As I understand it, a company buying a robot -- something that depreciates over time and will eventually break -- is included in investment because it provides a long term benefit (increase in GDP). But then why is a car considered consumption? It also depreciates over time (though not in a year) and provides long term benefits to GDP.
Because there is a definition of what is production and what is consumption, and households are generally outside the production boundary. From the 2008 System of National Accounts (at 6.24):
Economic production may be defined as an activity carried out under the control and responsibility of an institutional unit that uses inputs of labour, capital, and goods and services to produce outputs of goods or services. There must be an institutional unit that assumes responsibility for the process of production and owns any resulting goods or knowledge-capturing products or is entitled to be paid, or otherwise compensated, for the change-effecting or margin services provided.
The distinction therefore has nothing to do with cars versus robots, and everything to do with who purchases the car or robot. A car purchased by a consumer is considered consumption, but a car purchased by a firm is considered investment. This is intuitively reasonable; the stream of transport services that a household receives from owning an automobile is generally consumption, and likewise for a business it is generally an input into production. While it's true that a car owned by an individual may be used both for production and consumption, the point raised by denesp is precisely why no distinction is made: we simply do not know how people are using their personal cars at any moment in time, and it's probably not worthwhile to spend the resources to know, so we use the ownership of the automobile as a proxy for how it is used.
However, one might reasonably argue that even though the purchases are made by consumers, one should count the stream of transport services received by the household as consumption, and capitalize the purchase of the automobile. This is how we treat housing, as described in part in the answer here. Indeed, this point has been raised even by researchers at the US Bureau of Economic Analysis:
The treatment of consumer durable goods other than owner-occupied housing as final consumption expenditure rather than as fixed capital formation is also a long-standing criticism made by many users of the national accounts. Consumer durables are similar in many ways to owner-occupied dwellings, but the treatment in the accounts is quite different. The owner of a dwelling is treated as an owner of an unincorporated enterprise that produces housing services, but consumer durables are not assumed to provide services within the SNA production boundary (SNA 6.89, 9.40). Many durables, such as cars, trucks, and furniture, can be used either by consumers or by business enterprises—the SNA definitions count their purchase by households immediately as final consumption expenditure whereas they are to be capitalized by enterprises. “Extended” national accounts developed by researchers such as Eisner, Jorgenson and associates, Kendrick, and Ruggles and Ruggles include the services of consumer durables (for a review, see Eisner 1988). Fraumeni and Okubo (2001) illustrate the possible options of capitalizing motor vehicles or all consumer durables.
Why this is not done is a fair question, but I would speculate that (in the US at least) the answer is probably simply that given the limited resources available to the BEA, this potential improvement to the national accounts simply isn't as high a priority as other projects.
If the statisticians knew what each and every car was used for, it might be different. If you only use your car to transport furniture when you are moving it would make sense to count it as an investment because you can avoid renting a moving truck. Unfortunately we do not know what individual cars are used for, and this example is probably very rare, so it is assumed that most cars are used for leisure, e.g. getting to places faster and in more comfort.
Why is there a need to count leasure and economic activites in separate accounts (consumption and investment)? It is because people behave differently when they are making decisions about personal consumption and when they do so about business. Corporations also have a different decision making process to achieve this. An example: You may be reluctant to sell your car when you lose your job, but a corporation will probably start downsizing if it loses a big customer. Because of this, the size of these accounts (money spent on consumption, and on investment) reacts in differing degrees to changes in the economic environment.
If we separate the two accounts it is easier to model what their main determining factors are and you can use econometric models to estimate the paramaters separately.
I could not find a reference but I believe there is some debate about which account should include puchasing newly built housing, for similar reasons. (Please correct me if I am wrong.)