Assistive Force Design Parameters

• Assistive force design parameters are defined as the mechanical, control, and interface settings that govern the magnitude, timing, and adaptability of forces in assistive devices.
• They encompass hardware elements like springs and actuators, control gains, and user interface properties to balance task performance and user comfort.
• Optimization using adaptive control and human-in-loop methods enhances device transparency, responsiveness, and overall safety.

Assistive force design parameters define the mechanical, control, and system settings that determine the form, magnitude, timing, and adaptability of forces delivered by assistive robots and wearable devices. These parameters encompass hardware elements (springs, actuators, linkages), control gains, physical interface properties, and human–machine interaction models. Their selection and optimization is foundational to balancing user comfort, task effectiveness, safety, and device transparency in assistive technology.

1. Mechanical and Structural Parameters

The mechanical configuration establishes the feasible workspace, inherent compliance, and force-generation envelopes for assistive devices. Key physical design variables include:

• Stiffness and Compliance: The selection of spring stiffness $k$ (linear, torsional, or non-linear), which directly scales assistive torque or force for a given displacement, dominates the behavior in both passive and active orthoses. Example: adjustable coil springs in ankle-foot orthoses, $k=0.01$–$2\,\mathrm{N{\cdot}m}/\mathrm{deg}$, provide up to $12\,\mathrm{N{\cdot}m}$ assistive torque (Lora-Millan et al., 2023).
• Variable and Programmable Springs: Devices with human-selectable stiffness allow tuning $k_i$ over wide ranges, such as $6$–$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$ in variable-stiffness hip springs, with stiffness mapped by $k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$ (Mathews et al., 2023).
• Compliant Actuators: Series elasticity in SEAs is defined by $k_s$, balancing safety (low impedance) against bandwidth and torque ($k_s=8$–$k=0.01$0) (Lora-Millan et al., 2023, Qian et al., 2022). Nonlinear, reconfigurable actuators specify stiffness profiles $k=0.01$1 parameterized by geometry and pretension.
• Geometric Linkage and Moment Arms: The attachment geometry (moment arms, linkage lengths) directly scales assistive torque for a given actuator force—moment arms $k=0.01$2–$k=0.01$3 are common targets for joint efficacy (Lora-Millan et al., 2023).
• Number and Arrangement of Actuator Cells: In soft robotic actuators, parameters such as air-cell count $k=0.01$4, cell width $k=0.01$5, and material thickness set the effective force–pressure scaling, e.g., $k=0.01$6 (force $k=0.01$7 in N for pressure $k=0.01$8 in Pa and width $k=0.01$9 in m) (Sahin et al., 2022).
• Bias Point and Cell Count in Auxetic Structures: For electrically-driven auxetic actuators, the rest auxetic angle $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$0 and number of cells $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$1 enable programmable stiffness and blocked force profiles, with $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$2 and $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$3 (spring constant) scaling nonlinearly with both (Good et al., 2021).

2. Control and Modulation Parameters

Control-system settings shape the timing, magnitude, and feedback regulation of assistive forces:

