A finite‐element approach to control the end‐point motion of a single‐link flexible robot

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Abstract
A structural finite‐element technique based on Bernoulli‐Euler beam theory is presented which will permit the finding of the torques (or forces) that are necessary to apply at one end of a flexible link to produce a desired motion at the other end. This technique is suitable for the open loop control of the tip motion. It may also provide a good control law for feedback control. The finite‐element method is used to discretize the equations of motion. This method has a major advantage in the fact that different material properties and boundary conditions like hubs, tip loads, changes in cross sections, etc., can be handled in a very simple and straightforward manner. The resulting differential equations are integrated via the frequency domain. This allows for the expansion of the desired end motion into its harmonic components and helps to visualize the complex wave propagation nature of the problem. The performance of the proposed technique is illustrated in the solution of a practical example. Results point out the potential that this technique has in the study of the dynamics and control not only of flexible robots, but also of any other flexible mechanisms like those used in biomechanics, where high precision at the tip of very light flexible arms is required.

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