thumb has abduction, MCP, PIP, and distal interphalangeal (DIP) joints. Its routing is more complex.
$$
\Delta \mathbf{l}_{t} = \mathbf{R}_{t}^T \Delta \boldsymbol{\theta}_{t}
$$
$$
\begin{bmatrix}
\Delta l_{t1} \\
\Delta l_{t2} \\
\Delta l_{t3} \\
\Delta l_{t4} \\
\Delta l_{t5}
\end{bmatrix}
=
\begin{bmatrix}
r_{t11} & r_{t21} & r_{t31} & r_{t41} \\
r_{t12} & r_{t22} & -r_{t32} & -r_{t42} \\
-r_{t13} & r_{t23} & r_{t33} & 0 \\
-r_{t14} & r_{t24} & -r_{t34} & 0 \\
0 & -r_{t25} & 0 & 0
\end{bmatrix}
\begin{bmatrix}
\Delta \theta_{t1} \\
\Delta \theta_{t2} \\
\Delta \theta_{t3} \\
\Delta \theta_{t4}
\end{bmatrix}
$$
3. Ring/Little Fingers (Coupled 2-DoF, 2 Tendons): These underactuated fingers share tendons.
$$
\Delta \mathbf{l}_{rl} = \mathbf{R}_{rl}^T \Delta \boldsymbol{\theta}_{rl}
$$
$$
\begin{bmatrix}
\Delta l_{rl1} \\
\Delta l_{rl2}
\end{bmatrix}
=
\begin{bmatrix}
r_{rl11} & r_{rl21} \\
-r_{rl12} & -r_{rl22}
\end{bmatrix}
\begin{bmatrix}
\Delta \theta_{rl1} \\
\Delta \theta_{rl2}
\end{bmatrix}
$$
The motor command in counts, $P_{moj}$, for a tendon displacement $\Delta l_j$ is calculated based on the lead screw pitch and encoder resolution:
$$
P_{moj} = N_{\text{enc}} \cdot \frac{\Delta l_j}{p_{\text{pitch}}}
$$
where $N_{\text{enc}}$ is the encoder counts per motor revolution (e.g., 53248) and $p_{\text{pitch}}$ is the screw lead (e.g., 1 mm/rev).
Real-Time Multi-Finger Coordinated Motion Control
A stable grasp requires all fingertips to contact the object simultaneously. In a tendon-driven system, differences in initial tendon pre-tension, friction, and drive response can cause fingers to reach their target positions at different times if controlled independently. To solve this, we propose a real-time velocity-scaling algorithm based on joint-space error feedback.
The algorithm executed at each control cycle is as follows:
1. Compute Joint Error: For each controlled joint $k$, calculate the error $\Delta q_k = \theta_{k,\text{desired}} – \theta_{k,\text{actual}}$ from Hall sensor feedback.
2. Map to Tendon/Motor Displacement: Using the decoupling matrices ($\mathbf{R}^T$), convert the joint error vector $\Delta \mathbf{q}$ into the required displacement $d_j$ for each of the $J$ motors ($j=1,…,16$). Find the maximum absolute displacement among all motors: $d_{\text{max}} = \max(|d_1|, |d_2|, …, |d_J|)$.
3. Scale Motor Velocities (Basic): Assign a velocity $v_j$ to each motor proportional to its required displacement, such that the motor with the largest displacement moves at the predefined maximum safe speed $v_{\text{max}}$:
$$
v_j = v_{\text{max}} \frac{d_j}{d_{\text{max}}}
$$
This ensures all motors complete their proportional motion in the same time, promoting synchronicity.
