The automation of finishing processes like grinding and polishing represents a significant challenge and opportunity within industrial robotics. While these tasks are crucial for improving part surface quality and performance, they remain predominantly manual, suffering from issues of low efficiency, inconsistent quality, and high labor costs. Industrial robots offer a compelling solution, but their application hinges on the precise control of the contact force between the tool and the workpiece. Excessive or insufficient force leads to over-polishing or under-polishing, resulting in uneven surface finishes. Traditional high-speed, high-payload industrial robots are not inherently designed for sensitive force interaction. A prevalent and effective solution is to delegate the force control task to a specialized end effector attached to the robot’s wrist. This approach decouples the problem: the robot handles gross positional guidance with relaxed precision requirements, while the end effector manages the delicate force interaction. This not only improves force control accuracy and dynamic response but also reduces inertial shocks transmitted to the robot arm. My research focuses on the design and control of a novel end effector specifically for this purpose. This document details the motivation, mechanical design, control strategy, and experimental validation of this pneumatic-electric hybrid force-controlled end effector.
My primary design goal was to create an end effector that combines high bandwidth and precision force control with inherent compliance and damping to handle the hard contact environments typical of grinding and polishing. Many existing end effectors utilize either purely electric (e.g., voice coil actuators) or purely pneumatic actuation. Electric actuators offer excellent precision and frequency response but can transmit high-frequency vibrations and lack passive compliance. Pneumatic actuators provide good damping and compliance but often suffer from slower response times and nonlinear behavior due to air compressibility. I conceived a hybrid architecture to synergize the strengths of both. The core idea is a parallel connection of three force-generating elements between the moving platform (which holds the tool) and the base platform (attached to the robot): a voice coil motor (VCM) for active, high-fidelity force control; an air spring for passive restoring force and vibration damping; and a tension spring to increase the overall system stiffness, which is beneficial for response speed. This hybrid configuration aims to deliver a system that is precise, fast, well-damped, compact, and capable of handling significant process forces.
The detailed mechanical design of the end effector is shown in the figure above. The main structural components are the upper bracket (fixed to the base/platform connected to the robot), the lower bracket, and a moving platform in between. Three linear guide blocks, evenly distributed circumferentially, connect the upper and lower brackets, allowing for precise axial motion of the entire moving assembly. The voice coil motor and the tension spring are mounted symmetrically on opposite sides. One end of each is fixed to the lower bracket, and the other end is connected to the moving platform. The air spring is positioned along the central axis, with its upper end attached to the upper bracket and its lower end connected to the moving platform. This layout effectively creates a parallel mechanical connection between the VCM, air spring, and tension spring. The entire end effector is remarkably compact, with a maximum diameter of 128 mm and a total mass of approximately 5.5 kg. The sleeve-type air spring was chosen for its high load capacity and excellent shock absorption characteristics, which are vital for suppressing vibrations during machining. When maintained at a constant, low pressure, its output force remains nearly constant over its stroke, providing a stable passive force baseline. The voice coil motor is a direct-drive actuator, meaning it produces linear motion without any transmission elements like ball screws or gears. This eliminates backlash and friction associated with such mechanisms, granting the end effector high bandwidth, precision, and a compact form factor. The tension spring, while simple, plays a crucial role in increasing the system’s mechanical stiffness, which directly contributes to a higher control bandwidth.
Given the emphasis on lightweighting for a robot-mounted end effector, both the upper and lower brackets were designed with extensive hollowed-out, lattice structures. It was imperative to verify that this lightweight design did not compromise the structural stiffness, which is critical for force control fidelity and overall robustness. I performed a finite element analysis (FEA) to compare the deformation under load between a solid bracket design and the proposed hollow design. The model was simplified to focus on key geometric features, material was set to aluminum alloy, and a concentrated radial force of 20 N was applied to the moving platform surface to simulate tangential process forces. The results were insightful.
| Structural Type | Mass (kg) | Deformation under 20N (mm) | Deformation under 50N (mm) | Deformation under 100N (mm) |
|---|---|---|---|---|
| Solid Structure | 1.771 | 0.0012 | 0.0030 | 0.0060 |
| Hollow Structure | 1.137 | 0.0049 | 0.0122 | 0.0245 |
The analysis confirmed that while the hollow structure deformed more than the solid one (approximately 0.0245 mm vs. 0.0060 mm under a 100 N load), the absolute deformation was still very small. According to common mechanical design principles for such force-interaction devices, the rigid displacement of primary load-bearing components should generally be less than 0.3 mm. The calculated 0.0245 mm is well within this limit, confirming adequate stiffness. Furthermore, the hollow design achieved a mass reduction of about 35%, a significant gain for a robot end effector where lower inertia is always desirable. This validated the structural integrity of the lightweight design.
