The manufacturing industry, particularly in sectors like shipbuilding, faces significant challenges in finishing operations such as grinding and polishing. Traditional methods, heavily reliant on manual labor or inflexible abrasive belt systems, struggle with issues of low efficiency, inconsistent quality, high labor intensity, and environmental pollution from dust. The advent of intelligent manufacturing demands more automated, precise, and flexible solutions. Robotic systems offer a promising path forward due to their inherent flexibility, high degree of automation, and efficiency. However, most existing industrial robots excel in non-contact tasks like painting, welding, and material handling. For continuous contact operations—essential for achieving high-quality surface finishes on complex contours like ship hulls, propellers, or engine components—robots must not only control the tool’s trajectory and velocity but also precisely regulate the contact force normal to the workpiece surface. This requirement leads to the concept of hybrid force/position control.
Force control in robotics can be implemented through two primary approaches: direct and indirect control. Direct force control involves sophisticated torque control at the robot’s joints, necessitating an accurate dynamic model and robust, real-time control algorithms. This method is often suitable for newer generations of lightweight robots. Indirect force control, on the other hand, employs an add-on, force-controlled end-effector. This approach naturally decouples the force and position control problems; the robot manages the gross positioning and path following, while the dedicated end-effector handles the delicate force regulation. Although it adds to the system cost, the indirect method offers superior static and dynamic force control characteristics and greater generality, making it highly suitable for heavy-duty robots used in demanding applications like shipyard manufacturing. This article focuses on the development and analysis of such a device.
Existing solutions, often based solely on pneumatic compliance, suffer from limitations such as low control accuracy, slow response, and poor resistance to load disturbances. To overcome these drawbacks, I propose a novel pneumoelectric (pneumatic-electric) hybrid force-controlled end-effector designed specifically for robotic grinding and polishing tasks in marine applications. This end-effector synergistically combines the high force-to-mass ratio and excellent impact resistance of pneumatic systems with the high precision, fast response, and superior controllability of electric direct-drive technology. The core innovation lies in the coordinated control of the pneumatic force from an asymmetric cylinder and the electromagnetic force from a high-thrust permanent magnet linear synchronous motor (PMLSM). An adaptive variable-parameter PID controller is employed to achieve real-time compensation and precise regulation of the tool-workpiece contact force. Through comprehensive modeling and numerical simulation of the pneumatic system, PMLSM system, environmental workpiece interaction, and the control strategy, this study investigates the end-effector’s response to load fluctuations and its resistance to load shocks, demonstrating significant performance improvements over purely pneumatic systems.
System Overview and Working Principle
Mechanical System Design
The proposed pneumoelectric end-effector is designed as a parallel connection of a pneumatic actuator and an electric linear motor. This configuration allows both subsystems to contribute to the total output force (Fout = Fpneu + Felec) while undergoing identical displacement (Sout = Spneu = Selec). The primary mechanical components include:
- Asymmetric Single-Rod Cylinder: Provides the primary, high-force actuation. The rod-side chamber pressure is often set to a constant value, while the piston-side chamber pressure is controlled.
- Permanent Magnet Linear Synchronous Motor (PMLSM): Provides fast, precise force compensation and adjustment. Its mover is connected to the piston rod of the cylinder.
- Proportional Valve: Typically a proportional pressure-reducing valve, used to accurately regulate the pressure in the cylinder’s piston-side chamber.
- Force Sensor: Mounted at the tool interface to provide direct feedback of the contact force.
- Ball Spline: Used to prevent rotation of the moving assembly while allowing linear motion.
- Upper and Lower Flanges: Interface for mounting the end-effector to the robot wrist and the grinding/polishing tool, respectively.
The parallel arrangement ensures that the robust pneumatic system bears the majority of the steady-state force, reducing the thermal load on the electric motor. The PMLSM acts as a high-bandwidth “trim” actuator, making fine, rapid adjustments to counteract disturbances and track force commands precisely.
Control System Architecture
The control system for this hybrid end-effector integrates both pneumatic and electric drives.
Pneumatic Subsystem: This loop consists of the asymmetric cylinder, an electro-pneumatic proportional pressure valve, a pressure source (compressor and tank), and filters. The control signal to the proportional valve adjusts the pressure in the cylinder’s cap-end chamber (pa), thereby controlling the pneumatic force output.
