Path Planning with A* and RRT | Autonomous Navigation, Part 4

Summary

In this video, the presenter explores motion planning using a map generated from simultaneous localization and mapping (SLAM). The focus is on graph-based methods for path planning, such as search-based algorithms (e.g., A*) and sampling-based algorithms (e.g., RRT and RRT*). The video covers how these algorithms help robots find efficient paths through environments, addressing challenges like obstacles and complex state spaces. The presenter also discusses how path planning differs from motion planning and how these methods can be adapted to more complex systems like multi-jointed robotic arms. The session concludes with insights on tracking moving obstacles in dynamic environments.

Takeaways

• 😀 Path planning is the process of finding a trajectory from a robot's starting pose to a goal pose, typically in environments represented by maps like binary occupancy grids.
• 😀 Motion planning extends path planning by considering not just the path but also the robot's motion parameters like velocity and acceleration.
• 😀 Path planning focuses on determining the path (sequence of poses), while motion planning handles the specific movement dynamics.
• 😀 Graph-based methods discretize the environment by breaking it into nodes, allowing for the search of the shortest path through these discrete locations.
• 😀 A random approach to path planning generates a tree of nodes, refining estimates of the shortest cost to reach each node by comparing different paths.
• 😀 A tree, which is a subset of a graph, ensures each node has a single parent, simplifying the structure by removing longer paths.
• 😀 The A* algorithm prioritizes nodes based on a heuristic, combining the cost to reach a node and the estimated cost to the goal, leading to more efficient pathfinding.
• 😀 A* offers a guaranteed optimal path in terms of cost when searching through a grid-based map, but it can be computationally expensive in larger state spaces.
• 😀 Sampling-based algorithms, like RRT, reduce computational complexity by randomly selecting nodes in the state space, focusing on rapidly exploring uncharted areas.
• 😀 RRT* refines the RRT approach by reconnecting nodes within a search radius, optimizing the path as more nodes are added, leading to near-optimal solutions for pathfinding.

Q & A

What is the difference between path planning and motion planning?

Path planning is concerned with finding a sequence of poses that connects the starting position to the goal position. It doesn't take into account the velocity, acceleration, or rotation of the robot. Motion planning, on the other hand, includes the consideration of these derivatives, aiming to control how the robot moves through the environment, not just the path it follows.

What are the three states that make up the pose of a robot that moves along the ground?

The pose of a robot that moves along the ground typically includes three states: the x and y location (position) and its orientation (rotation).

What is the general idea behind graph-based motion planning algorithms?

Graph-based algorithms work by discretizing the environment into nodes, then finding the shortest path to the goal by connecting these nodes. The robot moves from node to node, and the cost of each node represents how far it is from the starting point. The goal is to find the path with the lowest total cost.

How does a tree differ from a full graph in graph-based motion planning?

In a graph, nodes can be connected in any way, whereas in a tree, each node has only one parent. This reduces the number of paths considered, ensuring that only the shortest paths are kept, and branches do not recombine.

What is the A* algorithm and how does it improve upon simple graph-based approaches?

The A* algorithm improves upon simple graph-based approaches by prioritizing nodes that are more likely to lead to the optimal path. It uses a heuristic, such as the straight-line distance to the goal, and combines it with the cost to reach the node, helping to search more efficiently and avoid unnecessary nodes.

Why are search-based algorithms like A* computationally expensive in high-dimensional state spaces?

Search-based algorithms like A* become computationally expensive in high-dimensional state spaces because the number of grid cells grows exponentially with the number of dimensions, which leads to a larger number of calculations required to explore the entire space.

What is the key advantage of sampling-based algorithms in motion planning?

Sampling-based algorithms, such as RRT (Rapidly Exploring Random Tree), reduce the number of nodes by randomly selecting them, which speeds up the exploration of large or high-dimensional state spaces. This allows the algorithm to find a valid path with fewer calculations compared to grid-based methods.

What is the main difference between RRT and RRT* algorithms?

The main difference between RRT and RRT* is that RRT* not only builds a tree by adding random nodes but also refines the tree by reconnecting nodes in a way that minimizes the total path length, leading to a near-optimal path, whereas RRT focuses solely on finding any valid path.

How does RRT* refine its paths to approach an optimal solution?

RRT* refines paths by checking for nodes within a specified search radius and reattaching them to reduce the overall path length. This is done by reconnecting the nodes within the radius if doing so leads to a shorter path, improving the overall solution over time.

What is the significance of random node selection in RRT and RRT* algorithms?

Random node selection in RRT and RRT* algorithms allows the tree to quickly explore unexplored areas of the state space. RRT focuses on rapidly exploring open spaces, while RRT* refines the paths by choosing random nodes and optimizing the connections to minimize total distance.