This work presents the design, modeling, and experimental validation of a novel flexible pneumatic end-effector specifically engineered for robotic tomato harvesting. The core motivation stems from addressing the significant challenges associated with manual harvesting in protected cultivation environments, which is labor-intensive, costly, and increasingly difficult to sustain. While robotic solutions offer a promising alternative, conventional rigid grippers often cause unacceptable levels of damage to delicate fruit. Therefore, the development of a compliant, adaptive end-effector is crucial for enabling efficient, low-damage, and commercially viable automated harvesting. This research contributes a three-fingered, pneumatically actuated end-effector designed to conform gently to the natural shape of tomatoes, minimizing grasping pressure and potential bruising.
The global production of tomatoes is immense, with China being one of the largest producers. Harvesting constitutes the most laborious and expensive phase in the tomato production cycle. Robotic harvesters present a compelling solution to mitigate these issues, offering the potential for 24/7 operation, reduced labor costs, and improved consistency. However, the transition from laboratory prototypes to field-ready systems has been slow, particularly due to the bottleneck created by the end-effector—the component that physically interacts with the crop. A successful harvesting end effector must satisfy multiple, often competing criteria: high success rate, speed, gentleness (low damage), robustness, and adaptability to natural variations in fruit size, shape, and placement.
Traditional rigid end-effectors, often borrowed from industrial robotics, typically fail in the gentleness criterion, applying concentrated point loads that can puncture or bruise the fruit flesh. Consequently, research has pivoted towards soft robotics and compliant mechanisms for agricultural applications. Flexible or soft end-effectors, often inspired by biological grasping strategies (like the human hand or an octopus tentacle), can distribute contact forces over a larger area and adapt their shape to the target object. This intrinsic compliance significantly reduces the risk of damage. Among various actuation methods for soft robots—including tendon-driven, fluidic elastomer, and shape memory alloy—pneumatic actuation offers a favorable combination of relatively high force, simple control, low cost, and lightweight construction, making it suitable for integration onto a robotic manipulator.
This article details the comprehensive development of a pneumatic flexible end-effector. We begin by outlining the mechanical design and operating principle of the three-finger gripper. Subsequently, a kinematic model based on the piecewise constant curvature (PCC) assumption is formulated to describe the finger’s bending behavior. Finite Element Analysis (FEA) simulations are then employed to predict the performance of individual bellows actuators and the complete finger assembly under various pressure inputs. Finally, a physical prototype is fabricated and tested to validate the design’s grasping capabilities and to compare its real-world performance against the simulated models.
1. Design of the Flexible End-Effector
1.1 Structural Configuration and Working Principle
The designed harvesting end-effector is a three-fingered, pneumatically driven system. The primary design goals were to achieve adaptive enveloping grasps, minimize mechanical complexity, and ensure low-cost manufacturability. The end-effector consists of a central flange onto which three identical flexible fingers are mounted at evenly spaced intervals (120° apart) using fixed collars.
Each flexible finger is a composite structure comprising three key elements:
- Bellows Actuator: This is the core driving element, made from a flexible, air-tight material (e.g., silicone rubber). It features a corrugated structure that allows for significant axial expansion and contraction.
- Flexible Strain-Limiting Layer: A layer of inelastic, flexible material (e.g., fabric-embedded polymer) bonded along one side of the bellows.
- Connecting Blocks: Rigid segments at the base and tip of the finger that provide attachment points and house the air inlet.
The working principle leverages the differential strain between the extensible bellows and the inextensible limiting layer. When positive air pressure is applied to the internal chamber of the bellows, each corrugated segment expands axially, causing the entire actuator to elongate. Because the strain-limiting layer on one side cannot stretch, the finger bends towards that side, creating a curling motion suitable for grasping. Conversely, applying negative pressure (vacuum) causes the bellows to contract axially. With the limiting layer remaining constant in length, the finger bends in the opposite direction, facilitating the release of the object. This bio-inspired design allows the end effector to gently conform to the tomato’s surface, distributing contact pressure and significantly reducing the risk of damage compared to a rigid two-jaw gripper.
