This paper presents a formal approach to the automatic synthesis of compliant fine-motion strategies for robots, particularly for assembly tasks. The authors address the challenge of achieving tasks despite significant sensing and control errors by using active compliance. The approach involves geometric descriptions of parts and explicit estimates of measurement and motion errors to produce fine-motion strategies. Key aspects include the use of pre-images to determine reachable positions from initial states, handling uncertainty in velocity and position, and incorporating compliant motion to ensure successful task completion. The paper also discusses the role of friction and the use of configuration space to simplify the problem of motion constraints. The authors propose a general framework for fine-motion synthesis, emphasizing the importance of termination predicates that make use of current sensor readings and historical information to ensure successful task execution.This paper presents a formal approach to the automatic synthesis of compliant fine-motion strategies for robots, particularly for assembly tasks. The authors address the challenge of achieving tasks despite significant sensing and control errors by using active compliance. The approach involves geometric descriptions of parts and explicit estimates of measurement and motion errors to produce fine-motion strategies. Key aspects include the use of pre-images to determine reachable positions from initial states, handling uncertainty in velocity and position, and incorporating compliant motion to ensure successful task completion. The paper also discusses the role of friction and the use of configuration space to simplify the problem of motion constraints. The authors propose a general framework for fine-motion synthesis, emphasizing the importance of termination predicates that make use of current sensor readings and historical information to ensure successful task execution.