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Compliant motion of a manipulator occurs when the manipulator position is constrained by the task geometry. Compliant motion may be produced either by a passive mechanical compliance built in to the manipulator, or by an active compliance implemented in the control servo loop. The second method, called force control, is the subject of this paper. In particular a theory of force control based on formal models of the manipulator and the task geometry is presented. The ideal effector is used to model the manipulator, the ideal surface is used to model the task geometry, and the goal trajectory is used to model the desired behavior of the manipulator. Models are also defined for position control and force control, providing a precise semantics for compliant motion primitives in manipulation programming languages. The formalism serves as a simple interface between the manipulator and the programmer, isolating the programmer from the fundamental complexity of low-level manipulator control. A method of automatically synthesizing a restricted class of manipulator programs based on the formal models of task and goal trajectory is also provided by the formalism.