Table 1.
Components of the decoupled simulation framework.
Table 2.
Grid independence test: evaluation of numerical accuracy and computational performance.
Fig 1.
Grid convergence analysis for the LBM solver.
Relative errors are calculated against the benchmark resolution.
Table 3.
Lattice Boltzmann Method (LBM) implementation parameters.
Table 4.
Computational environment specifications.
Table 5.
Comparison of controller frameworks for AUV navigation.
Fig 2.
The fundamental components of model predictive control (MPC): the receding horizon principle.
At each time step, the controller calculates an optimal sequence of control actions across a finite prediction horizon. Only the initial control action is executed, and the procedure is replicated at the subsequent time step [38].
Table 6.
Descriptive statistics of robot position, orientation, and Euclidean error during simulation.
Table 7.
Descriptive statistics of robot obstacle avoidance performance in simulation and distance metrics.
Fig 3.
Comparison of the robot’s linear and angular velocities over time, illustrating the stability of linear motion versus the extreme fluctuations in angular velocity.
Fig 4.
Euclidean goal-directed error reduction illustrates the decreasing linear distance between the robot and the target location over time.
Fig 5.
Fluid-robot interaction in a dynamic environment: The color map represents fluid velocity magnitude (blue = high, white = low).
Fig 6.
The robot’s trajectory from its initial point (green) to the target goal (red), demonstrating its ability to navigate while successfully avoiding the obstacles.
Fig 7.
Minimum distance to obstacle, which represents the obstacle avoidance safety margin.
It illustrates that the robot is maintaining distance from surrounding obstacles during the simulation.
Table 8.
Robot performance metrics of the robot in simulation.
Fig 8.
The temporal evolution of the navigation trajectory, which shows the robot’s path at various time steps.
Table 9.
Fluid dynamics parameters calculated from LBM simulations.
Fig 9.
The Reynolds number evolution during robot navigation, which shows significant variations across simulation frames, with values starting low and increasing over time.
Fig 10.
An initial laminar flow regime (low values) resulting from the fluid interaction pattern at the bottom.
Fig 11.
Boundary-driven fluid flow patterns: Color gradients represent velocity magnitude (blue = high, white = low).
Fig 12.
Complex fluid-robot interaction at time step 266: Color-coded velocity magnitude (white = low to blue = high) with directional vectors illustrating complex fluid dynamics, including vortices and recirculation zones around the obstacles.
Fig 13.
Directional drag forces on the robot, showing an initial increase in the X and Y components due to robot-fluid interaction at the start of the simulation.
Fig 14.
The fluid energy dissipation profile shows a transition from low dissipation during laminar flow to high dissipation during turbulent flow.
Fig 15.
The average fluid velocity increases over the simulation, influenced by the movement, and the average vorticity illustrates the fluid’s rotational dynamics.
The most striking observation is the time history of the average velocity, which does not follow a single path but separates into two distinct, stable ranges, a phenomenon known as bimodal oscillation. This indicates the fluid rapidly cycles between two energetic states, likely transitioning between its high-power thrust generation phase and a lower-power recovery stroke.
Fig 16.
Spatial visualization illustrating the formation of wake turbulence vortex behind the robot, resulting from the robot’s movement.
Table 10.
Methodological comparison of robotic navigation studies.