Control of flexible joint robots via external linearization approach

Based on the feedback linearization structure algorithm of differential geometric nonlinear control theory, an external linearization approach to the control of multilink flexible joint robots is considered in this article. The resulting externally linearized and input-output decoupled closed-loop system contains a linear subsystem and a nonlinear subsystem. The linear part describing the rigid motor motions is suitable for the design of nominal trajectory following control. However, the nonlinear joint deformation subsystem will cause perturbations in the nominal trajectory. To actively damp out the elastic vibrations and to render the complete closed-loop system robust to uncertainty in system parameters, a combined LQR stabilizer and servocompensator is used as the internal stabilization and error correcting control. The tracking errors of the end effector caused by the quasi-static joint deflections due to gravity can be compensated for by taking into account the nominal deflections in the trajectory planning and LQ regulation. A three-link PUMA type arm is tested via simulation.

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