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Mobile real-time systems must sense constraints imposed by a dynamically changing environment and predictably react to those changes in real-time. Mobile real-time systems add yet one more level of complexity in that the computing platform travels through the environment with which the system is interacting. These systems have spatio-temporal requirements in the sense that correct behavior is defined in terms of both space and time. We present a design and analysis methodology for these platforms that integrates spatio-temporal attributes with fixed priority real-time scheduling. To support dynamic environments, we divide the path the mobile platform traverses into zones and associate with each zone a processing window. We also present an algorithmic framework for adjusting platform speed, performance parameters or processing windows such that the maximum speed less than or equal to the desired speed (or performance) is maintained or maximized while adjusting the processing window to maintain schedulability of the platform's real-time tasks. We test our theory and methodology on two different case studies representing two different mobile robotic applications.