Testing iterative robotic algorithms by their rate of convergence

The authors discuss a number of principles associated with the rate of convergence of iterative robotic calculations that have been found to be helpful in testing the correctness of such programs. One example of an iterative robotic calculation is performing inverse kinematics by an indirect method such as Jacobian control. Because such a method is based on a local approximation, the numerical results are not supposed to be perfect after changing joint angles a finite amount. It is not obvious how much error is inherent in the method. It is known that if the interval size is reduced to zero, the results will reach the ideal value. It has been the authors´ experience, however, that even when the errors numerically reduce to zero in the limit, there can still be serious errors in the formulation or the computer program. Based on the authors´ experience in developing and debugging new algorithms, several principles that will greatly aid in detecting errors are presented