• Admittance and Impedance Gains: Admittance (virtual mass $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$4, damping $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$5) and impedance (stiffness $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$6, damping $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$7) gains determine how external forces translate into device motion or resistive feedback (Zhou et al., 2019, Jr. et al., 2024, Fortuna et al., 2024). For instance, hand-exoskeleton admittance controllers showed optimal reduction in interaction force at $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$8 kg, $2\,\mathrm{N{\cdot}m}/\mathrm{deg}$9 (Zhou et al., 2019).
• Personalizable or Adaptive Gain Tuning: Preference-based optimization (PBO) or fuzzy-logic rulesets adapt $12\,\mathrm{N{\cdot}m}$0 (mass, damping) to user needs during operation (Fortuna et al., 2024, Jr. et al., 2024). Subjects optimized $12\,\mathrm{N{\cdot}m}$1 in [44.8–100] kg and $12\,\mathrm{N{\cdot}m}$2 in [40–105] N·s/m, tracked by pressure-sensor feedback.
• Bandwidth and Feedback Observer Parameters: Closed-loop force control bandwidth (e.g., target $12\,\mathrm{N{\cdot}m}$3 Hz with overshoot $12\,\mathrm{N{\cdot}m}$4) is tuned via DOB/RFOB filters using $12\,\mathrm{N{\cdot}m}$5 and $12\,\mathrm{N{\cdot}m}$6, respectively, with adaptive selection to track environment variations (Sariyildiz et al., 2019).
• Sensorless vs. Sensor-Based Feedback: Systems employ either explicit sensor feedback (EMG, FT, force sensors) or observer-based estimation (RFOB, adaptive admittance) to regulate force output (Sariyildiz et al., 2019, Wijayarathne et al., 2020).
• Switchable Passive/Active Modes: Hybrid systems dynamically engage variable-stiffness elements or clutches (e.g., electroadhesive or electromagnetic), changing $12\,\mathrm{N{\cdot}m}$7 and active force profiles in response to detected user states (Khatavkar et al., 4 Mar 2026).

3. Interaction and Interface Design

The coupling of device to user dictates comfort, efficacy, and safety:

• Interface Stiffness and Padding: The physical interface compliance, pressure distribution, and anatomical compatibility (e.g., Bowden cable routing, limb sleeves) impact both the peak force transmission and user-perceived comfort (Palacios et al., 2023, Abboodi, 8 Nov 2025).
• Anthropometric Scaling: Segmental lengths, joint positions, and user mass are parameterized for accurate force/moment computation—e.g., in adaptive arm support, link lengths $12\,\mathrm{N{\cdot}m}$8 set required compensation torques, while Jacobian conditioning affects the transparency of support (Yang et al., 2024).
• Safety Margins: Design safety is governed by allowable fabric burst strengths, actuator stall torques, and force limits for human tolerance—e.g., operation at $12\,\mathrm{N{\cdot}m}$9 burst pressure is recommended for textile actuators with factors-of-safety $k_i$0 (Nguyen et al., 2019).

4. Force Profile Scheduling and Adaptation

The generation and adaptation of force profiles is parameterized for task responsiveness and user experience:

• Phase and Timing Windows: Assistive force application is often scheduled in phase with biomechanical events (e.g., stance for push-off assistance, flexion for lifting), with actuation windows of specified duration (e.g., $k_i$1 s for jump assist) (Yoneda et al., 11 May 2026).
• Curriculum and Decay Schedules: In learning-based systems, assistive force magnitudes are scheduled under curriculum algorithms parameterized by initial bounds $k_i$2, shrink step $k_i$3, hysteresis $k_i$4, and random masking probability $k_i$5 (Cao et al., 29 Jun 2025). For example, maximum vertical assist was $k_i$6 N for walking, decayed by a factor of $k_i$7 per curriculum step.
• User-Selectable and Automated Adjustment: Devices enable real-time adjustment by the user (e.g., gear-shifter for $k_i$8 selection in hip springs, $k_i$9 s transition per index (Mathews et al., 2023)) or by automatic controller logic (fuzzy, preference-based, or weight-detection triggered).
• Total Assistance Law: In parallel active/passive systems (e.g., soft back braces), total assistive force $6$0 is parameterized as a sum: $6$1, with empirical tuning of IPAM force law coefficients and passive band stiffness (Khatavkar et al., 4 Mar 2026).

