Control algorithms of many Degrees-of-Freedom (DOFs) systems based on Inverse Kinematics (IK) or Inverse Dynamics (ID) approaches are two well-known topics of research in robotics. The large number of DOFs allows the design of many concurrent tasks arranged in priorities, that can be solved either at kinematic or dynamic level. This paper investigates the effects of modeling errors in operational space control algorithms with respect to uncertainties affecting knowledge of the dynamic parameters. The effects on the null-space projections and the sources of steady-state errors are investigated. Numerical simulations with on-purpose injected errors are used to validate the thoughts.

Operational space control of industrial robots is addressed in this document. We analyze a two-loop hierarchical control with the resolved motion rate controller (RMRC) as outer loop and the joint velocity PI controller as inner loop; the latter is the typical velocity controller used in industrial robots. We prove, by the first time, that these simple controllers make the solutions of the closed-loop system uniformly ultimately bounded. Additionally, we give some simple guidelines for the selection of the control gains so as to ensure an explicit bound of the tracking error.