This report, "Compliance and Force Control for Computer Controlled Manipulators," by Matthew Thomas Mason, focuses on the development of a theoretical framework for force control in computer-controlled manipulators. The primary goal is to enable compliant motion, where the manipulator's position is constrained by the task geometry, either through passive mechanical compliance or active compliance implemented in the control servo loop. The report introduces a formal model of force control based on the ideal effector and the task geometry, which includes the ideal surface, the locus of all positions accessible to the ideal effector. The models are useful for two main reasons: they provide a precise semantics for force control primitives in manipulator programming languages, simplifying the programming process, and they offer a method for synthesizing force control programs for compliant motion. The synthesis problem involves constructing control strategies that, when combined with the task geometry, produce a unique solution that matches the goal trajectory. The report emphasizes the importance of orthogonality and non-redundancy in the equations to ensure good performance in the presence of planning model errors. The report also discusses various control strategies, such as pure position control, pure force control, and guarded moves, and their relevance to compliant motion. It provides examples and detailed analyses of different types of surfaces, including zero-energy surfaces, non-homogeneous surfaces, and half-surfaces, to illustrate the synthesis of control strategies. The transformations between the ideal domain and the real world are discussed, and the report concludes with a discussion of related work and suggestions for further research.This report, "Compliance and Force Control for Computer Controlled Manipulators," by Matthew Thomas Mason, focuses on the development of a theoretical framework for force control in computer-controlled manipulators. The primary goal is to enable compliant motion, where the manipulator's position is constrained by the task geometry, either through passive mechanical compliance or active compliance implemented in the control servo loop. The report introduces a formal model of force control based on the ideal effector and the task geometry, which includes the ideal surface, the locus of all positions accessible to the ideal effector. The models are useful for two main reasons: they provide a precise semantics for force control primitives in manipulator programming languages, simplifying the programming process, and they offer a method for synthesizing force control programs for compliant motion. The synthesis problem involves constructing control strategies that, when combined with the task geometry, produce a unique solution that matches the goal trajectory. The report emphasizes the importance of orthogonality and non-redundancy in the equations to ensure good performance in the presence of planning model errors. The report also discusses various control strategies, such as pure position control, pure force control, and guarded moves, and their relevance to compliant motion. It provides examples and detailed analyses of different types of surfaces, including zero-energy surfaces, non-homogeneous surfaces, and half-surfaces, to illustrate the synthesis of control strategies. The transformations between the ideal domain and the real world are discussed, and the report concludes with a discussion of related work and suggestions for further research.