Create a rigorous scientific journal figure illustrating the control framework described in the text "Motion Control Research of Rigid-Flexible Multibody Manta Ray Submersible." The image must be a clean, professional vector illustration with an academic color palette (blues, teals, scientific grays, with red highlights for constraints/errors). The figure should be divided into four logical panels labeled A, B, C, and D.** **Panel A: Coupled Rigid-Flexible Dynamics Challenge.** * **Title:** A. Rigid-Flexible Coupled System & Multi-Source Propulsion. * **Visuals:** A central diagram of a robotic manta ray submersible. Clearly differentiate the central "Rigid Body" (metallic texture) from the "Flexible Pectoral Fins" (showing wavelike deformation grid lines) and "Caudal Fin." * **Inputs/Outputs:** On the left, show input arrows labeled: "Pectoral Flapping (Freq ω, Amp A)," "Caudal Oscillating," and "Buoyancy/Glide Trim." Use curved arrows to show complex interplay between fins and body. On the right, show a resulting output vector arrow labeled: "Highly Non-linear Hydrodynamic Forces & Moments ()." Add a small text box noting: "Complex Dynamics: Hard to model analytically." **Panel B: Physics-Informed Neural Network (PINN) Forward Modeling.** * **Title:** B. Data-Physics Driven PINN Forward Modeling Mechanism. * **Visuals:** A detailed neural network architecture diagram. * **Left (Input Layer):** A vector labeled Input : . * **Center (DNN):** Several layers of interconnected neurons labeled "Deep Neural Network (DNN)." * **Right (Output Layer):** A vector labeled Predicted Output : . * **Bottom (The Core Physics):** Below the DNN, draw a large block labeled "Physics Constraints Embedding (PDEs/ODEs)." Inside this block, include stylized mathematical notation for the governing equations: "Rigid Body Eq: " and "Flexible Fin PDE: ." * **Loss Function:** Show arrows from the Predicted Output and the Physics Constraints block feeding into a "Total Loss Function ()" node. Visualize the loss equation: . An arrow labeled "Automatic Differentiation Backprop" points back to the DNN weights. **Panel C: Real-Time Inverse Control Allocation Strategy.** * **Title:** C. PINN-based Inverse Solving as Constrained Optimization. * **Visuals:** A closed-loop control diagram representing the "Control Allocation" block. * **Start:** An input box labeled "Desired Forces/Moments ()." * **Optimizer:** This feeds into an "Optimization Solver (e.g., Gradient Descent)." * **The Proxy:** The solver iteratively queries a block labeled "Frozen Trained PINN Proxy Model" (referencing Panel B). * **Constraints:** A block labeled "Physical Constraints (Motor limits, Angles)" feeds into the solver. * **Result:** The output of the solver is a vector labeled "Optimal Control Parameters ()" which is sent to the submersible actuators. Add text: "Fast Iterative Solution (< ms)." **Panel D: Multi-Task Scenarios & Experimental Validation.** * **Title:** D. Multi-Modal Motion Control & Water Tank Validation. * **Visuals (Top):** Three small vignettes showing different modes: * "Cruising Mode": Manta ray moving straight and fast, fins flapping symmetrically. Text focus: "Thrust Maximization." * "Maneuvering Mode": Manta ray turning sharply. Text focus: "Precise Moment Control (Differential Flapping)." * "Gliding Mode": Manta ray descending slowly in a sawtooth pattern. Text focus: "Buoyancy/CG Trim, Low Energy." * **Visuals (Bottom):** A schematic of a "Water Tank Experiment Platform." Show a prototype in a tank, overhead truss with "Motion Capture Cameras." A data screen shows two lines plotting a trajectory: a solid blue line labeled "PINN Theoretical Prediction" and a dotted red line labeled "Experimental Observation," showing close agreement. **Overall Style Notes:** Use clear sans-serif fonts (e.g., Helvetica or Arial style) for all labels. Ensure mathematical symbols are rendered clearly as if in LaTeX. The background should be plain white. Lines connecting blocks should be clean and arrow-headed to show direction of data flow.