This paper presents a formal approach to the automatic synthesis of compliant motion strategies for robot assembly tasks. The approach uses geometric descriptions of parts and estimates of measurement and motion errors to produce fine-motion strategies. The key aspect of the approach is that it provides correctness criteria for compliant motion strategies. The paper discusses the challenges of robot programming in the presence of uncertainty and the need for automatic synthesis tools for robot programming, especially for compliant motion. It describes the use of pre-images to determine the range of positions from which a goal can be reached by a single motion. The approach is based on the belief that the set of possible geometric interactions in a task should directly determine the structure of the fine-motion strategy for the task. The paper also discusses the effects of uncertainty in position and velocity, the use of compliant motion, and the handling of friction. It presents a general framework for the synthesis of fine-motion strategies, including the use of termination predicates to determine when a goal has been achieved. The paper illustrates the approach with examples of peg-in-hole insertion and discusses the use of configuration space to represent motion constraints. The approach is based on the idea that the geometric constraints should "guide" the parts to their destination without necessarily having to know exactly where the parts are relative to each other. The paper concludes that the approach provides a structured way of thinking about fine-motion strategies and may be helpful to human programmers of fine-motion strategies.This paper presents a formal approach to the automatic synthesis of compliant motion strategies for robot assembly tasks. The approach uses geometric descriptions of parts and estimates of measurement and motion errors to produce fine-motion strategies. The key aspect of the approach is that it provides correctness criteria for compliant motion strategies. The paper discusses the challenges of robot programming in the presence of uncertainty and the need for automatic synthesis tools for robot programming, especially for compliant motion. It describes the use of pre-images to determine the range of positions from which a goal can be reached by a single motion. The approach is based on the belief that the set of possible geometric interactions in a task should directly determine the structure of the fine-motion strategy for the task. The paper also discusses the effects of uncertainty in position and velocity, the use of compliant motion, and the handling of friction. It presents a general framework for the synthesis of fine-motion strategies, including the use of termination predicates to determine when a goal has been achieved. The paper illustrates the approach with examples of peg-in-hole insertion and discusses the use of configuration space to represent motion constraints. The approach is based on the idea that the geometric constraints should "guide" the parts to their destination without necessarily having to know exactly where the parts are relative to each other. The paper concludes that the approach provides a structured way of thinking about fine-motion strategies and may be helpful to human programmers of fine-motion strategies.