Series Elastic Actuators in Robotics

• Series Elastic Actuators are actuation systems that embed a compliant element between a motor and its load to enable precise force sensing and safe interaction.
• They facilitate physical human–robot interaction and versatile manipulations by providing tunable compliance and impact absorption in various robotic applications.
• Advanced control strategies, including observer-based and adaptive methods, optimize SEA performance by balancing trade-offs among bandwidth, energy efficiency, and stability.

A Series Elastic Actuator (SEA) is an actuation system in which a compliant (elastic) element is intentionally inserted in series between a motor and its load. This design imparts controlled mechanical compliance, with substantial impact on force control fidelity, safety, robustness, and overall system performance. In modern robotics, SEAs are widely adopted for physical human–robot interaction (pHRI), rehabilitation, collaborative manipulation, legged locomotion, and high-impact dynamic tasks due to their key role in mitigating impact forces and rendering controllable impedance.

1. Fundamental Architecture and Operating Principles

An SEA typically consists of a high-bandwidth actuator (e.g., an electric or hydraulic motor) connected to a load through a mechanical elastic element, commonly realized as a linear or torsion spring, or—in emerging variants—through continuously compliant materials or fluidic transmission elements (Bendfeld et al., 11 Nov 2024, Wang et al., 2020). The defining characteristic is that torque or force output is determined by measuring the deflection of this elastic component, governed by relations such as: $$\tau_{SEA} = k \cdot (\theta_{motor} - \theta_{load})$$ where $k$ is the spring constant and $\theta_{motor}, \theta_{load}$ are the angular positions on either side of the elastic element (Koda et al., 24 Sep 2024, Lee et al., 16 Sep 2025).

This architecture fundamentally shifts the closed-loop dynamics: The actuator's output impedance is lowered, making the system more backdrivable, safer during unplanned collisions, and capable of direct force sensing through elastic deflection measurement.

Transmission Topologies

• Traditional rigid SEA: Conventional design with discrete elastic elements, often linear or torsional springs (Zou et al., 2016, Koda et al., 24 Sep 2024).
• Cable-driven SEA: Elasticity introduced via a cable–spring transmission, enabling remote actuation and flexible installation (Zou et al., 2016, Zou et al., 2017).
• Continuously Compliant Structures: Structural compliance is distributed, e.g., a flexible curved steel leg serving as the "spring" (Bendfeld et al., 11 Nov 2024).
• Fluid-based SEAs: Compliance arises from hydraulic or pneumatic elements with internal pressure sensing (Wang et al., 2020).
• Integrated miniaturized SEAs: Compact, high-resolution designs for proprioceptive sensing in dexterous or underactuated grippers (Lee et al., 16 Sep 2025).

2. Control Strategies and Trade-offs

2.1 Linear Control Architectures

SEAs require sophisticated control due to the inherent compliance, which introduces resonance modes and reduces achievable bandwidth. Control architectures include:

• Load-side feedback control: Controllers using load sensor feedback to regulate position or force at the output. While straightforward, passivity and bandwidth are tightly coupled to the spring properties; increasing gain for better tracking can violate passivity, leading to instability (Mehta et al., 21 Sep 2025).
• Actuator-side feedback control: Controllers that use actuator-side sensing (motor encoders, velocities). Such architectures allow much higher controller gains while preserving passivity, especially when combined with physical damping in the spring–damper transmission (Mehta et al., 21 Sep 2025).
• Cascaded architectures: Incorporating inner velocity and/or torque loops nested within an outer impedance or position loop is standard for achieving robust disturbance rejection and systematic gain assignment (Tosun et al., 2019, Zhao et al., 2018). In such cascade controllers, velocity-sourcing the actuator is especially beneficial for decoupling inner and outer loop dynamics.

2.2 Passivity and Safety

Passivity is critical for ensuring stable physical human–robot interaction. Systematic passivity analysis yields necessary and sufficient conditions on controller gains and physical parameters, revealing, for example, that actuator-side PD controllers with appropriate damping can be passive over a wide range of gains, decoupling performance and safety (Mehta et al., 21 Sep 2025, Tosun et al., 2019, Mengilli et al., 2020). Physical damping (either explicit in the transmission or virtual via control) extends the safe range of renderable stiffness well beyond that possible with spring-only configurations.

