Single and Multi-Cable Actuation in Robotics

• Single and multi-cable actuation are cable-driven robotic techniques that employ one or multiple cables per degree of freedom to transmit force and motion.
• Single-cable actuation uses one cable with a passive return, favoring lighter and simpler designs, while multi-cable actuation employs antagonistic pairs for active bidirectional torque and tunable stiffness.
• The topic covers rigorous mechanical design, analytical modeling, and sophisticated control algorithms applicable to dexterous hands, continuum robots, and aerial payload systems.

Single and multi-cable actuation refer to two fundamental paradigms for transmitting force and motion in cable-driven robotic systems. Single-cable actuation employs one cable per actuated degree of freedom (DoF), typically generating motion in only one direction with passive return. Multi-cable actuation uses two or more cables per DoF, often in antagonistic arrangements, enabling bidirectional force control, co-contraction for stiffness modulation, and greater precision at the cost of added complexity. These schemes are widely used in dexterous hands, continuum and soft robots, cable-driven parallel robots, aerial cable-suspended payloads, and tensegrity platforms. Rigorous modeling, system identification, and real-time control strategies are essential to achieve high performance and robustness under each scheme.

1. Mechanical Architectures of Single and Multi-Cable Actuation

Single- and multi-cable actuation schemes differ fundamentally in how force is transmitted, generated, and returned in each joint or segment:

• Single-Cable Actuation: Each actuated DoF is driven by a single cable, anchored typically at the distal end and routed through a series of low-friction pulleys or conduits to a motorized reel. The cable generates torque or force in one direction, with motion in the opposite direction effected by a pretensioned return spring or passive elastic element. For example, in a 15-DoF bionic hand, flexion in PIP/DIP joints is accomplished by a single end-to-end tendon, while extension is achieved via a preloaded spring; the return spring opposes extension, but active torque/force in extension is not possible (Han et al., 4 Dec 2025).
• Multi-Cable (Antagonistic) Actuation: Two or more cables per DoF are tensioned antagonistically, often routed over opposing pulleys and pulled by separate motors. Both flexion and extension torques can be controlled actively and simultaneously, allowing modulation of joint stiffness via co-contraction. In the same bionic hand, MCP joints employ two orthogonally routed tendon pairs for flexion/extension and ab/adduction, each driven by independent motors for full bidirectional torque command and stiffness tuning (Han et al., 4 Dec 2025). Bowden-cable hands further exploit geometry such that the sum of cable length changes is nearly constant, achieving negligible cable-length deviation through optimized rolling-contact joint design (Min et al., 31 Dec 2025).
• Hybrid Architectures: Many advanced systems deploy multi-cable antagonistic actuation in joints where posture and load control are critical, while reserving single-cable actuation for lower-torque or predominantly unidirectional DoFs, balancing complexity, weight, and dexterity (Han et al., 4 Dec 2025, Xu et al., 2024).

2. Mathematical Modeling

Analytical and numerical models capture the mapping from motor input or cable displacement to joint angle, torque, and system compliance:

• Kinematic Relations:
  • For single-cable actuation, the cable length change is directly proportional to motor shaft rotation: $\Delta l = r_p \Delta\theta_m$, with joint angle $\theta_j = \Delta l / r_j$ under a pure rolling assumption.
  • For antagonistic multi-cable actuation, net joint torque is $\tau_j = r_j (T_1 - T_2)$, allowing both tension equilibrium and co-contraction for stiffness tuning. The tension distribution for a target torque $\tau_{des}$ and co-contraction $T_c$ is:

  $$T_1 = \frac{\tau_{des}}{2 r_j} + T_c, \quad T_2 = -\frac{\tau_{des}}{2 r_j} + T_c$$

  (Han et al., 4 Dec 2025).

• Joint Compliance and Friction:

  • The cable is often modeled as a linear spring with compliance $K_c$, with lengthening $\delta l = T / K_c$ (single-cable) or $\delta l = (T_1+T_2)/(2 K_c)$ (antagonistic).
  • Friction in sheaths and pulleys is typically modeled via the capstan equation: $$T_{\text{out}} = T_{\text{in}} e^{-\mu \theta_{\text{wrap}}}$$, directly impacting transmission efficiency and force output (Min et al., 31 Dec 2025, Xu et al., 2024).
• Workspace and Non-Redundancy:
  • In cable-driven parallel robots, multi-cable (e.g., eight cables) non-redundantly actuate an 8-DoF reconfigurable end-effector, with unique tension solutions via $J^\top \lambda = w_{\text{des}}$ (Zhang, 26 Oct 2025).
  • In continuum robots, actuation-space potential energy models analytically link both single- and multi-cable cases, showing that multi-cable actuation decouples bending and axial extension, increasing shape controllability (Wu et al., 4 Sep 2025).

3. Control Algorithms and Feedback Architectures

• Single-Cable Control: Position or torque control of a single-cable joint is realized via a feedback loop from measured joint angle or spring elongation. Example control law:

$$\tau_{\text{cmd}} = K_p(\theta_{\text{des}} - \theta_{\text{meas}}) + K_d (\omega_{\text{des}} - \omega_{\text{meas}})$$

with commanded current $i_{\text{ref}} = \tau_{\text{cmd}} / K_t$ (Han et al., 4 Dec 2025, Xu et al., 2024). Feedback may be based on motor current, cable elongation, or rotary potentiometers.

