Path planning and obstacle avoidance are crucial for autonomous underwater vehicles (AUVs). These algorithms help AUVs navigate safely and efficiently in complex underwater environments. From global to local planning, various techniques like Dijkstra's, A, RRT, and PRM are used to find optimal routes.

Grid-based and sampling-based methods offer different approaches to path planning. Obstacle avoidance algorithms, both reactive and deliberative, work alongside path planning to ensure safe navigation. Evaluating these algorithms involves considering efficiency metrics and robustness to uncertainties in the underwater environment.

Path planning algorithms for AUVs

Classifications and characteristics of path planning algorithms

• Path planning is the process of finding a feasible and optimal route for an autonomous vehicle to navigate from a start position to a goal position while avoiding obstacles in the environment
• Path planning algorithms can be classified into two main categories: global path planning and local path planning
  • Global path planning generates a complete path from the start to the goal based on a priori knowledge of the environment, such as a map or a grid representation
  • Local path planning generates a partial path based on the immediate surroundings of the vehicle, using real-time sensor data to avoid obstacles and adjust the path dynamically
• Path planning algorithms need to consider the kinematic and dynamic constraints of the AUV, such as its turning radius, maximum velocity, and acceleration limits, to generate feasible paths

Common path planning algorithms for underwater navigation

• Dijkstra's algorithm: A graph-based algorithm that finds the shortest path between nodes in a graph by iteratively expanding the path with the lowest cost
  • Dijkstra's algorithm guarantees the optimal path but can be computationally expensive for large graphs
  • It can be used for global path planning when the environment is known and represented as a graph
• A algorithm: An extension of Dijkstra's algorithm that uses heuristics to guide the search towards the goal, reducing the number of nodes explored
  • A algorithm combines the actual cost from the start node with an estimated cost to the goal node, using heuristics such as the Euclidean distance
  • It is more efficient than Dijkstra's algorithm for large environments and can be used for both global and local path planning
• Rapidly-exploring Random Trees (RRT): A sampling-based algorithm that incrementally builds a tree of feasible paths by randomly sampling points in the configuration space and connecting them to the nearest node in the tree
  • RRT can handle high-dimensional configuration spaces and complex environments with obstacles
  • It is probabilistically complete, meaning that it will find a feasible path if one exists, given enough time
• Probabilistic Roadmaps (PRM): Another sampling-based algorithm that constructs a graph of feasible paths by randomly sampling points in the configuration space and connecting them with collision-free edges
  • PRM is suitable for multi-query path planning, where multiple paths need to be generated in the same environment
  • It can be combined with graph search algorithms, such as Dijkstra's or A, to find the optimal path in the constructed roadmap

Grid-based vs sampling-based path planning

Grid-based path planning techniques

• Grid-based path planning techniques discretize the environment into a grid of cells, where each cell represents a small portion of the environment
  • Occupancy grids represent the environment as a binary grid, where each cell is either occupied (contains an obstacle) or free (navigable)
  • Elevation grids represent the environment as a grid of cells with varying heights, allowing for 3D path planning in underwater environments with varying depths
• Grid-based path planning algorithms, such as A, can be applied to the discretized environment to find the optimal path from the start cell to the goal cell
  • The cost function for grid-based path planning can include factors such as the distance traveled, the time taken, and the risk of collision with obstacles
  • Heuristics, such as the Euclidean distance or the Manhattan distance, can be used to estimate the cost from a given cell to the goal cell and guide the search
• Grid-based techniques are simple to implement and can guarantee the optimal path, but they may suffer from the curse of dimensionality in high-dimensional configuration spaces

Sampling-based path planning techniques

• Sampling-based path planning techniques, such as RRT and PRM, explore the continuous configuration space of the AUV by randomly sampling points and connecting them with feasible paths
  • The configuration space represents all possible states of the AUV, including its position, orientation, and velocity
  • Sampling-based techniques can handle high-dimensional configuration spaces and complex environments more efficiently than grid-based techniques
• RRT incrementally builds a tree of feasible paths by randomly sampling points and connecting them to the nearest node in the tree
  • The tree is expanded towards unexplored regions of the configuration space, allowing for efficient exploration
  • RRT can be extended to handle dynamic environments and moving obstacles, using variants such as RRT and RRT-Connect
• PRM constructs a graph of feasible paths by randomly sampling points and connecting them with collision-free edges
  • The graph can be preprocessed offline and used for multiple path queries in the same environment
  • PRM can be combined with graph search algorithms to find the optimal path in the constructed roadmap
• Implementing path planning techniques for AUVs requires considering the specific characteristics of the underwater environment, such as the presence of currents, the limited communication range, and the uncertainty in sensor measurements

