Antagonistic Cable Actuation in Robotics

• Antagonistic cable actuation is a mechanical paradigm where paired cables are differentially tensioned to modulate joint torque and stiffness for precise control.
• It utilizes diverse architectures—two-motor, single-motor switch-based, and rolling-contact designs—to optimize slack management and transmission efficiency.
• Applications in soft exosuits, anthropomorphic hands, and continuum robots demonstrate its benefits in compliant actuation, torque-stiffness decoupling, and energy-efficient control.

Antagonistic cable actuation is a mechanical and control paradigm in which a pair of cables—configured in an agonist/antagonist arrangement—impart joint torque or continuous deformation to a system. By differentially tensioning the two cables, a net moment or distributed force is generated, with the degree of antagonism (i.e., simultaneous tension in both cables) allowing for modulation of system stiffness, compliance, and equilibrium positioning. This paradigm is widely adopted in soft exosuits, tendon-driven exoskeletons, anthropomorphic hands, and continuum robots, offering remote actuation, high force-to-weight ratio, and inherent compliance. Antagonistic configurations are especially significant for cable-driven robotic systems, where slack management, torque–stiffness decoupling, and actuation bandwidth critically affect practical performance.

1. Mechanical Architectures

Antagonistic cable actuation can be implemented in multiple architectures, ranging from double-motor synchronization to single-motor switch-based designs and specialized rolling-contact joint layouts.

• Two-Motor Antagonism: Conventional exoskeletons and continuum robots often utilize two electric motors per DoF, each winding a cable that applies force in opposing directions. The flexion ("lead") motor provides net positive tension, while the extension ("follower") maintains minimal opposing tension to prevent slack. The net joint torque is given by

$\tau = r (T_{fl} - T_{ex})$

where $r$ is pulley radius; $T_{fl}$ and $T_{ex}$ are flexion/extension cable tensions (Chang et al., 2021).

• Single-Motor Switch-Based Actuation: Actuator-count reduction can be achieved through mechanical switches, where a single brushless DC motor, interfaced with a planetary "switch gear", alternately drives the agonist or antagonist spool. A state variable $s\in\{-1,0,+1\}$ denotes which spool is engaged. Engaging one spool winds the corresponding cable while maintaining spring tension on the idle cable to avoid slack. Switching latency is a critical trade-off; experiments report ≈300 ms per direction change for a typical Maxon EC-45 Flat drive (Vadeyar et al., 7 Feb 2025).
• Rolling Contact Joint (RCJ) Design: High-dexterity applications, such as anthropomorphic hands, deploy rolling-contact joints shaped so that the sum of cable-length variations for an antagonistic pair remains near-zero over full RoM. Each DoF is actuated by a single motor directly winding both flexor and extensor cables with built-in geometrical antagonism, strictly avoiding the need for inter-motor synchronization (Min et al., 31 Dec 2025).

2. Dynamic Modeling and Transmission Characteristics

Antagonistic cable systems are modeled by integrating cable tension/length relationships, series compliance, frictional losses, and joint/inertial parameters:

• Cable–Spring–Joint Model: Each cable incorporates a series spring (stiffness $k$), and path length transforms any relative joint–motor displacement into incremental cable force:

$T_i(t) = T_0 + k [R_i q_m - r_{i}(q)]$

with $T_0$ the pretension, $R_i$ spool radius, $q_m$ motor rotation, $r_{i}(q)$ effective cable path as function of joint angle (Yadav et al., 2023).

• Friction and Sheath Dynamics: Sheath friction is modeled via the capstan equation,

$T_{out} = T_{in} \exp(-\mu \kappa_{eff}),$

where $\mu$ is the friction coefficient ($\approx$0.07), $\kappa_{eff}$ is the total bending angle in the sheath, and $T_{in}/T_{out}$ are input/output cable tensions (Yadav et al., 2023, Min et al., 31 Dec 2025).

• Joint Transmission Efficiency: For coaxial antagonistic spools, the transmission efficiency

$$\eta(\theta) = \frac{J_f\,T_a + J_e\,T_b}{R_a\,T_a - R_b\,T_b}$$

(with $J_{f/e}$ joint Jacobians, $T_{a/b}$ tensions) can be maximized through spool geometry selection and friction minimization (Yadav et al., 2023).

• Redundant Energy Formulations: For continuum robots, the actuation–space energy functional

$$\Pi[\theta] = \int_0^L \tfrac12 EI \left(\frac{d\theta}{ds}\right)^2 ds - (F_1 \Delta l_1 + F_2 \Delta l_2)$$

yields closed-form curvature and tip position relations, supporting real-time kinematic modeling and control (Wu et al., 4 Sep 2025).

3. Control Strategies and Slack Elimination

Cable antagonism necessitates robust control to manage tension balance, slack prevention, and stability under switching:

• Hierarchical Control (Exoskeletons): A two-layer approach employs joint-level robust tracking (e.g., high-gain, Lyapunov-based) combined with sliding-mode motor synchronization. Role assignment (lead/follower) is switched based on control sign, with average dwell time enforced to avoid chattering and reintroduction of slack. Exponential convergence of synchronization errors is proven via Lyapunov analysis (Chang et al., 2021).
• Single-Motor Control with Series Compliance: For soft exosuit systems, pretension and series-spring design are optimized to ensure $T_{min}>0$ throughout motion,

$T_0 \geq k |R_a - R_b| \Delta \theta_{max}$

with pretension $T_0$ set just above the worst-case dynamic swing and typical $k=2-3$ kN/m. Fixed spool radii ratios $R_e/R_f\approx0.85-0.9$ eliminate slack up to substantial external loads (Yadav et al., 2023).

