Subsumption works by defining the robot's behaviours and organising them on to the 'subsumption stack'. Each layer has access to the sensor input and can specify the action to be taken. The higher layers are more abstract and work to achieve the robot's overall goal whereas the lower layers are simpler actions which need to respond immediately to environmental stimulus. The details of the architecture are well worth looking into. Reactive robots are still in use especially in swarm robotics.
Check out YouTube for some examples, I found this one illustrating an avoid behaviour:
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