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A structured programming and teaching system is described for a robot manipulator where stress is laid on the consistent integration of programming and teaching. In the PAL programming system being developed at Purdue University, tasks are represented in terms of structured Cartesian coordinates. Every motion statement is a request to position and orient the manipulator such that a position equation, representing a closed kinematic chain of homogeneous transformations, is satisfied. In the teaching process, the transformation which represents the position of the end of the manipulator is defined using the manipulator itself, and an equation relating any undefined transformations is obtained. By defining these equations during the interpretation of the task program and progressively solving them, the task is taught. The method is applicable both to practical industrial robot control and to intelligent robot control.