The algorithms have been implemented in the general-purpose motion planning software Move3D, developed at LAAS-CNRS. We are currently working on an optimized stand-alone library that will be available to the scientific community.

Abstract-We propose a technique to speedup the learning of the inverse kinematics of a robot manipulator by decomposing it into two or more virtual robot arms. Unlike previous decomposition approaches, this one does not place any requirement on the robot architecture, and thus, it is completely general. Parametrized self-organizing maps are particularly adequate for this type of learning, and permit comparing results directly obtained and through the decomposition. Experimentation shows that time reductions of up to two orders of magnitude are easily attained.

The expectation of a function of random variables can be modeled as the value of the function in the mean value of the variables plus a penalty term. Here, this penalty term is calculated exactly, and the properties of different approximations are analyzed. Then, a deterministic algorithm for minimizing the expected error of a feedforward network of random weights is presented. Given a particular feedforward network architecture and a training set, this algorithm accurately finds the weight configuration that makes the network response most resistant to a class of weight perturbations. Finally, the study of the most stable configurations of a network unravels some undesirable properties of networks with asymmetric activation functions.

The main drawback of using neural networks or other example-based learning procedures to approximate the inverse kinematics (IK) of robot arms is the high number of training samples (i.e., robot movements) required to attain an acceptable precision. We propose here a trick, valid for most industrial robots, that greatly reduces the number of movements needed to learn or relearn the IK to a given accuracy. This trick consists in expressing the IK as a composition of learnable functions, each having half the dimensionality of the original mapping. Off-line and on-line training schemes to learn these component functions are also proposed. Experimental results obtained by using nearest neighbors and parameterized self-organizing map, with and without the decomposition, show that the time savings granted by the proposed scheme grow polynomially with the precision required.

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