
kriechen
to crawl
To move forward on one's stomach or on all fours with the body close to the ground.
Das Baby hat gerade angefangen, durch das Wohnzimmer zu kriechen.
The baby has just started to crawl through the living room.
to crawl / grovel
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to crawl
To move forward on one's stomach or on all fours with the body close to the ground.
Das Baby hat gerade angefangen, durch das Wohnzimmer zu kriechen.
The baby has just started to crawl through the living room.

to grovel
To behave submissively and flatteringly in order to gain advantages from a person in a higher position. This meaning has a strongly negative connotation.
Er ist nur deshalb befördert worden, weil er ständig vor dem Chef kriecht.
He was only promoted because he constantly grovels before the boss.

to crawl
To move extremely slowly. Often used for vehicles in traffic jams or for very slow processes.
Im Feierabendverkehr kriecht der Verkehr auf der Autobahn nur noch voran.
In rush-hour traffic, traffic on the highway is only crawling along.
'Kriechen' (to crawl) describes a form of movement. Therefore, the perfect tense is always formed with the auxiliary verb 'sein' (to be), not with 'haben' (to have).
Die Schnecke ist langsam über das Blatt gekrochen.
The snail crawled slowly across the leaf.
The subject of the sentence reveals the meaning: babies or animals crawl on the ground. Traffic or time crawls when it is very slow. A person 'kriecht vor jemandem' (grovels before someone) when they behave submissively.
Das Baby ist unter den Tisch gekrochen.
The baby crawled under the table.
In the figurative, negative meaning, 'kriechen' (to grovel) is often used with the preposition 'vor' and a person in the dative: 'vor jemandem kriechen' (to grovel before someone).
Ich werde sicher nicht vor dem neuen Abteilungsleiter kriechen, nur um beliebt zu sein.
I certainly won't grovel before the new department head just to be popular.
When it is about slow movement, 'kriechen' (to crawl) is often used for vehicles in traffic jams or abstract things like time.
Die Autos krochen Stoßstange an Stoßstange über die Brücke.
The cars crawled bumper to bumper across the bridge.
to crawl
Robben and kriechen both describe moving close to the ground. Robben more specifically means lying on your stomach and pulling your body across the ground, while kriechen also includes moving on all fours. Use robben for this particular body position and kriechen as the more general expression.

Das Kind kroch auf allen Vieren durch das nasse Gras.
The child crawled on all fours through the wet grass.
Der Soldat musste bäuchlings durch das nasse Gras robben.
The soldier had to crawl on his stomach through the wet grass.