Robotic Transplanter Tool

• Transplanter Tool is a robotic system designed for precise sapling transplantation and harvesting in compact, containerized vertical farms using constraint extraction techniques.
• It leverages a 7-DOF collaborative robot with an eye-in-hand RGB-D camera and advanced vision algorithms to achieve real-time performance and high success rates.
• The tool’s minimal-programming paradigm, modular software architecture, and validated closed-loop control highlight its potential for scalable automation in agri-robotics.

The Transplanter Tool is a robotic module for sapling insertion within the constrained geometry of containerized vertical farms. It leverages a 7-DOF collaborative robot (cobot) equipped with an eye-in-hand RGB-D camera and a two-finger parallel jaw gripper. The system employs a demonstration-based constraint extraction framework, exploiting the geometry of constant-screw motions in SE(3), and achieves real-time, generalizable transplantation of saplings via a minimal-programming paradigm. The approach enables both transplantation and harvesting tasks to be executed without extensive task-specific programming, demonstrating high success rates in compact, hydroponic farm settings (Mahalingam et al., 2023).

1. System Architecture and Hardware Integration

The hardware configuration centers on the Franka Emika Panda cobot, a 7-degree-of-freedom serial manipulator with a 3 kg payload and repeatability of ±0.1 mm. The end-effector is a parallel jaw gripper with 80 mm finger length, 8 mm thickness, and an 80 mm stroke, optionally augmented by an FT-150 ATI force/torque sensor for haptic feedback. Visual perception is achieved through an Intel RealSense D415 RGB-D camera, rigidly mounted to the robot's wrist (eye-in-hand), operating at 1280×720 resolution at 30 Hz, with depth accuracy of approximately 2 mm at 1 m. Extrinsic calibration between robot and camera utilizes a standard checkerboard protocol.

The horticultural interface comprises grow panels with three vertical PVC tubes (62 mm outer diameter), featuring cylindrical slots (30 mm and 35 mm diameters tested) spaced at 100 mm intervals along a tube angled 20° down from the horizontal. Panel–tube spacing is 300 mm. This physical configuration informs both slot pose priors in the robot frame and constraints in the perceptual pipeline.

2. Demonstration-Based Constraint Extraction

The task constraints for transplantation are extracted from a single kinesthetic demonstration performed by a human operator. The Panda is set to zero-gravity mode and manually guided through the full sapling transfer sequence: pod grasp, slot approach, insertion, and withdrawal. The system records a timestamped joint trajectory θ(t), and forward kinematics yield a dense end-effector pose sequence $D = \{g_1, ..., g_n\} \subset SE(3)$ at 50 Hz.

The trajectory is segmented into constant-screw motions, where each segment is modeled as a one-parameter subgroup in SE(3). For consecutive poses, the incremental twist is computed as

$$\xi_i = \frac{1}{\Delta t} \log( g_{i-1}^{-1} g_i ) \in se(3),$$

decomposed into Plücker parameters (ω, m, h). The segmentation algorithm identifies boundaries where the screw axis experiences changes exceeding a threshold $\epsilon \approx 0.05$ rad. The resulting sub-trajectories define equality constraints on the allowable motion:

$$f_j(q) = \log( g_{k_{j-1}}^{-1} FK(q) ) - \theta(q) \xi_j = 0,$$

with $FK(q)$ the forward kinematics and $\theta(q)$ the subgroup parameter. Only those screw segments terminating within 50 mm of pod or slot frames are retained, yielding approach and insertion subsequences.

3. Task-Space Motion Planning and Control

For a new transplantation instance, the demonstration-derived screw parameters are mapped to new local pod and slot frames (g_p', g_s') via the adjoint transformation:

$$\xi_{p,i}' = Ad(g_p' g_p^{-1}) \xi_{p,i},\quad \xi_{s,j}' = Ad(g_s' g_s^{-1}) \xi_{s,j},$$

where $Ad(k)\cdot\xi = k\xi k^{-1}$. The planned pose sequence is concatenated and parameterized via Screw-Linear Interpolation (ScLERP), with poses generated by