• Multi-Cable Control: Coordinated tension regulation is achieved via a multi-loop architecture:
  • Inner Loop: Enforces motor torques mapped to cable tensions.
  • Outer Loop: Computes desired tensions for specified joint torque and stiffness, often via quadratic programming with equality and bound constraints for unique tension solutions (Han et al., 4 Dec 2025, Zhang, 26 Oct 2025).
  • Example: For variable stiffness tensegrity robots, each QDD actuator is regulated by closed-loop control at 4 kHz, with stiffness and shape specified at higher control levels across multiple cables (Mi et al., 2024).
• Switch-Based and Multiplexed Actuation: Single-motor multi-cable arrangements (e.g., switch-based antagonistic actuation or time-division multiplexing) require real-time management of which cable is driven and sophisticated timing to ensure smooth and independent control, compensating for switching latency and drift (Vadeyar et al., 7 Feb 2025, Xu et al., 2024).

4. Performance Characteristics and Comparative Evaluation

Metric	Single-Cable	Multi-Cable (Antagonistic)	TDMM/Mux (Multi-Cable, Single-Motor)
Bidirectional Force	No (unidirectional)	Yes (full control both directions)	No (only one cable at a time actively driven)
Stiffness Modulation	Limited (spring)	Tunable (co-contraction)	No direct co-contraction
Bandwidth (Hand Actuator)	Up to ~1kHz	Up to ~1kHz	Reduced: per-cable ~110ms rise (Xu et al., 2024)
Complexity (Routing/Control)	Low	High	Moderately High (switching logic/overhead)
Position Accuracy	~0.8°–1°	~1.5°	~1.5°
Motor Utilization	Low (< 25%)	High (> 80%)	High (85% multiplexed)
Robustness	Hysteresis, drift	High, robust under perturbation	Sensitive to switching latency

Single-cable joints favor simplicity, low weight, and minimal routing but are limited to unidirectional torque and passive extension. Multi-cable antagonistic joints provide active bidirectional torque, tension-based stiffness control, and robust posture under load at the expense of actuator/sensor count, routing complexity, and system weight. Switch-based or multiplexed multi-cable actuation reduces actuator count at the cost of reduced bandwidth and control flexibility (Han et al., 4 Dec 2025, Xu et al., 2024, Min et al., 31 Dec 2025, Vadeyar et al., 7 Feb 2025).

5. Application-Specific Design Guidelines and Trade-Offs

• Dexterous Robotic Hands: Multi-cable actuation at high-DoF MCP (Metacarpophalangeal) joints is critical for precise grasping, ab/adduction, and postural control, whereas single-cable segments at PIP/DIP (Proximal/Distal Interphalangeal) joints suffice for simple flexion where weight and simplicity are prioritized (Han et al., 4 Dec 2025).
• Cable-Driven Parallel Robots: Multi-cable, non-redundantly actuated end-effectors (e.g., 8 cables for 8-DoF) deliver unique tension distributions, expanded workspace, and simple kinematic control without tension sensors, critical for high-speed, high-precision manipulation (Zhang, 26 Oct 2025).
• Soft and Continuum Robots: Multi-cable actuation enables independently tunable extension and bending, critical for complex path following and compliance. In modular soft arms, multi-cable models describe both global moment balance and per-cable length-to-curvature maps, forming the basis of Jacobian-based planners (Qi et al., 2024, Wu et al., 4 Sep 2025).
• Wearable and Exosuit Devices: Switch-based antagonistic actuation combines single-motor efficiency with dual-direction cable drives, reducing weight and complexity while accepting switching latency and lack of true co-contraction (Vadeyar et al., 7 Feb 2025).
• Aerial Cable-Suspended Systems: Multi-cable aerial towed or continuum systems allow full pose control (SE(3)) of a payload, modulating tensions for dynamic reconfiguration; single-cable arrangements only offer 1-DoF translational control (Li et al., 2020, Gabellieri et al., 6 Mar 2025).

6. Experimental Benchmarks and Validation

• Hand Systems: Bidirectional antagonistic drives demonstrated net joint torques up to 2 Nm per axis, doubled joint stiffness via co-contraction, and robust load support up to 10 kg in power grasps, while single-cable joints achieved peak fingertip force of 11 N and exhibited ~2° hysteresis due to passive spring return (Han et al., 4 Dec 2025).
• Tensegrity Robots: Precision proprioceptive length sensing (<1% bar length error), force-tracking RMSE <6 N, and variable stiffness range >7× were achieved across single and multi-cable modules, supporting stable locomotion and payload adaptation (Mi et al., 2024).
• Time-Division Multiplexed Hands: Rise times per channel were 45 ms (single-cable) and 110 ms (TDMM multi-cable), with maximum load 1 kg, ~1.5° positioning accuracy, and 55% reduction in motor cost (Xu et al., 2024).
• Switch-Based Exosuits: 298 ms average switching latency was measured for single-motor dual-cable antagonistic pull, with a 56 g 3D-printed mechanism and up to 750 N continuous tension capability (Vadeyar et al., 7 Feb 2025).

7. Summary and System-Level Engineering Considerations

Choice of single vs. multi-cable actuation is determined by trade-offs among dexterity, actuator count, mechanical complexity, weight, and the required control authority. For underactuated, low-stiffness, or predominantly flexion tasks, single-cable actuation (with springs) provides simplicity and weight minimization. Full bidirectional torque, postural accuracy, and tunable impedance under dynamic or perturbed conditions necessitate antagonistic multi-cable actuation, as does precise multi-DoF control in parallel, continuum, or tensegrity systems. Hybrid architectures, time-multiplexed drives, and switch-based mechanisms provide intermediate approaches for reducing actuator count while retaining operational flexibility, though often with reduced per-DoF bandwidth and increased control complexity (Han et al., 4 Dec 2025, Xu et al., 2024, Min et al., 31 Dec 2025, Zhang, 26 Oct 2025, Vadeyar et al., 7 Feb 2025). Integration of compliance and tension distribution algorithms into real-time control is critical for high-bandwidth, robust performance across all architectures.