Identification of Position-Independent Robot Parameter Errors Using Special Jacobian Matrices

Abstract

Common production manipulators are designed to be controlled through the use of a closed-form kinematic solution algorithm. This closed-form solution uses manufacturer-specified nomi nal parameter values to model the given manipulator. These position-independent parameters, link lengths, twists, and off sets are geometrical and do not change as the manipulator is driven. However, manufacturing tolerances or usage may cause the actual parameters to deviate from the nominal robot para meters. In some cases, this deviation may be large and thus may cause the closed-form inversion to yield inaccurate joint value results.

To assure proper end-effector positioning, it is important to identify these position-independent error values. The identifi cation algorithm to be presented uses the Denavit-Hartenberg (D-H) parameter notation to model any given M-jointed manip ulator. For the given model, a set of special Jacobian matrices are formulated with respect to the four D-H parameters (J_θ, J_s, J_α, and J_a). This set of four special Jacobian matrices is used to determine a set of D-H error parameter values, which will allow one to estimate the actual D-H parameter values.

The iterative regression algorithm for parameter identifi cation uses the end-effector information at several arbitrary manipulator positions, as well as nominal parameter and joint variable information to compute the parameter error values. The use of the special Jacobian matrices allows for easy de termination of mathematical singularity conditions. In addition, statistical methods are employed to provide numerical uni formity between examples and aid in the evaluation process. Through several examples, it will be shown that the use of this parameter identification algorithm produces accurate results. This article will discuss the possibilities of deterministic as well as probabilistic parameter errors. Through the use of this parameter identification algorithm, one is able to identify the D-H parameter error values that will otherwise cause a loss in end-effector accuracy.

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