Force/Motion Actuator Architecture

• Force/Motion Actuator is a dual-input, single-output electromechanical system that employs parallel actuation paths to decouple force and motion for enhanced performance.
• It uses differential gear systems, such as planetary or star-compound arrangements, to achieve distinct high-force and high-speed modes enabling precise control.
• The architecture is applied in various fields like patient-assist robotics and industrial automation, where advanced control strategies ensure safety and efficiency.

A Force/Motion Actuator (FMA) is a dual-input, single-output electromechanical actuator architecture that leverages parallel actuation paths with distinct transmission characteristics to decouple and optimize force and motion capabilities at the output. By integrating two motors geared at substantially different ratios—one providing high-speed, low-torque motion and the other yielding low-speed, high-torque force generation—FMAs enable selective and simultaneous force–motion control while expanding the attainable force–velocity performance envelope beyond conventional single-motor or clutch-based systems. This architecture is realized through differential gear trains, most recently exemplified by planetary or star-compound arrangements, and is at the core of performance-critical applications such as patient-assist robots, industrial automation, and systems requiring programmable endpoint impedance (Lalonde et al., 2024, Rabindran, 2014).

1. Mechanical and Transmission Architecture

The FMA comprises two brushless-DC electric motors that both drive a common output shaft or drum via parallel gear-reduction paths and a differential gear arrangement. Typically, the "motion side" is routed through a high-ratio (e.g., 600:1 or 150:1) gear stage, granting high stiffness for fast, low-torque movements. The "force side" uses a substantially lower-ratio (e.g., 18:1) reduction, rendering it backdrivable and optimized for slow, high-force tasks. In ceiling-robot implementations, a planetary differential is used with the high-force motor acting on the planet-carrier and the high-speed motor acting on an independent sun or ring gear; output is rigidly attached to the differential carrier (see Figure 1 in (Lalonde et al., 2024), Fig 5-4 in (Rabindran, 2014)).

A spring-loaded carbon-fiber disk brake is employed on the high-speed motor path to lock or slip during dynamic transitions, notably for rapid downshifting and energy dissipation in fall-prevention scenarios (Lalonde et al., 2024). This switching mechanism enables discrete high-force and high-speed operating modes as well as mode-blending under redundant actuation.

Branch	Gear Ratio	Motor Role	Main Function
High-Force	600:1	EM1 (heavy)	Slow lifting, transfer
High-Speed	18:1	EM2 (light)	Fast, assistive motion

The mechanical architecture achieves a built-in 14:1 or greater scaling between force and motion input effectiveness, attributed to the star-compound or planetary gear geometry (Rabindran, 2014). The result is that the force path is approximately 14 times more effective in torque transfer but operates at one-fourteenth the speed of the motion path. This division underpins the selective flow of force and motion attributes to the output.

2. Kinematics and Dynamic Modeling

The FMA's parallel actuation is described kinematically by a linear combination of motor speeds mapped to output speed via gear ratios:

$\omega_{out} = g_1 \omega_1 + g_2 \omega_2$

where $g_1, g_2$ are determined by planetary or hypocyclic reductions. For the canonical star-compound case:

$$g_1 = \frac{g_{hypo}}{1 + g_{hypo}} \approx 0.0073,\quad g_2 \approx -0.1011$$

and $|\frac{g_2}{g_1}| \approx 14$ (Rabindran, 2014).

The equations of motion for a load with inertia $I_{out}$ subject to gravity, Coriolis, and friction are:

$$I_{out} \ddot \theta + V(\theta, \dot \theta) + F_{fric}(\dot \theta) + G(\theta) = \tau_1 + \tau_2 + \tau_{ext}$$

and the parallel prime-mover system:

$$I_M \ddot \theta_M + B_M \dot \theta_M + F_M(\dot \theta_M) + [G]\left(\tau_1 + \tau_2 + \tau_{ext}\right) = K_M V_{in}$$

with $[G]=[g_1, g_2]$ (Rabindran, 2014).

Recent implementations employ a lumped state-space model for translational force-actuated drums, leveraging inertia and damping reflection through the parallel reductions. The full-dynamics 2-DOF system is:

$$\dot x = -H^{-1}Dx + H^{-1}B[u], \quad x = [v_0; \omega_1]$$

with $$u = [\tau_1; \tau_2 - \tau_B\,\mathrm{sign}(\omega_2); F_m]$$ and matrices $H, D, B$ detailed in (Lalonde et al., 2024).