To develop an effective control strategy, a dynamic model of the end effector is essential. Considering the motion direction (tool approaching the workpiece) as positive, the forces acting on the moving mass include the air spring force ($$F_a$$), the voice coil motor force ($$F_v$$), the contact force from the workpiece ($$F_c$$), the tension spring force ($$F_s$$), system friction ($$f$$), damping ($$c\dot{x}$$), and the component of gravity ($$mg\cos\theta$$). Applying Newton’s second law yields:
$$ m\ddot{x} = F_a + mg\cos\theta – F_v – F_c – F_s – f – c\dot{x} $$
From this, the expression for the actual contact force, which is the variable we wish to control, can be derived:
$$ F_c = F_a + mg\cos\theta – F_v – F_s – f – c\dot{x} – m\ddot{x} $$
The voice coil motor force is governed by the Lorentz force principle: $$F_v = k_e i$$, where $$k_e$$ is the force constant and $$i$$ is the coil current. The electrical dynamics of the VCM can be modeled simply as $$U = Ri + L\frac{di}{dt} + k_e \dot{x}$$, where $$U$$ is the input voltage, $$R$$ is the resistance, and $$L$$ is the inductance. For the operating speeds of this end effector, the back-EMF term ($$k_e \dot{x}$$) is relatively small and can be neglected in the initial controller design. The resulting transfer function from voltage to force is:
$$ G_1(s) = \frac{F_v(s)}{U(s)} = \frac{k_e}{Ls + R} $$
The choice of control methodology is pivotal for the end effector’s performance. Direct force control, where the force error directly commands the VCM current, is sensitive to model inaccuracies, friction, and external disturbances. In a hard contact environment with an imperfect dynamic model, this can lead to instability or poor tracking accuracy. Therefore, I adopted an indirect force control strategy based on admittance control. This method does not directly command a force from the VCM. Instead, it uses the force error to generate a position command for the VCM. By moving the end effector’s tool against the environment, the actual contact force is altered until it matches the desired force. This approach is more robust to model uncertainties and environmental stiffness variations.
The implemented control structure features an outer force loop and an inner motion loop. The outer loop is a PID controller that takes the desired force ($$F_r$$) and the measured force ($$F_c$$) as input and outputs a desired position ($$x_d$$). The PID law is given by:
$$ u(t) = K_p e(t) + K_i \int_{0}^{t} e(\tau) d\tau + K_d \frac{de(t)}{dt} $$
where $$e(t) = F_r(t) – F_c(t)$$ is the force error and $$u(t)$$ is the controller output, which maps to $$x_d$$.
This desired position ($$x_d$$) is then fed into a cascaded inner motion control loop embedded within the VCM driver. This inner loop itself consists of nested position, velocity, and current (torque) loops, each typically employing a PI controller. This cascade structure allows the inner loops to quickly reject disturbances like friction and forces from the passive springs ($$F_a$$, $$F_s$$), providing a well-behaved position response for the outer force loop to command. The overall control law for the end effector thus cleverly leverages the fast, precise motion control of the VCM to regulate contact force indirectly, enhancing stability in hard-contact scenarios.
To validate the design and control performance of the hybrid end effector, a comprehensive experimental testbed was established. The setup consists of the end effector mounted on a fixed frame, with its tool contacting a rigid load cell to simulate a hard workpiece. The pneumatic system includes an air compressor, filter, regulator, and a large-volume auxiliary chamber connected to the air spring. This auxiliary chamber is critical; its volume is much larger than the air spring’s, ensuring that the internal pressure remains nearly constant during the spring’s deformation, effectively creating a constant-force spring element without the need for a fast but expensive servo valve. The air spring was pressurized to 1 bar and maintained at constant pressure for all experiments. The electrical system comprises a PC running the outer-loop control algorithm, a data acquisition system (DAQ), the VCM driver (housing the inner motion loops), and a force sensor. The control scheme was implemented with a 2 ms sampling period.
The first test involved step force tracking to evaluate transient response and steady-state accuracy. The desired force was commanded to change from 10 N to 20 N and back to 10 N. The results were excellent. The end effector achieved a rapid response time of approximately 70 ms with no observable overshoot. The absence of overshoot is particularly important in finishing applications to prevent tool gouging or surface damage upon initial contact. The steady-state force control accuracy was within ±0.2 N, demonstrating high precision.
| Performance Metric | Experimental Result |
|---|---|
| Step Response Time | ~70 ms |
| Steady-State Force Accuracy | ±0.2 N |
| Continuous Tracking Error (1Hz sine) | < ±1.0 N |
| Control Bandwidth (-3dB) | 20 Hz |
The second test assessed continuous force tracking capability. The desired force was a sinusoidal signal with a 15 N bias, 5 N amplitude, and a frequency of 1 Hz. The end effector tracked the reference signal faithfully. The amplitude ratio between the actual and desired force was close to unity, and the phase lag was minimal. The tracking error remained bounded within ±1.0 N, varying sinusoidally with the reference, which indicates a linear and well-controlled system response.
Finally, a frequency sweep was conducted to determine the control bandwidth of the force-controlled system. The amplitude ratio and phase shift were measured across a range of frequencies. The bandwidth, defined as the frequency at which the output magnitude drops to -3 dB (about 0.707) of the input magnitude, was found to be 20 Hz. At this frequency, the phase margin was approximately 71°, indicating a robust and stable control system. This bandwidth is significantly higher than that typically achieved by purely pneumatic or simpler electric end effectors, and it is ample for most grinding and polishing processes where force variations are relatively low-frequency.
In conclusion, the research presented here successfully details the development of a high-performance pneumatic-electric hybrid force-controlled end effector. The mechanical design ingeniously combines a voice coil motor, an air spring, and a tension spring in parallel within a lightweight, stiff structure. The proposed indirect force control strategy, based on admittance control with an outer PID loop and an inner cascaded motion loop, proved to be highly effective. It provides robustness against model uncertainties and the hard contact environment, a critical requirement for finishing applications. Experimental results validate that the end effector possesses a compelling combination of fast response (~70 ms), high steady-state accuracy (±0.2 N), good continuous tracking, and a wide control bandwidth (20 Hz). This combination of attributes, realized in a compact and robust package, makes this hybrid end effector a highly promising solution for enabling industrial robots to perform precise and reliable automated grinding and polishing tasks. The performance of this end effector marks a substantial step forward in the practical implementation of force-controlled robotic finishing.