On the Robust Control of Robot Manipulators

Mark W. Spong textbook [13] for background of the robotics application of this technique. The novelty of our result in the present paper lies in the fact that the uncertainty bounds needed to derive the control law and to prove uniform ultimate boundedness of the tracking error depend only on the inertia parameters of the robot. Previous applications of the Leitmann approach to robot manipulators [13], [3] have required uncertainty bounds that depend not only on the inertia parameters but also on the reference trajectory and on the manipulator state vector. As a result, precise bounds on the uncertainty have been difficult to compute. Moreover, some further assumptions regarding “closeness in norm” of the computed inertia matrix to the actual inertial matrix have generally been required as well [l], [13]. The design in this note removes these assumptions. The result is achieved by exploiting the skew-symmetry property and linear parameterizability of robot dynamics [9], [13]. Thus, while previous robust controllers have been based upon the idea of robust feedback linearization, our controller uses the skew-symmetry property and linearity in parameters of the robot dynamics in a fundamental way.