The inverse dynamics of robot manipulators based on flexible arm models are considered. Actuator torques required for a flexible arm to track a given trajectory are formulated and computed by using special moving coordinate systems, called virtual rigid link coordinates. Dynamic deformations of the flexible arm can be represented in a simple and compact form with use of the virtual coordinate systems. This eliminates a number of terms involved in the equations of motion and significantly reduces complexity in the inverse dynamics computation. An efficient algorithm for computing the actuator torques is then presented on the basis of the simplified formulation, and applied to a two-link arm problem.
Inverse Dynamics of Flexible Robot Arms: Modeling and Computation for Trajectory Control
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Asada, H., Ma, Z., and Tokumaru, H. (June 1, 1990). "Inverse Dynamics of Flexible Robot Arms: Modeling and Computation for Trajectory Control." ASME. J. Dyn. Sys., Meas., Control. June 1990; 112(2): 177–185. https://doi.org/10.1115/1.2896124
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