Inversion techniques for trajectory control of flexible robot arms

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Abstract
A general framework is given for computing the torques that are needed for moving a flexible arm exactly along a given trajectory. This torque computation requires a dynamic generator system, as opposed to the rigid case, and can be accomplished both in an open‐ or in a closed‐loop fashion. In the open‐loop case, the dynamic generator is the full or reduced order inverse system associated to the arm dynamics and outputs. In order to successfully invert the arm dynamics, the torque generator should be a stable system. The stability properties depend on the chosen system output, that is on the robot variables (e.g., joint or end‐effector) to be controlled. The same inversion technique can be applied for closed‐loop trajectory control of flexible robots. A simple but meaningful nonlinear dynamic model of a one‐link flexible arm is used to illustrate different feasible control strategies. Simulation results are reported that display the effects of the system output choice on the closed‐loop stability and on the overall tracking performance.

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