5. Quantitative Ranges and Empirical Benchmarks

Published ranges and validation data provide reference points for parameter selection across modalities:

Device/Domain	Stiffness/Compliance Range	Peak Assistive Force/Torque	Bandwidth/Fidelity
Passive ankle orthosis	$6$2–2 N·m/deg; $6$3–40 mm	4–12 N·m	n/a
Variable hip spring	$6$4–70 N·m/rad	$6$5 N·m @ $6$6	n/a
Fabric soft actuator (fSPL)	$6$7–600 MPa; $6$8–20	F_tip=$6$9–$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$0 N	Design P<0.3 MPa
Pneumatic sleeve actuator	$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$1–80mm; $70\,\mathrm{N{\cdot}m}/\mathrm{rad}$2–2; P<0.6bar	$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$3–10 N for w=50–80 mm	t_inflate <4 s
SEA for assistive robots	$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$4–133 N·m/rad, adjustable by geometry	$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$5 N·m @ $70\,\mathrm{N{\cdot}m}/\mathrm{rad}$6	$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$7–$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$8 Hz closed-loop
Admittance gain (upper-limb)	$70\,\mathrm{N{\cdot}m}/\mathrm{rad}$9–$k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$0 kg, $k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$1–$k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$2 Nm/rad	F_interact reduction 64% (vs passive)	Stable for $k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$3 at $k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$4
Exosuit (WANDER, admittance)	$k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$5–100 kg, $k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$6–105 Ns/m, $k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$7	User-optimized to comfort/jitter	Personalized via PBO
Soft sleeve actuator (SSA)	$k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$8–10mm, $k_i = k_S \left(\frac{x_i}{l+d-x_i}\right)^2$9–1.2 mm, $k_s$0–30°	$k_s$1–$k_s$2 N (P=20–80kPa)	Response linear <80kPa
Bowden cable hand exoskeleton	n/a	Not specified (functional GRT: 1→11)	Operator-tuned via feedback

6. Optimization and Personalization Methods

Optimization across the above parameter space leverages algorithmic and empirical approaches:

• Dynamic System Optimization: Explicit human–robot models parameterized by link lengths, joint orientations, and force application points are solved via PSO (particle swarm optimization), with cost functions including user joint torque, actuator effort, and geometric constraints (Moosavian et al., 2019).
• Human-in-the-Loop and Preference-Based Optimization: Experimentally, the use of human preference feedback directly guides mass/damping parameter selection, outperforming generic literature values in both objective (energy, jerk) and subjective (NASA-TLX) outcome measures (Fortuna et al., 2024).
• Surrogate Models and Rule-Encoded Tuning: Fuzzy logic controllers encode expert-based rules for real-time adjustment of proportional and damping gains in exoskeleton controllers; hyperparameters (membership function centers, gain increments, output bounds) are pre-defined for stability and generalizability (Jr. et al., 2024).
• Adaptive and Recursive Estimation: On-line recursive identification of environmental parameters $k_s$3 supports real-time update of admittance control gains for safe assistive force modulation on compliant and time-varying surfaces (Wijayarathne et al., 2020).

7. Task-Specific and Modality-Dependent Parameter Selection

Assistive force parameterization is modality- and task-dependent:

• Gait-Phase Synchronization: For ambulatory devices, assistive force is maximized in late-stance plantarflexion and dorsiflexion (42–55% and 70–90% gait, respectively) (Lora-Millan et al., 2023).
• User Category: Elderly users benefit from gentle assistive profiles (low $k_s$4), whereas high-performance or athletic users require higher stiffness and torque (Mathews et al., 2023).
• Upper Limb vs. Lower Limb: Parameters such as required support force, bandwidth, and compliance differ substantially between arm, hand, and leg devices, driven by respective segment mass, joint torques, and task kinematics (Yang et al., 2024).
• Robotic Learning Contexts: In RL-driven curriculum learning, force schedule hyperparameters—initial force bounds, decay rate, success thresholds—are chosen to facilitate progressive skill autonomy, with robustness to ±20% magnitude and window variation (Cao et al., 29 Jun 2025, Yoneda et al., 11 May 2026).

Across all categories, the concurrent consideration of mechanical, control, interaction, and scheduling parameters—and their adaptation to both user and environment—constitutes the modern paradigm in assistive-force design. Each parameter is chosen and tuned in the context of physiologic safety, task dynamics, and empirical user feedback, aiming for high transparency, efficacy, and stability.