[Preprint] Dynamic Modeling, Gait Synthesis, and Control of a Novel Subsurface Bore Propagator

Technical Summary: Dynamic Modeling, Gait Synthesis, and Control of a Novel Subsurface Bore Propagator

Problem Statement
Autonomous exploration of underground environments faces significant challenges, including the lack of pre-existing hollow space, feature-poor surroundings, and limited sensing capabilities. Current subterranean robotic designs often struggle to simultaneously excavate, anchor, and propagate within confined tunnel-like environments. While previous works have addressed specific layers of this problem—such as drilling bit mechanics or gait control—few have offered a unified framework that co-designs drilling heads, anchoring subsystems, body configuration, and control under quantified granular mechanics. Furthermore, existing designs often limit movement to linear propulsion or test drilling and locomotion separately, leaving gaps in the verification of complete design spaces for deep subsurface exploration.

Methodology
The authors propose a novel modular robot design inspired by the drilling mechanism of tunnel-boring machines and the peristaltic locomotion of earthworms. The system is decoupled into five distinct modules:

1. Excavation Head Module (EHM): Drills through the subsurface, with material expelled via an auger mechanism through the robot's body.
2. Drilling Propulsion Module (DPM): Connects the EHM to the front anchoring module, utilizing three lead-screw systems to push the robot forward.
3. Front Anchoring Module (FAM): Equipped with pads to anchor the robot against tunnel walls during drilling and locomotion.
4. Body Propulsion Module (BPM): Mimics the DPM to enable body elongation and contraction.
5. Back Anchoring Module (BAM): Mimics the FAM to provide rear anchoring.

Modeling and Control Design
The core of the methodology involves developing dynamic models for each module using the Euler-Lagrange framework. The modules are treated as independent units with prismatic joints (for anchoring and propulsion) or revolute joints (for the drill head), connected by coordinate systems that account for external wrenches.

• Dynamics: The equations of motion (EoM) include mass matrices, Coriolis terms, gravity, contact forces (modeled via an enhanced cylindrical contact model), and actuator forces.
• Control: A centralized state machine orchestrates a peristaltic gait cycle involving seven steps: drilling, disengaging front pads, elongating the body, engaging front pads, disengaging back pads, contracting the body, and engaging back pads.
• Implementation: Individual PID controllers are designed for each module (controlling normal force for anchors, position for propulsion, and motor velocity for the drill). These controllers are first tuned in a MATLAB/Simulink environment and subsequently integrated into a physics-based Unity simulation using the Robot Operating System (ROS) for sim-to-real verification.

Key Contributions
The paper presents three primary contributions:

1. A Mathematical Framework: A decoupled modeling approach using the Euler-Lagrange framework allows for the separate derivation of EoM for each module. This facilitates faster verification of controllers and provides flexibility for analyzing robots with different module configurations.
2. Gait Synthesis Strategy: A centralized state machine is designed to synthesize the peristaltic gait, integrating the feedback controllers to manage the complex sequence of anchoring, drilling, and propagating.
3. Sim-to-Real Integration: The study demonstrates a workflow where controllers derived from mathematical models are lifted to a high-fidelity Unity simulation (using CAD geometry) interfaced via ROS, bridging the gap between theoretical modeling and physical implementation.

Results
The proposed design and control strategy were validated through simulations:

• Module Verification: Simulations of individual modules (Anchoring, Propulsion, and Excavation) confirmed that the derived EoM and PID controllers could successfully manage contact forces, counteract disturbances (simulated via white noise), and maintain stability during drilling operations.
• Full System Simulation: A 300-second Unity simulation demonstrated the robot completing three full gait cycles.
• Performance Metrics: The robot achieved a total forward advancement of 30 mm into the soil. The authors note that while a theoretical maximum of 60 mm was possible, the reduction was attributed to slippage during the contraction of the Body Propulsion Module (BPM). This slippage is hypothesized to result from the chosen anchoring force (250 N) being insufficient to counteract the increased load caused by the BPM's lever arm.
• Stability: The simulation confirmed that at least one anchoring module remained engaged with the tunnel wall at all times, preventing the robot body from touching the tunnel walls during operation.

Significance and Claims
The paper claims that the proposed design, controllers, and gait synthesis strategy collectively enable a modular robot to anchor itself and propagate into soil in a human-free environment. The work highlights the importance of a unified framework that addresses drilling, anchoring, and locomotion simultaneously. The authors modestly conclude that while effective forward propagation was demonstrated in simulation despite drilling disturbances, future work is required to update the robot and simulation to achieve true 3-dimensional movement and to develop trajectory tracking controllers for contour following. The study does not claim field deployment but establishes a verified baseline for the operation of such a subsurface propagator.