Systemic properties of robotic manipulators during compliant task execution and their impact on controller design

The generic properties of robotic manipulator dynamics are investigated during tasks in which the manipulator end effector comes in contact with a compliant work environment. The dynamics of an n-degree-of-freedom rigid link manipulator with an r-axis wrist-mounted force-torque sensor is modeled during contact with a work environment that is represented as a mechanical impedance. A local linear model of the robotic system dynamics is derived from this nonlinear model. A system output is defined that corresponds to the generalized forces and positions that are to be controlled during compliant motion. With this local model, it is shown from linear system theory that certain necessary and sufficient conditions must be satisfied for a solution to the compliant motion control problem to exist. Insight into the compliant motion control problem is gained through examination of the conditions imposed on the structure of the manipulator model in order to satisfy the necessary and sufficient conditions. Certain control objectives, which are intuitively known to be attainable, are shown to violate these necessary and sufficient conditions. Explicitly modeling the force-torque sensor dynamics results in a system with a poorly conditioned eigensystem. Well-known methods are used to internally balance the system permitting reliable control system synthesis. Two numerical examples are included to illustrate the concepts discussed