Electric Subsystem: This is designed as a compact, drive-control integrated unit based on an ARM+DSP/FPGA+IPM architecture with CAN bus communication. This integration reduces size, power consumption, and heat generation while improving reliability and enabling perfect synchronization between motion control computations and servo drive loops.
- ARM Controller: Handles high-level tasks: communication with the host robot controller and sensors, logic processing, implementation of the adaptive coordination algorithm for pneumatic and electric forces, and system status monitoring.
- DSP/FPGA Drive Module: Executes low-level, high-speed servo control loops (current, velocity, position) for the PMLSM, performs motor parameter detection, and drives the IPM (Intelligent Power Module).
- Interface & Communication Modules: Provide isolated I/O (Digital, Analog) and CAN bus connectivity for robust data exchange.
This architecture allows the end-effector to function as an intelligent, semi-autonomous device that receives force setpoints and mode commands from the robot, executing precise internal force control.
Mathematical Modeling of the System
To analyze and simulate the system’s performance, mathematical models for both the pneumatic and electromechanical subsystems are developed. Standard assumptions are made: ideal gas behavior, negligible gas kinetic/potential energy, isentropic flow processes, and initially, leakage is neglected.
Modeling of the Pneumatic Force Control System
The dynamics of the pneumatic system are derived from energy conservation and Newton’s second law.
Pressure Dynamics in the Cylinder Chamber (Chamber a):
Applying the energy conservation law to the control volume of the cylinder’s cap-end chamber yields:
$$ \frac{dp_a}{dt} = \frac{C_p R T_s}{C_v V_a} q_{ma} – \frac{C_p}{C_v} \frac{p_a A_a}{V_a} \frac{dx}{dt} $$
where:
- $p_a$: Pressure in chamber a (Pa)
- $q_{ma}$: Mass flow rate into chamber a (kg/s)
- $T_s$: Supply air temperature (K)
- $V_a$: Volume of chamber a (m³), $V_a = A_a (x + L/2)$
- $A_a$: Piston area in chamber a (m²)
- $x$: Piston displacement from midpoint (m)
- $L$: Cylinder stroke (m)
- $C_p, C_v$: Specific heats at constant pressure and volume
- $R$: Gas constant
Force Balance Equation (Motion Dynamics):
The equation of motion for the combined moving mass (piston, rod, PMLSM mover) is:
$$ p_a A_a – p_b A_b + F_e – F_L – F_f = M \frac{d^2x}{dt^2} + B_p \frac{dx}{dt} + K(x – y) $$
where:
- $p_b, A_b$: Pressure and area in the rod-side chamber (b)
- $F_e$: Electromagnetic force from the PMLSM (N)
- $F_L$: External load force (N)
- $F_f$: Friction force (N), modeled as $F_{fj} \leq k_j N$ (static) and $F_{fv} = k_v N$ (dynamic)
- $M$: Total moving mass (kg)
- $B_p$: Viscous damping coefficient (N·s/m)
- $K$: Equivalent contact stiffness between tool and workpiece (N/m)
- $y$: Workpiece displacement (treated as a disturbance) (m)
Valve Flow Equation:
The mass flow through the proportional valve is a nonlinear function of the control signal $u$ and the pressures:
$$ q_{ma} = f(A(u), p_s, p_a) \approx k_q u – k_p p_a $$
where $k_q$ is the flow gain and $k_p$ is the flow-pressure coefficient. For linear analysis, this relationship is linearized.
Contact Force:
The force exerted on the workpiece, which is the primary controlled variable, is given by:
$$ F_o = K (x – y) $$
By linearizing the nonlinear equations and applying Laplace transforms, a transfer function block diagram of the pneumatic force control system can be constructed. The relationship between the contact force disturbance due to workpiece motion $y(s)$ and the force output $F_o(s)$, under the assumption of high workpiece stiffness ($K$ is large), can be approximated as:
$$ \frac{F_o(s)}{y(s)} \approx -K \left( Ms^2 + B_p s + \frac{C_p p_a A_a}{C_v V_a s + RC_v T_s k_p} \right) $$
This reveals that the system’s dynamic response to load displacement is governed by a combination of proportional, derivative, and complex dynamic terms stemming from the pneumatic compressibility and inertia. The inherent low bandwidth and oscillatory tendencies of pneumatic systems are evident in this formulation.
Modeling of the Permanent Magnet Linear Synchronous Motor (PMLSM)
The electric drive subsystem is modeled using standard dq-axis theory for PMLSMs, with assumptions of sinusoidal back-EMF, negligible iron losses, and symmetric windings.
