The singularity problem is an inherent problem in controlling robot manipulators with articulated configuration. In this paper, we propose to determine the joint motion for the requested motion of the endeffector by evaluating the feasibility of the joint motion. The determined joint motion is called an inverse kinematic solution with singularity robustness, because it denotes feasible solution even at or in the neighborhood of singular points. The singularity robust inverse (SR-inverse) is introduced as an alternative to the pseudoinverse of the Jacobian matrix. The SR-inverse of the Jacobian matrix provides us with an approximating motion close to the desired Cartesian trajectory of the endeffector, even when the inverse kinematic solution by the inverse or the pseudoinverse of the Jacobian matrix is not feasible at or in the neighborhood of singular points. The properties of the SR-inverse are clarified by comparing it with the inverse and the pseudoinverse. The computational complexity of the SR-inverse is considered to discuss its implementability. Several simulation results are also shown to illustrate the singularity problem and the effectiveness of the inverse kinematic solution with singularity robustness.

"Mimesis" theory focused in the cognitive science field and "mirror neurons" found in the biology field show that the behavior generation process is not independent of the behavior cognition process. The generation and cognition processes have a close relationship with each other. During the behavioral imitation period, a human being does not practice simple joint coordinate transformation, but will acknowledge the parents' behavior. It understands the behavior after abstraction as symbols, and will generate its self-behavior. Focusing on these facts, we propose a new method which carries out the behavior cognition and behavior generation processes at the same time. We also propose a mathematical model based on hidden Markov models in order to integrate four abilities: (1) symbol emergence; (2) behavior recognition; (3) self-behavior generation; (4) acquiring the motion primitives. Finally, the feasibility of this method is shown through several experiments on a humanoid robot.

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This paper describes a novel approach for autonomous and incremental learning of motion pattern primitives by observation of human motion. Human motion patterns are abstracted into a dynamic stochastic model, which can be used for both subsequent motion recognition and generation, analogous to the mirror neuron hypothesis in primates. The model size is adaptable based on the discrimination requirements in the associated region of the current knowledge base. A new algorithm for sequentially training the Markov chains is developed, to reduce the computation cost during model adaptation. As new motion patterns are observed, they are incrementally grouped together using hierarchical agglomerative clustering based on their relative distance in the model space. The clustering algorithm forms a tree structure, with specialized motions at the tree leaves, and generalized motions closer to the root. The generated tree structure will depend on the type of training data provided, so that the most specialized motions will be those for which the most training has been received. Tests with motion capture data for a variety of motion primitives demonstrate the efficacy of the algorithm.

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Abstract-This paper describes an approach for on-line, incremental learning of full body motion primitives from observation of human motion. The continuous observation sequence is first partitioned into motion segments, using stochastic segmentation. Motion segments are next incrementally clustered and organized into a hierarchical tree structure representing the known motion primitives. Motion primitives are encoded using hidden Markov models, so that the same model can be used for both motion recognition and motion generation. At the same time, the relationship between motion primitives is learned via the construction of a motion primitive graph. The motion primitive graph can then be used to construct motions, consisting of sequences of motion primitives. The approach is implemented and tested on the IRT humanoid robot.