1.2 Dimensional Analysis Based on Target Fruit
To ensure the end-effector can successfully grasp the intended crop, a dimensional analysis was performed based on the geometric properties of the target tomato cultivar. A sample of mature tomatoes was measured. Key dimensions recorded were the major (equatorial) diameter and the minor (polar) diameter. The average values were calculated to inform the design envelope.
The sphericity of the fruit, a measure of how closely its shape resembles a perfect sphere, was calculated to simplify mechanical analysis. The geometric mean diameter \(d_g\) and the sphericity \(\Psi\) are given by:
$$d_g = \sqrt{L \times H}$$
$$\Psi = \frac{(L \times L \times H)^{1/3}}{D_c} \times 100\%$$
where \(L\) is the average major diameter, \(H\) is the average minor diameter, and \(D_c\) is the largest diameter (approximately \(max(L, H)\)). Analysis of the sample yielded an average sphericity greater than 92%, justifying the approximation of the tomato as a sphere for the purposes of gripper sizing. The effective grasping diameter range was determined to be between 50 mm and 80 mm.
Based on this range, the critical dimensions of the flexible finger were determined. The minimum finger length must be sufficient to wrap around at least one-quarter of the circumference of the largest target sphere (80 mm diameter). The maximum finger width must be less than the side length of the equilateral triangle formed by the three fingers when gripping the smallest target sphere (50 mm diameter), to prevent finger-to-finger interference during closure. These constraints guided the final finger dimensions.
The key parameters for the bellows actuator were defined as follows:
| Parameter | Symbol | Value (mm) |
|---|---|---|
| Single Section Length | L_s | 12.0 |
| Wavelength | b | 3.0 |
| Wall Thickness | h | 1.0 |
| Internal Air Channel Diameter | d_i | 3.0 |
| Peak Circle Diameter | d_p | 18.0 |
| Number of Corrugations per Section | n | 4 |
| Total Finger Length | L_f | 108.0 |
| Finger Width | W_f | 20.0 |
2. Kinematic Modeling of the End-Effector Finger
2.1 Modeling Approach: Piecewise Constant Curvature
Accurate modeling and control of soft robotic structures like this flexible end-effector finger is challenging due to their continuous deformation and infinite degrees of freedom. A widely adopted and effective simplification is the Piecewise Constant Curvature (PCC) model. This model assumes that the soft actuator deforms into a series of arcs, each with a constant curvature. The kinematics can be decomposed into two mappings: one from the actuator space (e.g., input pressures) to a configuration space described by arc parameters, and another from this configuration space to the task space (end-effector position and orientation).
For this pneumatic finger, the actuator space variable is the input gauge pressure \(q = P\). The configuration space is described by parameters for each assumed constant-curvature section: the curvature \(\kappa\), the angle of the bending plane \(\phi\), and the arc length \(l\). The mapping \(f_1: q \rightarrow (\kappa, \phi, l)\) is specific to the actuator’s design and material properties. However, the mapping \(f_2: (\kappa, \phi, l) \rightarrow \textbf{x}\) (the end-pose) is generic for any PCC structure. In our design, the strain-limiting layer ensures a fixed total length, simplifying the model by making the total arc length \(L\) a constant. The finger’s bending is primarily in a single plane determined by the location of the strain-limiting layer, so \(\phi\) is also constant. Thus, the primary variable linking actuation to pose is the curvature \(\kappa\) (or its inverse, the radius of curvature \(\rho = 1/\kappa\)), which is directly related to the bending angle \(\theta\) by \(\theta = \kappa l = l / \rho\).
2.2 Derivation of End-Effector Pose Using D-H Parameters
The transformation from the base of a PCC section to its tip can be elegantly derived using a modified Denavit-Hartenberg (D-H) convention. Consider a single PCC section of length \(l\), bending with a constant curvature \(\kappa\) in a plane defined by angle \(\phi\). The arc forms an angle \(\theta = \kappa l\). The transformation involves a sequence of rotations and translations as follows:
- Rotate by \(\phi\) about the initial z-axis to align the x-axis with the bending plane.
