A new technique for solving robot calibration equations with partially known constraints

This paper presents an improved method for deducing kinematic parameters from constrained calibration data. The method assumes that the calibration data is constrained such that for each recorded set of joint angles, the endpoint of the robot satisfies some parameterized mathematical constraint. Suitable mathematical constraint equations include points, lines, circles, spheres, planes, hyperplanes, and others. The constraint equations do not need to be fully known; some parameters of the constraints can be unknown, and the method can still be employed. The method prescribes a nonlinear transformation of the solution equations into a new space in which a vector function of parameters multiplies a vector function of joint variables. In this transformed space, the vector function of parameters can be identified using a linear, least-squares approach. Subsequently, the transformed parameter-function vector is solved analytically for the actual parameter values. This approach differs from existing, iterative techniques in that there are no numerical problems of local-minima traps, slow convergence rates, null-space wandering or instability. Examples are presented to illustrate the method, and results are presented for calibration of an AdeptOne robot