Obstacle avoidance in underwater navigation

Reactive and deliberative obstacle avoidance algorithms

• Obstacle avoidance is the process of detecting and avoiding collisions with obstacles in the environment while navigating towards the goal
• Obstacle avoidance algorithms can be classified into two main categories: reactive and deliberative
  • Reactive obstacle avoidance algorithms generate immediate control commands based on the current sensor readings, without maintaining a long-term plan. Examples include the potential field method and the vector field histogram method
  • Deliberative obstacle avoidance algorithms incorporate the obstacle information into the path planning process, generating a new path that avoids the detected obstacles. Examples include the dynamic window approach and the elastic band approach
• Reactive obstacle avoidance algorithms are computationally efficient and can handle dynamic obstacles, but they may suffer from local minima and oscillations in complex environments
• Deliberative obstacle avoidance algorithms can generate globally optimal paths, but they require more computational resources and may not be suitable for real-time navigation in fast-changing environments

Integration of obstacle avoidance with path planning

• Integrating obstacle avoidance with path planning involves continuously updating the planned path based on the newly detected obstacles and the changing environment
  • Local path planning techniques, such as the dynamic window approach, can be used to generate short-term paths that avoid obstacles while following the global path
  • The global path can be re-planned periodically or triggered by significant changes in the environment, such as the detection of a new obstacle or a change in the goal position
• Hybrid approaches combining reactive and deliberative obstacle avoidance can be used to balance the trade-off between efficiency and optimality
  • For example, a reactive algorithm can be used for immediate obstacle avoidance, while a deliberative algorithm is used for long-term path planning and re-planning
  • The switching between the reactive and deliberative modes can be based on the urgency of the situation and the available computational resources
• Obstacle avoidance algorithms for AUVs need to handle the uncertainty in underwater perception, such as the limited field of view of sonar sensors and the presence of noise and false positives in the sensor data
  • Sensor fusion techniques, such as Kalman filters or particle filters, can be used to combine data from multiple sensors and estimate the state of the environment more accurately
  • Probabilistic obstacle avoidance methods, such as the probability roadmap method or the belief roadmap method, can incorporate the uncertainty in the obstacle detection into the path planning process

Evaluating path planning efficiency and robustness

Metrics for evaluating path planning efficiency

• The efficiency of a path planning algorithm can be measured by various metrics, such as:
  • Path length: The total distance traveled by the AUV from the start to the goal position
    • Shorter paths are generally preferred to minimize energy consumption and time taken
    • However, the shortest path may not always be the most efficient path, considering other factors such as the risk of collision and the energy required for turning and accelerating
  • Computation time: The time taken by the algorithm to generate the path, which is critical for real-time navigation in dynamic environments
    • Faster computation times allow for more frequent re-planning and adaptation to changing environments
    • However, faster computation times may come at the cost of suboptimal paths or reduced robustness
  • Memory usage: The amount of memory required by the algorithm to store the environment representation and the generated path
    • Lower memory usage is preferred for AUVs with limited onboard computational resources
    • However, lower memory usage may limit the complexity of the environment representation and the length of the generated path
• The relative importance of these metrics depends on the specific application and the available resources of the AUV

Robustness evaluation and comparative analysis

• The robustness of a path planning algorithm refers to its ability to handle uncertainties and changes in the environment, such as:
  • Sensor noise and errors: The algorithm should be able to generate feasible paths even with noisy and incomplete sensor data
    • Robust algorithms should incorporate sensor uncertainty models and use probabilistic techniques to estimate the true state of the environment
    • Redundancy in sensing, such as using multiple sensors with different modalities, can improve the robustness to sensor failures and errors
  • Dynamic obstacles: The algorithm should be able to avoid moving obstacles and adapt the path in real-time
    • Robust algorithms should predict the future motion of the obstacles based on their current velocity and direction
    • Reactive obstacle avoidance techniques can be used to quickly respond to sudden changes in the obstacle motion
  • Environment changes: The algorithm should be able to re-plan the path when the environment changes, such as when new obstacles are detected or when the goal position is updated
    • Robust algorithms should continuously monitor the environment and update the internal representation based on the new information
    • Incremental path planning techniques, such as D* and LPA*, can efficiently repair the existing path when the environment changes, instead of re-planning from scratch
• Comparative analysis of different path planning and obstacle avoidance approaches can be performed through simulations and real-world experiments
  • Simulation environments, such as Gazebo or UWSim, can be used to test and evaluate the algorithms in various scenarios with different environment configurations and obstacle types
    • Simulations allow for controlled and repeatable experiments, facilitating the comparison of different algorithms under the same conditions
    • However, simulations may not capture all the uncertainties and challenges of real-world environments, such as the effects of currents and the variability in sensor performance
  • Real-world experiments with physical AUVs can validate the simulation results and assess the practicality and reliability of the algorithms in actual underwater conditions
    • Real-world experiments provide the most realistic evaluation of the algorithms, considering the full range of environmental factors and the limitations of the AUV hardware and software
    • However, real-world experiments are more costly and time-consuming than simulations, and they may not be feasible for all scenarios and environments
• The choice of the path planning and obstacle avoidance approach depends on the specific requirements and constraints of the application, such as the available computational resources, the sensor capabilities, and the mission objectives
  • For example, a mission requiring long-range navigation in a largely unknown environment may prioritize the robustness and adaptability of the algorithm over the optimality and efficiency of the generated path
  • On the other hand, a mission requiring precise and fast navigation in a well-known environment may prioritize the efficiency and computational speed of the algorithm over its robustness to environmental changes and uncertainties