- Rotate by \(\theta/2\) about the new y-axis.
- Translate by a distance \(d = 2\rho \sin(\theta/2)\) along the new z-axis (towards the arc’s center).
- Rotate again by \(\theta/2\) about the current y-axis.
- Rotate by \(-\phi\) about the current z-axis to realign the frame.
The corresponding D-H parameters for this sequence are:
| Link | \(\theta_i\) | \(d_i\) | \(a_i\) | \(\alpha_i\) |
|---|---|---|---|---|
| 1 | \(\phi\) | 0 | 0 | \(-\pi/2\) |
| 2 | \(\theta/2\) | 0 | 0 | \(\pi/2\) |
| 3 | 0 | \(2\rho \sin(\theta/2)\) | 0 | \(-\pi/2\) |
| 4 | \(\theta/2\) | 0 | 0 | \(\pi/2\) |
| 5 | \(-\phi\) | 0 | 0 | 0 |
The homogeneous transformation matrix \(^{i-1}T_i\) for this section is the product of the individual transformation matrices:
$$^{i-1}T_i = R_z(\phi) R_y(\theta/2) T_z(d) R_y(\theta/2) R_z(-\phi)$$
Carrying out this multiplication yields the compact form:
$$ ^{i-1}T_i = \begin{bmatrix}
\cos^2\phi(\cos\theta – 1) + 1 & \sin\phi\cos\phi(\cos\theta – 1) & \cos\phi\sin\theta & \rho\cos\phi(1-\cos\theta)\\
\sin\phi\cos\phi(\cos\theta – 1) & \sin^2\phi(\cos\theta – 1) + 1 & \sin\phi\sin\theta & \rho\sin\phi(1-\cos\theta)\\
-\cos\phi\sin\theta & -\sin\phi\sin\theta & \cos\theta & \rho\sin\theta\\
0 & 0 & 0 & 1
\end{bmatrix} $$
For a finger modeled as a single constant-curvature segment (a valid approximation for initial analysis), the transformation from base frame \(\{0\}\) to fingertip frame \(\{n\}\) is simply \(^0T_n = ^{0}T_1\). The position of the fingertip \(\textbf{p}\) is extracted from the fourth column of \(^0T_n\):
$$\textbf{p} = \begin{pmatrix} p_x \\ p_y \\ p_z \end{pmatrix} = \begin{pmatrix} \rho\cos\phi(1-\cos\theta) \\ \rho\sin\phi(1-\cos\theta) \\ \rho\sin\theta \end{pmatrix}$$
The orientation can be described by ZYZ Euler angles \((\alpha, \beta, \gamma)\) derived from the rotation submatrix of \(^0T_n\). This kinematic model provides a fundamental relationship between the input (curvature \(\kappa\) or bending angle \(\theta\)) and the output (fingertip pose) for the flexible end-effector finger. The challenge remains to characterize the relationship between the input pneumatic pressure \(P\) and the resulting curvature \(\kappa\), which is addressed through simulation and experiment.
3. Simulation Analysis of the End-Effector Components
3.1 Bellows Actuator Expansion/Contraction Simulation
Prior to assembling the full finger, the mechanical performance of the bellows actuator alone was evaluated using Finite Element Analysis (FEA). A 3D model of a single bellows section was created and analyzed in ANSYS. The hyperelastic silicone material was modeled using the Mooney-Rivlin model with constants calibrated from material data. The base of the bellows was fixed, and internal pressure loads were applied to the inner surface. Simulations were run for both positive pressure (0 to 120 kPa in 10 kPa increments) and negative pressure (0 to -20 kPa).
The key output was the axial displacement (elongation or contraction) of the bellows tip. The results confirmed the actuator’s functionality:
- Under positive pressure, the bellows elongated linearly with increasing pressure, reaching a maximum elongation of approximately 57.3 mm at 120 kPa.
- Under negative pressure, the bellows contracted, with a contraction of about 19.7 mm at -20 kPa. This contraction is sufficient for the release motion of the end-effector.
