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Robots are generally composed of multiple sensors , actuators and electromechanical parts. The overall behavior of a robot is emergent from coordination among its various parts and its interaction with its environment. Designing a `correct' robot which does`the right thing' in a given environment is an important and challenging problem. The question posed in the title is decomposed into two questions. First, what is the right thing? Second, how does one guarantee the robot will do it? We answer these questions in this paper by establishing a formal approach to the design and analysis of robotic systems and behaviors. Building control systems for intelligent, reliable, robust and safe autonomous robots working in complex environments is an increasingly important challenge for research in electrical and mechanical engineering, and computer science. Robots are generally composed of multiple sensors, ac-tuators and electromechanical parts. Robots should be reactive as well as purposive systems, closely coupled with their environments; they must deal with inconsistent , incomplete and delayed information from various sources. Such systems are usually complex, hierarchical and physically distributed. Each component functions according to its own dynamics. The overall behavior of a system is emergent from coordination among its various parts and its interaction with its environment. We call the integration of a robot and its environment a robotic system, and the relation on the state of a robot and its environment over time the robotic behavior. The current trend for developing intelligent robots is to combine AI techniques with traditional control theory Schoppers, 1991]. However, most of this work is ad hoc; there is no well deened interface between the higher level (AI) and the lower level (control). The coordination between these levels is not fully understood, and the Shell Canada Fellow, Canadian Institute for Advanced Research behavior of the whole system cannot be analyzed. One fundamental problem is the mismatch of the underlying computational models. AI is based on oo-line computational models and control is based on on-line computational models. (The distinction between oo-line and on-line models is analogous to the distinction between functions and processes.) In this paper, we advocate a formal approach to mod-eling a robotic system. We have developed a formal model, Constraint Nets (CN), for general dynamic systems Zhang and Mackworth, 1994a]. CN is an abstraction of general dynamic systems so that a system with discrete as well as continuous time, and asynchronous as well as synchronous …