Electrical Dynamics:
The voltage equation in the q-axis (which controls torque/force) is:
$$ u_q = R_s i_q + L_q \frac{di_q}{dt} + K_e v $$
where:
- $u_q, i_q$: q-axis voltage (V) and current (A)
- $R_s, L_q$: Stator resistance (Ω) and inductance (H)
- $K_e$: Back-EMF constant (V/(m/s))
- $v = dx/dt$: Velocity (m/s)
Electromagnetic Force:
The thrust force generated is directly proportional to the q-axis current:
$$ F_e = K_f i_q $$
where $K_f$ is the motor force constant (N/A).
In a typical servo drive, the current loop bandwidth is very high (kHz range), significantly faster than the mechanical system dynamics. Therefore, for system-level analysis, the current loop can be simplified to a unity gain, assuming perfect tracking. The resulting simplified relationship between the commanded current $i(s)$, the load disturbance $y(s)$, and the resulting contact force $F_o(s)$ is:
$$ F_o(s) = \frac{K_f K (Ms^2 + B_p s)}{Ms^2 + B_p s + K} i(s) – \frac{K (Ms^2 + B_p s)}{Ms^2 + B_p s + K} y(s) $$
This shows that the force from the electric drive responds rapidly to current commands (via a second-order filter representing the moving mass) and can actively compensate for load disturbances $y(s)$.
Coordinated Control Strategy
The operational sequence of the end-effector during a robotic grinding task involves several phases: approach, contact (collision), force-controlled tracking (conforming), and retraction.
- Velocity Control Mode (Approach/Retraction): The end-effector uses velocity feedback to move smoothly towards or away from the workpiece, preventing high-impact collisions.
- Force Control Mode (Conforming/Tracking): Upon stable contact, the system switches to force control. The force sensor provides feedback, and the controller adjusts the output to maintain the desired contact force.
The key innovation is the coordination strategy between the pneumatic and electric actuators. Given the high bandwidth of the PMLSM system compared to the pneumatic system, a cascade control structure is adopted:
- Inner High-Bandwidth Loop: The contact force feedback is used with the PMLSM in a closed-loop force (or current) control configuration. This loop is responsible for precision, disturbance rejection, and fast dynamic response.
- Outer Low-Bandwidth Action: The pneumatic system is operated predominantly in an open-loop or slow-closed-loop manner based on the force setpoint. Its command signal $u$ is set to generate a steady-state force roughly equal to the desired contact force, minimizing the steady-state current (and thus heat generation) in the PMLSM. The electric motor then provides the dynamic “trim” force around this pneumatic bias.
The overall control law for the end-effector is implemented with an adaptive variable-parameter PID controller. The “adaptive” aspect is crucial because the contact stiffness $K$ between the tool and workpiece is highly dependent on the material, tool type, and surface geometry, and is often nonlinear. The system can perform a pre-characterization routine (applying a small position modulation to estimate $K$) and then adjust the PID gains accordingly for optimal performance across different working conditions. Signal conditioning (filtering, limiting) is applied to the force feedback to ensure stability.
Simulation Analysis of Load Characteristics
To validate the performance advantages of the hybrid end-effector, a detailed nonlinear simulation model was built using the multi-domain simulation software LMS Imagine.Lab AMESim. This model integrates the pneumatic components, the PMLSM drive, the workpiece environment (modeled as a stiffness $K$ and source of disturbances $y$), and the adaptive PID controller. The simulations focus on two critical performance metrics: response to load fluctuations and resistance to load shocks.
Response to Load Fluctuations (Vibrational Disturbances)
In practice, robot arms, especially long-reach serial manipulators, can exhibit low-frequency structural vibrations. These vibrations translate into unwanted oscillatory motion ($y$) at the end-effector, which can ruin surface finish if not compensated for. This test evaluates the end-effector’s ability to maintain a constant contact force in the presence of such disturbances.
Simulation Setup: A sinusoidal displacement disturbance $y = A \sin(2\pi f t)$ with amplitude $A = 0.5$ mm is applied to the workpiece side. The frequency $f$ is swept from 0.1 Hz to 50 Hz. The force control system aims to maintain a constant contact force of approximately 300 N. The amplitude of the resulting force fluctuation $F_o$ is measured and analyzed.