The simulation validated that the custom bellows design possessed the necessary stroke to drive the intended bending motion of the final flexible end-effector.
3.2 Complete Finger Bending Simulation
Following the bellows analysis, a full FEA simulation of the complete finger assembly (bellows, strain-limiting layer, and connecting blocks) was conducted. Different material models (Mooney-Rivlin for the bellows, Yeoh for other silicone parts) were assigned, and all interfaces were defined as bonded contacts. The base was fixed, and internal pressure was applied to the bellows chamber.
The simulation successfully demonstrated the finger’s bending. The overall deformation vector at the fingertip was recorded for pressures from -40 kPa to 120 kPa. To quantify bending, the angle \(\theta\) was calculated from the simulated fingertip coordinates \((x, y)\) relative to the fixed base, using the relation derived from the geometry of a circular arc of fixed length \(L\):
$$\theta = 2 \arcsin\left(\frac{\sqrt{x^2 + y^2}}{2L}\right) \approx \arctan\left(\frac{y}{L – x}\right) \quad \text{(for small to moderate } x\text{)}$$
The relationship between input gauge pressure \(P\) and the resulting bending angle \(\theta\) was found to be nonlinear. The data was fit to an exponential model of the form:
$$\theta(P) = A e^{P/B} + C$$
where \(A\), \(B\), and \(C\) are fitting constants determined from the simulation data. This model provides a valuable prediction of the end-effector’s kinematic behavior for controller design. The FEA results established a strong theoretical foundation, indicating that the flexible end-effector finger would achieve significant bending angles (exceeding 90°) within the planned operating pressure range, confirming its feasibility for enveloping grasps of tomato-sized objects.
4. Prototype Fabrication and Experimental Validation
4.1 Prototype Assembly and Bending Characterization
A physical prototype of the three-fingered end-effector was constructed to validate the design. Flexible components like the bellows and strain-limiting layers were cast from silicone rubber using 3D-printed molds. Rigid components, such as the flange, connecting blocks, and finger mounts, were fabricated using fused deposition modeling (FDM) 3D printing. The assembled end-effector prototype is shown in the introductory figure.
A dedicated test platform was built to characterize the finger’s bending performance experimentally. The platform consisted of a regulated air supply (micro air pump with a regulator and pressure sensor), a data acquisition module (Arduino), a fixed mount for the finger base, and a calibrated backdrop for measuring fingertip position. One finger was tested independently. Gauge pressure was increased from 0 kPa to 120 kPa in steps, and at each step, the position of the fingertip was marked and recorded.
The experimental bending angle \(\theta_{exp}\) was calculated from the recorded positions using the same geometric relation as in the simulation. The results were plotted alongside the FEA-predicted bending angles. The trends matched well: bending angle increased monotonically with pressure. However, a consistent offset was observed, with the experimental angles being slightly lower than the simulated ones for a given pressure. This discrepancy is attributed to several practical factors not fully captured in the idealized simulation:
- Material Parameter Variance: The hyperelastic material constants used in FEA are approximations. Real-world silicone properties can vary between batches.
- Friction and Assembly Effects: The simulation assumed perfectly bonded interfaces. In reality, micro-slip and friction between the bellows and the strain-limiting layer can slightly resist bending.
- Manufacturing Imperfections: Minor variations in wall thickness or geometry from the ideal CAD model can affect performance.
- Hysteresis: Elastomeric materials exhibit hysteresis, meaning the deformation path during inflation may differ from during deflation, which was not modeled in the static FEA.
Despite these deviations, the experimental data confirmed the core functionality: the pneumatic flexible end-effector finger produced a reliable, pressure-controllable bending motion suitable for grasping.
4.2 Grasping Tests and Strength Validation
The final validation step involved testing the complete three-fingered end-effector’s ability to perform adaptive grasps on actual tomatoes. A variety of tomatoes with different sizes and shapes within the target range were selected. The end-effector was mounted on a simple manual positioning arm for these preliminary tests. Positive pressure was applied, causing all three fingers to simultaneously curl inward and envelop the fruit.