2.3 Advanced and Adaptive Control

• Two-Degree-of-Freedom (2-DOF) Control: Decouples reference tracking and disturbance/noise rejection by implementing separate feedforward (C₁(s)) and feedback (C₂(s)) paths, with tunable trade-offs via controller parameterization (e.g., spectral factorization) (Zou et al., 2016, Zou et al., 2017). Experiments confirm improved tracking robustness and fast disturbance recovery.
• H∞ Synthesis for Multi-band Stiffness Control: Enables the design of controllers meeting multiple, frequency-restricted norms (e.g., low-frequency torque tracking, high-frequency noise rejection) under actuator limitations and passivity constraints (Yu et al., 2019).
• Adaptive and Learning-based Control: L₁ adaptive resonance ratio control (RRC) integrates adaptive laws to guarantee transient performance across load uncertainties, reducing static error, vibration, and overshoot (Min et al., 2023). Model-free deep reinforcement learning (DRL), using on-hardware policy optimization (e.g., PPO), achieves force control in the presence of friction, stiction, and sensor noise, surpassing PID controllers in tracking precision and safety (Sambhus et al., 2023).

2.4 Observers and Sensor Fusion

Robust force estimation, beyond basic spring deflection measurement, is achieved via complementary observer structures. The Transmission Force Observer (TFOB) combines motor-side disturbance observation with deformation-based sensing to handle nonlinearities (hysteresis, backlash) and quantifiable noise, with observer tuning (Q-filter) guided by frequency-domain norm inequalities (Lee et al., 2019). Such methods enable accurate force control even in the presence of low-resolution or noisy sensors.

3. Performance Metrics, Limitations, and Design Trade-offs

3.1 Bandwidth and Torque Transmission

Elasticity imposes inherent performance limitations—chiefly reduced control bandwidth and a frequency-dependent maximum torque capability. The Maximum Torque Transmissibility (MTT) framework quantifies the frequency range (maximum torque frequency bandwidth) within which SEAs can reliably transmit the maximum continuous motor torque without violating actuator torque or velocity constraints (Lee et al., 2019). This imposes explicit, analytical trade-offs in spring stiffness, gear ratio, actuator selection, and controller gains.

3.2 Energy and Peak Power Optimization

SEA design for energy efficiency leverages non-parametric convex optimization to shape the nonlinear torque–elongation profile of the elastic element, minimizing a weighted sum of energy consumption and peak power, subject to monotonicity and actuator constraints (Bolívar et al., 2018). The framework assesses trade-offs via a convex surrogate for peak power and quadratic (convex) energy metrics. Case studies in ankle prosthesis show simultaneous reduction in energy and peak motor power, as well as expanded feasible operational regimes versus linear springs.

3.3 Mechanical Impact Robustness and Energy Reuse

The compliant element absorbs impact energy, reducing peak forces (as measured by current peaks or strain in experiments), and enables energy storage and reuse in cyclic tasks (e.g., walking, hopping, hammering). Mechanical resonance excited intentionally amplifies output velocities, allowing high-impact tasks without exceeding actuator power limits (Aiple et al., 2018, Koda et al., 24 Sep 2024). Closed-loop impedance ("Z-width") can span 50 dB in fluidic SEAs (Wang et al., 2020), demonstrating a wide range of safely renderable impedance.

3.4 Modeling of Nonlinearities and Infinite Dimensional Structure

While traditional SEAs approximate compliance with lumped parameters, emerging continuously compliant structures require model reduction (e.g., projection of continuous deformation onto a moving "spring frame" with a constant stiffness matrix) for tractable real-time control (Bendfeld et al., 11 Nov 2024). Energy-based modeling in tendon-driven hands couples elastic potential, joint torsion, and gravity for proprioceptive inference of grasp state (Lee et al., 16 Sep 2025).

