engineering

Probabilistic roadmap

Probabilistic roadmap is a engineering topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Probabilistic roadmap rather than just read about it. In short: The probabilistic roadmap planner is a motion planning algorithm in robotics, which solves the problem of determining a path between a starting configuration of the robot and a goal configuration while avoiding collisions. The basic idea behind PRM is to randomly sample points from the configuration space of the robot, test the samples for whether they are in the free space, and use a local planner to attempt to con…

Key takeaways

Probabilistic roadmap belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Probabilistic roadmap to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Probabilistic roadmap from memory before moving on to harder problems.

Reference excerpt

The probabilistic roadmap planner is a motion planning algorithm in robotics, which solves the problem of determining a path between a starting configuration of the robot and a goal configuration while avoiding collisions.

The basic idea behind PRM is to randomly sample points from the configuration space of the robot, test the samples for whether they are in the free space, and use a local planner to attempt to connect these configurations to other nearby configurations. The starting and goal configurations are added in, and a graph search algorithm is applied to the resulting graph to determine a path between the starting and goal configurations. The probabilistic roadmap planner consists of two phases: a construction and a query phase. In the construction phase, a roadmap (graph) is built, approximating the motions that can be made in the environment. First, a random configuration is created. Then, it is connected to some neighbors, typically either the k nearest neighbors or all neighbors less than some predetermined distance. Configurations and connections are added to the graph until the roadmap is dense enough. In the query phase, the start and goal configurations are connected to the graph, and the path is obtained by a Dijkstra's shortest path query. Given certain relatively weak conditions on the shape of the free space, PRM is provably probabilistically complete, meaning that as the number of sampled points increases without bound, the probability that the algorithm will find a path, if one exists, approaches one. The rate of convergence depends on certain visibility properties of the free space, where visibility is determined by the local planner. Roughly, if each point can "see" a large fraction of the space, and also if a large fraction of each subset of the space can "see" a large fraction of its complement, then the planner will find a path quickly. The invention of the PRM method is credited to Lydia E. Kavraki. There are many variants on the basic PRM method, some quite sophisticated, that vary the sampling strategy and connection strategy to achieve faster performance. See e.g. Geraerts & Overmars (2002) for a discussion.

References

Illustrations

Worked examples

Example 1 — a first encounter with Probabilistic roadmap

Start with the simplest possible case. Write down what Probabilistic roadmap claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Probabilistic roadmap before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Probabilistic roadmap ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Probabilistic roadmap

In research: Probabilistic roadmap appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Probabilistic roadmap in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Probabilistic roadmap is common in secondary-school and first-year university syllabi. It links to neighbouring topics Automated planning and scheduling, Path planning, Robot control, so understanding it makes those chapters shorter.
In everyday life: Look for Probabilistic roadmap outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Probabilistic roadmap in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Probabilistic roadmap means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Probabilistic roadmap out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Probabilistic roadmap in simple terms?

Why does Probabilistic roadmap matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Probabilistic roadmap?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Probabilistic roadmap.