China War

Systems where digital components are intimately coupled with their physical environment — often called cyber-physi- cal systems (CPS) – pose a challenge when we wish to specify their desired behavior. For purely digital computing sys- tems, the programming language or hardware description language itself can su ce. Often, the implementation lan- guage itself can express the desired behavior using asser- tions. Such assertions can then be used as dynamic checks, used by test-case generation tools, or used by formal verifi- cation tools. In contrast, for CPS applications we typically want to specify the desired behavior for a computational component in terms of its action on the physical environ- ment. For example, we may wish that for a particular robot controller the torque on one of the robot’s joints never ex- ceed a certain value. However, part of specifying “the robot’s joint” is to specify “the robot”. Rigorously specifying the latter, and in particular, its continuous mechanics, is most naturally and accurately expressed using the mathematical formalisms of analytical dynamics (c.f. [1]). Specifying a robot’s dynamics is neither naturally nor accurately speci- fied in the discrete-step language used to write the controller.

It is tempting, given that simulation of continuous systems is a well-established discipline [8], to assume that there is a tool for directly expressing the analytical dynamics of a physical system, and which can be automatically used to simulate the system. This does not seem to be the case. This absence is surprising, given the abundance of tools that seem relevant to this process, and suggests a need for closer scrutiny of the process for going from models to simulation codes.