$T_{j+1} = T_j \exp(\Delta \theta_j \hat{\xi}_j'),$

and interpolated within each segment as

$$T_j(\tau) = T_j \exp(\tau \hat{\xi}_j'), \quad \tau \in [0, \Delta\theta_j].$$

At 1 ms control intervals, the desired pose $$\xi_i = \frac{1}{\Delta t} \log( g_{i-1}^{-1} g_i ) \in se(3),$$0 determines the required end-effector twist, which is mapped to joint velocities by

$$\xi_i = \frac{1}{\Delta t} \log( g_{i-1}^{-1} g_i ) \in se(3),$$1

where $$\xi_i = \frac{1}{\Delta t} \log( g_{i-1}^{-1} g_i ) \in se(3),$$2 is the pseudo-inverse of the Jacobian, and $$\xi_i = \frac{1}{\Delta t} \log( g_{i-1}^{-1} g_i ) \in se(3),$$3 is a null-space damping vector. This closed-loop velocity control is executed at 1 kHz.

4. Perception and Software Pipeline

The visual pipeline obtains an RGB-D frame and estimates the slot region of interest (ROI) by projecting the known grid onto the image. Within this ROI, candidate slot masks are generated using Segment-Anything (SAM), and the mask nearest the ROI center is chosen. The selected mask pixels are deprojected to a 3D point cloud for oriented bounding box fitting, yielding an estimate of the slot frame $$\xi_i = \frac{1}{\Delta t} \log( g_{i-1}^{-1} g_i ) \in se(3),$$4. The pod tray frame $$\xi_i = \frac{1}{\Delta t} \log( g_{i-1}^{-1} g_i ) \in se(3),$$5 is fixed in the robot base.

The software stack is modular, comprising: (i) Perception pipeline (RGB-D frame processing and slot pose estimation); (ii) Constraint learning (screw segmentation and constraint storage); (iii) Trajectory optimizer (adjoint transformation and ScLERP discretization); and (iv) Execution framework (real-time closed-loop control, optional haptic compliance).

5. Experimental Validation and Performance Metrics

The system was evaluated using the Franka Panda platform, D415 camera, and parallel-jaw gripper on grow panels with variable slot diameters. Sapling pods had square cross-sections (15 mm). Across three demonstrations (five trials each) for transplantation and four demonstrations (four trials each) for harvesting, the tool achieved the following:

Task	Trials	Successes	Success Rate
Transplanting	15	13	86.7%
Harvesting	16	13	81.3%
Overall	31	26	83.8%

• Mean insertion depth error: 3.2 mm (σ = 1.1 mm)
• Mean orientation error: 2.3° (σ = 1.0°)
• Mean transplantation cycle time: 22 s (σ = 3 s)
• Harvest time: 18 s (σ = 4 s)

No significant differences were observed in transplantation success across tube slot diameters (30 mm vs 35 mm). Failures were attributed to gripper-slot interference or occlusion by foliage during harvesting.

6. Limitations and Proposed Extensions

Observed failure modes include gripper collision with the slot lip (attributed to finger thickness) and grasp errors during harvesting due to occlusion by neighboring foliage. The compact environment precludes the use of external/global cameras and large robot motions; all sensing is eye-in-hand.

Proposed avenues for improvement include: development of custom slim-profile or under-actuated grippers to minimize slot interference; incorporation of force-feedback (compliant insertion); deployment of multi-view or depth-completion models to overcome occlusions; integration of online complementarity-constraint collision avoidance (e.g., via Linear Complementarity Problems in task space); and extension to multi-arm coordination for reduced cycle times and reconfigurable planting geometries (Mahalingam et al., 2023).

7. Significance Within Automated Vertical Farming

The Transplanter Tool represents a demonstration-efficient, constraint-generalizable approach to automating robotically delicate tasks within the strict spatial constraints of containerized vertical farming. Its architecture—reliant on single-demonstration screw-extraction, modular perception, kinematic generalization, and fast closed-loop control—enables robust performance without task-specific programming or reliance on external perception systems. The methodology provides a clear path for future expansion to more complex manipulation tasks and collaborative multi-robot systems in similarly constrained agri-robotic environments (Mahalingam et al., 2023).