Such modeling enables accurate prediction of mode-dependent performance. For instance, reflected inertia at the drum output is dramatically mode-dependent: $\approx 3427$ kg·m² in high-force mode (brake locked), $\approx 8.5$ kg·m² in high-speed mode (brake released) (Lalonde et al., 2024).

3. Control Architecture and Torque Allocation

Control in FMAs is realized through dual-loop strategies:

• Inner current/velocity loops operate at high frequency (e.g., 250 Hz).
• Outer force or velocity controllers allocate torque demand between the motors.

Multiple allocation laws have been evaluated: open-loop current control, friction-compensation with or without EM1 offset, closed-loop PID on force feedback, and disturbance observer (DOB) structures (Lalonde et al., 2024). In force-assist (high-speed) mode, EM2 provides the primary output torque, with EM1 optionally commanded at a constant offset to mitigate stick-slip via nullspace control.

Friction is modeled using:

$$\tau_f(\omega_2) = (b|\omega_2| + c)\,\tanh(\omega_2)$$

Fall prevention exploits brake engagement coordinated with dynamic torque commands. The brake friction torque is set such that:

$\tau_B = \frac{r}{R_2} m(g + a_d)$

where $a_d$ is the desired deceleration, and the assist motor supplies:

$\tau_2 = K_p\left(\int a_d\,dt - v_0\right)$

ensuring both rapid energy absorption and trajectory regulation in critical events (Lalonde et al., 2024).

4. Performance Envelope and Experimental Metrics

The dual-path architecture produces a torque–speed envelope partitioned across operating regions:

• High-Force (HF): Maximum continuous output force 318 kgf at $v_0 = 0.05$ m/s.
• High-Speed (HS): Nominal assist force 59 kgf at $v_0 = 0.55$ m/s, with peak up to 34 m/s (Lalonde et al., 2024).
• Force-Tracking Error: 7.8% at low speed under friction-compensation/offset strategies, PID and DOB solutions achieving ≈15–35 N absolute error depending on task (Lalonde et al., 2024).
• Disturbance Rejection: Under simulated torque disturbances (<4 Nm), velocity tracking error remains <5%; with high-point loads, tracking drops to ≈84% (Rabindran, 2014).

Kinetic energy partitioning is asymmetric: the motion side routinely carries ≈83% of kinetic energy except under force-dominated or disturbance-intensive tasks (force side workload up to 20× the motion side in those phases) (Rabindran, 2014).

Torque–speed mapping illustrates actuator capabilities, with "conservative," "enhanced," and "risky" regions identified based on simulated surges and overloads (Rabindran, 2014).

Fall-prevention experiments demonstrate safety performance, with measured stopping distances below a 0.40 m bound for subject masses ≤90 kg at $a_d = 1$ m/s² (Lalonde et al., 2024).

5. Design Choices, Scaling, and Context

The FMA's principal design trade-off is embodied in the selection of gear ratio disparity, typically 10:1 to 15:1, between force and motion channels. This scaling ensures fast tasks favor the high-speed motor, while force-sensitive or disturbance rejection tasks are dominated by the low-speed, torque-optimized branch (Rabindran, 2014). The mechanical differential enforces summation at the output, such that any arbitrary trajectory can be followed subject to the mapped dual-input constraints.

Compared to single-motor or clutch-based dual-speed approaches, the dual-motor FMA achieves continuous range-of-motion, seamless transitions, and a superior mass/inertia trade-off (Table 1 and Figure 2 in (Lalonde et al., 2024)). The architecture supports backdrivability and high-fidelity force control, which are essential for assist-as-needed applications and contact-intensive manufacturing (Rabindran, 2014).

6. Application Domains and Broader Relevance

The FMA paradigm was originally proposed for expanding performance in intelligent machines targeting contact-rich tasks (e.g., deburring, fine surface finishing) and has since been employed in human augmentation (wearable robots), rehabilitation (body-weight support, overground gait trainers), and industrial automation (Rabindran, 2014, Lalonde et al., 2024). In ceiling-robot systems for patient mobility, the FMA achieves the dual objectives of high-torque for transfer and high-speed, direct-force assistance for fall prevention and mobility support. The core concept is readily transferable to any application requiring distinct operating points and programmable impedance across multiple force–motion domains while ensuring actuator-level disturbance rejection and sensitive force tracking.

A plausible implication is that further advances in criteria-based decision software and real-time control may further harness the FMA’s selective flow of force and motion, enabling broader deployment in dynamic contact environments and adaptable automation platforms.