The tests were successful. The flexible end-effector consistently achieved stable enveloping grasps on tomatoes of varying diameters. The compliance of the fingers allowed them to conform to the fruit’s surface without applying excessive point loads. No visible damage (punctures, significant bruising) was observed on the tomato skin after repeated grasping and release cycles. Furthermore, the structural integrity of the end-effector prototype was validated; it withstood the grasping forces without failure, demonstrating that the design and chosen materials were sufficiently robust for the intended application.
The following table summarizes the key outcomes from the simulation and experimental phases, highlighting the performance parameters of the developed flexible end-effector:
| Aspect | Method | Key Result / Parameter | Value / Observation |
|---|---|---|---|
| Bellows Stroke | FEA Simulation | Max Elongation @ 120 kPa | ~57.3 mm |
| Bellows Stroke | FEA Simulation | Max Contraction @ -20 kPa | ~19.7 mm |
| Finger Bending Model | Kinematic/PCC | Fingertip Position | \( \textbf{p} = [\rho\cos\phi(1-\cos\theta), \rho\sin\phi(1-\cos\theta), \rho\sin\theta]^T \) |
| Bending vs. Pressure | FEA Simulation (Fitted) | Model Equation | \(\theta(P) = A e^{P/B} + C\) |
| Bending Performance | Experimental Test | Functional Range | 0 to 120 kPa, Produced >70° bend |
| Grasping Function | Physical Prototype Test | Success Rate & Damage | High success on target sizes; No visible damage |
| Structural Integrity | Physical Prototype Test | Robustness | No failure during grasping tests |
5. Conclusion and Future Work
This research presented the complete development cycle of a novel flexible pneumatic end-effector for robotic tomato harvesting. The three-fingered design, driven by custom bellows actuators and employing a strain-limiting layer for directional bending, successfully addresses the critical need for gentle, adaptive grasping in agricultural robotics. The end-effector’s kinematics were effectively modeled using the Piecewise Constant Curvature assumption, providing a mathematical framework for relating actuation to end-pose. Finite Element Analysis proved instrumental in predicting the performance of both the actuator and the full finger, demonstrating significant bending capability under practical pressure ranges. Experimental validation with a physical prototype confirmed the core functionality, showing reliable pressure-controlled bending and successful, low-damage grasping of actual tomatoes.
The work establishes a solid foundation for a practical soft robotic end-effector. However, several avenues remain for further investigation and development to transition this end-effector from a functional prototype to a component of a fully autonomous harvesting system. Future work will focus on the following areas:
- Dynamic Modeling and Advanced Control: The current kinematic and static FEA models should be extended to include dynamics—accounting for inertia, damping, and hysteresis of the soft materials. This will enable the design of more sophisticated controllers (e.g., impedance control, force/position hybrid control) for managing the interaction forces during the delicate harvesting process.
- Integration with Perception and Manipulation: The standalone end-effector must be integrated with a robotic manipulator and a vision system. Research is needed to develop closed-loop control strategies that use real-time visual feedback to position the end-effector accurately and to determine the optimal grasping pose and required pressure for fruits of varying size and ripeness.
- Design Optimization and Durability Testing: The geometry and material composition of the bellows and fingers can be optimized (e.g., via topology optimization) for specific performance metrics like bending angle per pressure, force output, or fatigue life. Long-term durability testing in realistic greenhouse environments is essential to assess wear, material degradation, and reliability.
- Detachment Mechanism Study: This work focused on the grasping function. A complete harvesting end-effector requires a reliable, low-injury method for severing the peduncle (stem). Future iterations could explore integrating a small, coordinated cutting tool into the end-effector design or studying twist-and-pull detachment methods using the inherent dexterity of the flexible fingers.
In conclusion, the developed flexible pneumatic end-effector demonstrates a highly promising approach to solving the delicate grasping challenge in automated tomato harvesting. Its compliant nature, simple actuation, and proven functionality represent a significant step towards the development of robust, efficient, and commercially viable robotic harvesters, contributing to the broader advancement of intelligent agricultural equipment.