This paper presents a symbolic analysis of the base parameters for closed-chain robots by means of the completion procedure in polynomial ideal theory. The regressor of the robot dynamics is represented as a matrix of multivariate polynomials and reduced to the "normal form" based on Buchbergers' algorithm by constructing reduced Grobner bases from kinematic constraint equations. The linear independence of column vectors of the reduced regressor is examined by the Gauss-Jordan elimination method. The original dynamic parameters are regrouped and some of them are eliminated based on the results. This method derives all the base parameters systematically in theory. Two examples are presented to illustrate the merits of the new method.

This paper presents a new computational algorithm of the model-based adaptive manipulator control, adopting the basic method proposed by Slotine and Li (1987). The manipulator regressor that is represented by an actual velocity vector and a reference velocity vector is computed explicitly by a recursive algorithm based on the Newton-Euler formulation. The proposed algorithm is more efficient than other methods for a manipulator with six or fewer joints. An experimental result is also presented to show the possibility of an adaptive controller having a single DSP for a robot manipulator with six degrees of freedom.