Results and Comparison: The performance of the purely pneumatic force control system is compared against the proposed pneumoelectric hybrid system.
| Frequency Range | Pneumatic-Only System Force Ripple | Pneumoelectric Hybrid System Force Ripple | Key Observation |
|---|---|---|---|
| 0.1 – 6 Hz | Rises from ~1 N to ~25 N | Remains very low (~1 N, slowly increasing) | Pneumatic system shows increasing susceptibility. |
| 6 – 12 Hz | Decreases from peak | Remains low | Possible natural frequency region for pneumatic system. |
| 12 – 35 Hz | Rises sharply to 138 N at 35 Hz | Rises gradually to 25 N at 35 Hz | Hybrid system shows vastly superior disturbance rejection. |
The data reveals a dramatic improvement. For the pneumatic-only end-effector, the force ripple at 35 Hz is 138 N, which is about 46% of the steady-state force command (300 N). This level of fluctuation would cause severe inconsistencies in material removal rate and surface quality. In contrast, the pneumoelectric hybrid end-effector maintains a force ripple of only 25 N at the same frequency, which is about 8.4% of the setpoint. This significant reduction is directly attributable to the high-bandwidth compensating force generated by the PMLSM, which actively counteracts the disturbance introduced by $y(t)$.
Resistance to Load Shock (Step Disturbances)
Real workpieces are not perfectly smooth. Sudden changes in surface height, such as bumps, seams, or weld beads, act as step-like disturbances ($y$) to the end-effector. The system’s ability to quickly recover from such shocks without large overshoot or sustained oscillation is critical for preventing tool damage, workpiece gouging, or robot instability.
Simulation Setup: A step disturbance of $A = 1$ mm is applied to the workpiece displacement $y$. The transient response of the cylinder piston displacement $x(t)$ and the contact force $F_o(t)$ is observed for both control systems.
Results and Comparison:
| Performance Metric | Pneumatic-Only System | Pneumoelectric Hybrid System | Improvement Factor |
|---|---|---|---|
| Piston Displacement (x) Settling | Large oscillations (3 major, several minor). Settling time ~0.235 s. | Significantly damped (2 major oscillations). Settling time ~0.076 s. | Settling time reduced to 32.3% of pneumatic system. |
| Contact Force (Fo) Response | Extreme force spikes (multiple peaks in the kN range). Severe oscillation. Settling time ~0.341 s. | One significantly reduced force spike (hundreds of N). Rapid stabilization. Settling time ~0.093 s. | Settling time reduced to 27.3% of pneumatic system. Peak force drastically lower. |
| Overall Impact | The hybrid end-effector demonstrates exceptional shock absorption and recovery, maintaining process stability where the pneumatic system would likely fail or cause damage. | ||
The hybrid end-effector’s electric motor provides immediate, forceful compensation the moment the shock is detected by the force sensor. This active damping action rapidly arrests the piston’s motion and dissipates the impact energy, preventing the large, slow oscillations characteristic of underdamped pneumatic systems.
Conclusion
The development of a pneumoelectric hybrid force-controlled end-effector addresses a critical need in robotic finishing for heavy industries like shipbuilding. By fusing the strengths of pneumatic and electric direct-drive actuation through coordinated control, this end-effector overcomes the fundamental limitations of traditional purely pneumatic compliance devices. The mathematical modeling elucidates the dynamic characteristics of both subsystems, providing a foundation for controller design. The simulation results conclusively demonstrate the superior performance of the hybrid system.
Specifically, the pneumoelectric end-effector exhibits remarkably improved rejection of load fluctuations, reducing force ripple amplitude by nearly 80% at higher disturbance frequencies compared to a pneumatic-only system. Furthermore, its resistance to sudden load shocks is enhanced dramatically, with settling times for both displacement and force reduced to less than one-third of the pneumatic system’s values. This leads to a more stable, reliable, and precise grinding/polishing process, enabling consistent high-quality surface finishes on complex parts while protecting both the tool and the robot from damaging forces.
This intelligent end-effector represents a significant step towards enabling true force-controlled robotic automation in demanding manufacturing environments. The principles of hybrid actuation and adaptive coordination control are broadly applicable, promising to enhance the capabilities of robots in various continuous-contact tasks beyond grinding, such as deburring, polishing complex contours, and precise assembly operations. The integration of such a high-performance end-effector is pivotal for advancing the state of intelligent, flexible manufacturing in the maritime sector and other heavy industries.