# What is the difference between a holonomic and an omnidirectional robot?

I have seen the usage of the term "omnidirectional" in robotics, but I have not found a (precise) definition.

In the chapter Omni-Directional Robots from the book "Embedded Robotics", it is stated:

In contrast, a holonomic or omnidirectional robot is capable of driving in any direction

which seems to indicate that these words are synonyms.

What's an omnidirectional robot? What is the difference between a holonomic and an omnidirectional robot (if any)? What are examples of omnidirectional and holonomic robots (or other objects)?

Holonomic is a precise mathematical term; one definition is velocity constraints can be integrated into the form \begin{align} f(q1,q2,...,t) = 0. \end{align}