4. Mitigate Terminal Oscillation: The basic scaling can cause motors to approach their target at high speed, leading to overshoot and oscillation due to tendon stretch and backlash. To address this, a shaping function $g(d_{\text{max}})$ is introduced:
$$
v_j = v_{\text{max}} \frac{d_j}{d_{\text{max}}} \cdot g(d_{\text{max}})
$$
where $g(d_{\text{max}})$ is a convex, increasing function such as:
$$
g(d_{\text{max}}) = \frac{d_{\text{max}} + a}{d_{\text{max}} + b}
$$
with $a$ and $b$ being positive constants tuned based on the system’s typical displacement range. When $d_{\text{max}}$ is large (start of motion), $g(d_{\text{max}}) \approx 1$, allowing fast motion. As $d_{\text{max}}$ approaches zero (end of motion), $g(d_{\text{max}}) \approx a/b < 1$, automatically reducing the speed of all motors and enabling a smooth, stable approach to the target pose for the entire dexterous robotic hand.
Experimental Verification
The proposed control system was validated through a series of experiments on the physical tendon-driven dexterous robotic hand prototype.
1. Sensor Calibration and Joint-Level Control
Each Hall effect joint sensor was calibrated using a precision fixture. A typical calibration result showed a highly linear relationship between the sensor output voltage and the joint angle, with an average error of approximately $0.6^\circ$, which is sufficient for closed-loop position control of a tendon-driven system.
Subsequently, closed-loop position control was tested on individual fingers. Using the Hall sensor feedback and the joint-to-tendon mapping, the controller accurately drove the joints to their desired angles. For example, commanding the middle finger to $[0^\circ, 68^\circ, 79^\circ]$ for its abduction, MCP, and PIP joints respectively resulted in the actual trajectories closely tracking the setpoints, confirming the accuracy of the derived kinematic model and the basic control loop.
2. Multi-Finger Coordinated Motion
The coordinated control algorithm was tested with a multi-finger pose change. The thumb was commanded to $[0^\circ, 0^\circ, 20^\circ, 45^\circ]$, the index finger to $[0^\circ, 60^\circ, 50^\circ]$, and the middle finger to $[0^\circ, 30^\circ, 20^\circ]$ (abduction, MCP, PIP). The algorithm calculated the required motor displacements and dynamically scaled the velocities according to the described method. The resulting motor velocity profiles demonstrated key features: (a) all fingers began and ended their motion nearly simultaneously; (b) velocities were highest at the start of the movement and smoothly decayed to zero as the target was approached, preventing terminal oscillation; and (c) the controller automatically compensated for minor disturbances (e.g., unintended abduction) by adjusting individual tendon speeds, showcasing the robustness of the feedback-based coordination.
3. Integrated Grasping and Teleoperation
Finally, the complete system was tested in integrated scenarios. The dexterous robotic hand successfully performed dexterous grasping tasks, such as securely acquiring and holding objects like a spray bottle, relying on the coordinated position control. Furthermore, in teleoperation mode, the data glove successfully mapped human operator hand movements to the robotic hand in real-time, enabling remote performance of complex poses and manipulations. These experiments validated the stability, reliability, and practical utility of the entire control system for operating a tendon-driven dexterous robotic hand.
Conclusion
This paper presented a comprehensive real-time control system solution for a tendon-driven five-fingered dexterous robotic hand targeting on-orbit service applications. The system integrates a robust hardware architecture with a modular, real-time software framework based on RTX shared memory, which provides excellent scalability and deterministic performance. The core challenges of tendon-drive coupling and asynchronous motion were addressed through the explicit derivation of joint-to-tendon kinematic decoupling matrices and the development of a novel real-time, feedback-based multi-finger coordinated motion control algorithm. This algorithm ensures synchronous finger motion and incorporates a terminal velocity shaping function to mitigate the effects of tendon hysteresis and delay. Experimental results on a physical prototype confirmed the system’s precision in joint-level control, its effectiveness in achieving coordinated multi-finger motion, and its overall reliability in performing dexterous grasping and teleoperation tasks. The proposed system forms a solid foundation for the deployment of advanced, biologically-inspired manipulation capabilities in future space robotic systems.