This paper addresses the control-theoretic approach of an autonomous fog computing platform to process the of-ftoaded mobile robot vision data for warehouse applications. The approach entails polytopic linear parameter varying (PLPV) modelling of the fog platform and the design of an event-triggered control to process the vision data within a specified time frame called service time, by auto-scaling the computing nodes. The PLPV model is developed using dynamic mobile robot vision data with image resolution and frame rate as parameters. The developed theory is experimentally validated on a mobile robot that navigates in a warehouse application environment, and the results are presented to show the efficacy of the proposed controller in meeting the service time requirements.