• Position and Stiffness Control: In antagonistic tendon-driven continuum robots, passivity-based controllers employ port-Hamiltonian formalism, input transformations, and variable bias to independently modulate position and transverse stiffness. By maintaining $u_1,u_2\geq 0$, non-negative tension constraints are always enforced (Yi et al., 2023).

4. Torque–Stiffness Decoupling and Impedance Modulation

A defining objective in antagonistic actuation is plant-level decoupled control of torque and stiffness, emulating biological muscle behavior:

• Co-contraction/Bias Coordinates: Activation inputs are transformed into bias/co-contraction coordinates $b, c$, where net torque depends on $b = (\alpha_1-\alpha_2)/2$ and stiffness on $c = (\alpha_1+\alpha_2)/2$:
  • Torque: $T(\alpha) = r(F_1-F_2)$
  • Incremental stiffness: $$K_{tot} = r \xi [K_{1,step} + K_{2,step}] + K_j + K_g(\theta)$$
• Controller Architecture: Feedforward solution using analytical inverse dynamics is combined with PI feedback in $(b,c)$, enabling independent specification of $T_{des}$ and $K_{des}$ with demonstrated stability and disturbance rejection. Application to cable actuation is straightforward after incorporating cable compliance/friction, with robustness requiring adequate preload to avoid slack and anti-windup to mitigate friction-hysteresis (Kazemipour et al., 12 Nov 2025).
• Experimental Validation: Fast dynamic responses (settling time $t_{90}<10$ ms on soft surfaces) and stability are shown in antagonist-mimetic soft muscle simulation, with performance metrics such as 81% force reduction under stiff contact (Kazemipour et al., 12 Nov 2025).

5. Design Trade-Offs, Optimization, and Practical Considerations

Antagonistic cable actuation involves multiple design and operational trade-offs:

• Actuator Count vs. Latency: Single-motor switch-based systems halve actuator count per DoF but incur direction switch latency ($\sim$300 ms), acceptable for low-frequency ADL tasks but insufficient for dynamic activities. Future work aims for $<100$ ms switching via clutches or magnetic latches (Vadeyar et al., 7 Feb 2025).
• Pretension/Stiffness Range: Increasing pretension augments available stiffness but risks increased actuator load, cable wear, or buckling. Spring constants and spool ratios must be selected to balance low travel with minimal tension ripple (Yadav et al., 2023).
• Slack Control: Series compliance, dwell-time constrained switching, and geometric coordination (e.g., RCJ) ensure cables remain tensioned throughout operation (Chang et al., 2021, Min et al., 31 Dec 2025).
• Friction Management: For Bowden cable systems, large bend radii and periodic guides minimize $\mu \Theta$, yielding low frictional loss (<10%), though friction and hysteresis remain a limiting factor at low tensions and rapid motion (Min et al., 31 Dec 2025).

6. Application Domains and Performance Metrics

Antagonistic cable actuation underpins a broad range of mechatronic systems, with quantitative metrics guiding design decisions:

Domain/Device	Distinctive Features	Quantitative Performance
Soft Exosuits	Single-motor switch actuation, arbitrary path geometry	56 g mechanism, 298 ms switch latency (Vadeyar et al., 7 Feb 2025)
Upper-Limb Exosuits	Series spring, coaxial spools	Slack-free with $T_0=100-200$ N, $k=2-3$ kN/m (Yadav et al., 2023)
Anthropomorphic Hands	Rolling-contact joint, single motor/DoF	236 g distal mass, $>$18 N fingertip force, 25 kg payload (Min et al., 31 Dec 2025)
Lower-Limb Exoskeletons	Dual-motor, sliding-mode synchronization	$<2^\circ$ joint tracking error (Chang et al., 2021)
Continuum Robots	Energy-based port-Hamiltonian or LASEM	$K_T$ affine in pretension, $<$1.5 s transient, $<$0.2$^\circ$ RMS error (Yi et al., 2023, Wu et al., 4 Sep 2025)

Dexterous manipulation, high-speed position tracking, high payload, and compliance modulation have been demonstrated (Min et al., 31 Dec 2025, Wu et al., 4 Sep 2025, Yi et al., 2023).

7. Future Directions

Key open areas for antagonistic cable actuation include:

• Miniaturization and inertia reduction in switch-based mechanisms for faster switching (Vadeyar et al., 7 Feb 2025).
• Integration of variable-stiffness elements (e.g., antagonistic dual-cable springs, jamming layers) for simultaneous torque and impedance control (Kazemipour et al., 12 Nov 2025, Yi et al., 2023).
• Multi-DoF exosuit architecture studies to quantify mass/cost/comfort/control bandwidth trade-offs at scale (Vadeyar et al., 7 Feb 2025).
• Dynamic closed-loop stiffness profiling during human movement for adaptive assistance (Yadav et al., 2023).
• Extending analytical inverse dynamic controllers with full modeling of cable friction, elasticity, and real-time feedback for robust, high-bandwidth torque–stiffness decoupling (Kazemipour et al., 12 Nov 2025).

Antagonistic cable actuation remains central to wearable robotics, compliant manipulation, and continuum robot development, driven by continuing innovation in mechanism design, mathematical modeling, and real-time control theory.