Recursive methods in control of flexible joint manipulators

This paper considers recursive solving methods in the control of modular and reconfigurable robot systems. The focus lies on the end-point accuracy and recursive methods for its improvement. The modeling of the robot systems under consideration is done by the Projection Equation in Subsystem representation. Due to gear elasticities and the lack of position sensors at the gearbox output shaft, deflections of the end-point cannot be compensated by standard PD motor control. Therefore, a novel approach is presented in this contribution to correct the resulting position errors of the end-points of the robot systems. This proposed method enables to do a flat parameterization of such elastically modeled systems in a recursive manner, which is contrasted to the generally used non-recursive exact feed-forward linearization method in minimal form for such under-actuated systems. The ability to do the computation in such a recursive way offers the possibility to do the calculations systems for systems with many degrees-of-freedom (DOF) as well, where standard analytical methods reach their limits. And for modular systems, it is applicable as well. For validation, the proposed method is implemented for a robot arm with seven joints and simulation results are presented.