4. Applications in Robotics and Human–Robot Interaction

SEAs find widespread application wherever safety, compliance, and robust force control are essential:

• Physical Human–Robot Interaction (pHRI): SEAs are central to the design of collaborative robots, exoskeletons, upper- and lower-limb prostheses, and rehabilitation devices, providing intrinsic shock tolerance and safe compliance (Tosun et al., 2019, Zhao et al., 2018).
• Dexterous Manipulation and Grasping: Integrated compact SEAs enable proprioceptive sensing and robust object interaction without external tactile or vision sensors; energy-based modeling infers contact, object stiffness, and external disturbances during underactuated grasp (Lee et al., 16 Sep 2025).
• Legged Robotics and Locomotion: Series elastic elements in legs or actuators reduce weight and allow passive energy exchange for efficient locomotion; continuously compliant legs demonstrate reduced structural complexity and successful bipedal walking (Bendfeld et al., 11 Nov 2024, Koda et al., 24 Sep 2024).
• Teleoperation and Dynamic Tasks: Harnessing mechanical resonance through SEAs allows for performance amplification in impact-rich tasks (e.g., teleoperated hammering), even with simplified feedback or moderate communication delays (Aiple et al., 2018).
• Assistive and Wearable Devices: Optimized SEA architecture, especially with tailored nonlinear springs, enhances efficiency and bandwidth in variable-demand applications such as powered ankle prostheses (Bolívar et al., 2018).

5. Open Challenges, Advanced Methodologies, and Future Directions

• Controller Synthesis under Multiple Constraints: Synthesis techniques that balance torque/stiffness tracking, passivity, disturbance attenuation, actuator limitations, and robustness to sensing noise—potentially in a frequency-banded fashion—are critical for advancing SEA utility in demanding applications (Yu et al., 2019, Zhao et al., 2018).
• Global Stability Analysis for Data-driven Control: Iterative learning and DRL methods require the establishment of global convergence and safety guarantees, especially when deployed directly on hardware under uncertainty (Banka et al., 2017, Sambhus et al., 2023).
• Role of Damping: Both physical and virtual damping elements are shown to be necessary for rendering high stiffness in two-port settings and expanding passivity margins beyond what spring-only architectures offer (Mengilli et al., 2020, Mehta et al., 21 Sep 2025). The non-intuitive, potentially adverse interaction of physical damping with integrator-based controllers demands careful analytical consideration (Tosun et al., 2019).
• Nonlinear, Continuously Compliant, and Fluidic Architectures: Emerging designs challenge standard modeling and control, requiring systematic approaches to model order reduction, state estimation, and compliant force control across distributed or infinite-dimensional elastic structures (Wang et al., 2020, Bendfeld et al., 11 Nov 2024).
• Integrated Proprioception and Sensor Fusion: Embedding high-resolution, low-latency proprioceptive sensing within SEAs, especially via tendon/cable dynamics or compact miniaturized sensors, enables robust manipulation without exteroceptive sensors (Lee et al., 16 Sep 2025).
• Design Automation: Convex multi-objective and constraint-aware optimization frameworks for elastic element design and actuator dimensioning are poised to become foundational tools (Bolívar et al., 2018).

6. Representative Control and Mechanical Configurations

Control Paradigm	Safety (Passivity Range)	Tracking Performance
Load-side proportional	High at low gain (kₑ ≤ k)	Limited by spring constant
Actuator-side PD + damping	Wide at high gain, if damped	High, largely decoupled from spring
2-DOF tracking+robustness	Tunable via parameters	Independent tuning of performance
DRL/PPO model-free	Safety relies on training regime	Learns to compensate for nonlinearities

This table summarizes the trade-offs in key control/mechanical SEA configurations as established from comparative experiments and analytical models (Mehta et al., 21 Sep 2025, Zou et al., 2016, Zou et al., 2017, Sambhus et al., 2023).

7. Summary

Series Elastic Actuators are a mature and broadly utilized technology for imparting controlled mechanical compliance, robust force sensing, and safe interaction in modern robots. Their design and implementation involve intricate trade-offs between physical safety and tracking performance, mitigated through advanced linear, adaptive, observer-based, and learning-driven control strategies. State-of-the-art research leverages both rigorous analytical frameworks (passivity, bandwidth, convex optimization) and empirical validation (hardware-in-the-loop learning, proprioception) to maximize the effectiveness of SEAs across a range of demanding robotics applications. Future developments will likely focus on synthesis methodologies that optimize performance and safety under structural and actuation constraints, adaptive control for high-uncertainty environments, and the integration of advanced sensing modalities in compact, high-performance SEA designs.