This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for real-time applications in robotics, since it can produce near-globally optimal solutions orders of magnitude faster than standard methods. This paper establishes theoretical conditions on how many and where samples are needed over the space of problems to achieve a given approximation quality. The framework is applied to solve globally optimal collision-free inverse kinematics (IK) problems, wherein large solution databases are used to produce near-optimal solutions in sub-millisecond time on a standard PC.
In the context of inverse kinematics, researchers from computer animation have used learning from human motion capture data @cite_1 @cite_13 . In robotics, several authors have used machine learning methods to learn local inverse kinematics solutions for manipulator control in Cartesian space @cite_5 @cite_20 . Some researchers are also able to incorporate obstacles @cite_17 @cite_16 . By contrast, our work considers the global IK problem, which is more appropriate for determining goal configurations for motion and grasp planning. Perhaps the closest attempt to ours to address this problem is an approach that tries to discover structure in the IK problem space via clustering @cite_3 . We explore more fully some of the preliminary ideas in that work.
@cite_1 @cite_3 @cite_5 @cite_16 @cite_13 @cite_20 @cite_17
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Real-time control of the end-effector of a humanoid robot in external coordinates requires computationally efficient solutions of the inverse kinematics problem. In this context, this paper investigates inverse kinematics learning for resolved motion rate control (RMRC) employing an optimization criterion to resolve kinematic redundancies. Our learning approach is based on the key observations that learning an inverse of a nonuniquely invertible function can be accomplished by augmenting the input representation to the inverse model and by using a spatially localized learning approach. We apply this strategy to inverse kinematics learning and demonstrate how a recently developed statistical learning algorithm, locally weighted projection regression, allows efficient learning of inverse kinematic mappings in an incremental fashion even when input spaces become rather high dimensional. Our results are illustrated with a 30-DOF humanoid robot. Neural networks with their inherent learning ability have been widely applied to solve the robot manipulator inverse kinematics problems. However, there are still two open problems: (1) without knowing inverse kinematic expressions, these solutions have the difficulty of how to collect training sets, and (2) the gradient-based learning algorithms can cause a very slow training process, especially for a complex configuration, or a large set of training data. Unlike these traditional implementations, the proposed metho trains neural network in joint subspace which can be easily calculated with electromagnetism-like method. The kinematics equation and its inverse are one-to-one mapping within the subspace. Thus the constrained training sets can be easily collected by forward kinematics relations. For issue 2, this paper uses a novel learning algorithm called extreme learning machine (ELM) which randomly choose the input weights and analytically determines the output weights of the single hidden layer feedforward neural networks (SLFNs). In theory, this algorithm tends to provide the best generalization performance at extremely fast learning speed. The results show that the proposed approach has not only greatly reduced the computation time but also improved the precision. We introduce and demonstrate a bootstrap method for construction of an inverse function for the robot kinematic mapping using only sample configuration--space workspace data. Unsupervised learning (clustering) techniques are used on pre-image neighborhoods in order to learn to partition the configuration space into subsets over which the kinematic mapping is invertible. Supervised learning is then used separately on each of the partitions to approximate the inverse function. The ill-posed inverse kinematics function is thereby regularized, and a global inverse kinematics solution for the wristless Puma manipulator is developed. This paper investigates the neural network approach to solve the inverse kinematics problem of redundant robot manipulators in an environment with obstacles. The solution technique proposed requires only the knowledge of the robot forward kinematics functions and the neural network is trained in the inverse modeling manner. Training algorithms for both the obstacle free case and the obstacle avoidance case are developed. For the obstacle free case, sample points can be selected in the work space as training patterns for the neural network. For the obstacle avoidance case, the training algorithm is augmented with a distance penalty function. A ball-covering object modeling technique is employed to calculate the distances between the robot links and the objects in the work space. It is shown that this technique is very computationally efficient. Extensive simulation results are presented to illustrate the success of the proposed solution schemes. Experimental results performed on a PUMA 560 robot manipulator is also presented.