To continuously generate trajectories for serial manipulators with high dimensional degrees of freedom (DOF) in the dynamic environment, a real-time optimal trajectory generation method based on machine learning aiming at high dimensional inputs is presented in this paper. First, a learning optimization (LO) framework is established, and implementations with different sub-methods are discussed. Additionally, multiple criteria are defined to evaluate the performance of LO models. Furthermore, aiming at high dimensional inputs, a database generation method based on input space dimension-reducing mapping is proposed. At last, this method is validated on motion planning for haptic feedback manipulators (HFM) in virtual reality systems. Results show that the input space dimension-reducing method can significantly elevate the efficiency and quality of database generation and consequently improve the performance of the LO. Moreover, using this LO method, real-time trajectory generation with high dimensional inputs can be achieved, which lays a foundation for continuous trajectory planning for high-DOF-robots in complex environments.
The database for learning can be obtained by either recording the former data, or artificially generating. @cite_17 evenly chose variables in motion range to generate samples and drew a comparison of databases with different sizes. Hauser @cite_11 uniformly sampled an axis-aligned range of variables to generate a database. Besides, a lifelong learning mode was presented to continuously generate examples with a separate background thread. In addition, the sensitivity of the required database size to the input dimension and the requirement for the database to guarantee the quality of solutions were discussed. However, for the cases with high dimensional inputs, the above database generation methods of randomly or evenly choosing sample variables in the motion range are time-consuming. Thus, finding a way to elevate the efficiency of database generation is a key issue to be solved.
@cite_11 @cite_17
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To speed up multidimensional data analysis, database systems frequently precompute aggregates on some subsets of dimensions and their corresponding hierarchies. This improves query response time. However, the decision of what and how much to precompute is a difficult one. It is further complicated by the fact that precomputation in the presence of hierarchies can result in an unintuitively large increase in the amount of storage required by the database. Hence, it is interesting and useful to estimate the storage blowup that will result from a proposed set of precomputations without actually computing them. We propose three strategies for this problem: one based on sampling, one based on mathematical approximation, and one based on probabilistic counting. We investigate the accuracy of these algorithms in estimating the blowup for different data distributions and database schemas. The algorithm based upon probabilistic counting is particularly attractive, since it estimates the storage blowup to within provable error bounds while performing only a single scan of the data. *Work supported by an IBM CAS Fellowship, NSF grant IRI9157357, and a grant from IBM under the University Partnership Program. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying 1:s by permission of the Very Large Data Base Endowm.ent. To copy otherwise, 01‘ to republish, requires a fee and or special permission j orn the En.do?ument. Proceedings of the 22nd VLDB Conference Mumbai(Bombay), India, 1996 We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. Most previous work on trainable language generation has focused on two paradigms: (a) using a generation decisions of an existing generator. Both approaches rely on the existence of a handcrafted generation component, which is likely to limit their scalability to new domains. The first contribution of this article is to present Bagel, a fully data-driven generation method that treats the language generation task as a search for the most likely sequence of semantic concepts and realization phrases, according to Factored Language Models (FLMs). As domain utterances are not readily available for most natural language generation tasks, a large creative effort is required to produce the data necessary to represent human linguistic variation for nontrivial domains. This article is based on the assumption that learning to produce paraphrases can be facilitated by collecting data from a large sample of untrained annotators using crowdsourcing—rather than a few domain experts—by relying on a coarse meaning representation. A second contribution of this article is to use crowdsourced data to show how dialogue naturalness can be improved by learning to vary the output utterances generated for a given semantic input. Two data-driven methods for generating paraphrases in dialogue are presented: (a) by sampling from the n-best list of realizations produced by Bagel's FLM reranker; and (b) by learning a structured perceptron predicting whether candidate realizations are valid paraphrases. We train Bagel on a set of 1,956 utterances produced by 137 annotators, which covers 10 types of dialogue acts and 128 semantic concepts in a tourist information system for Cambridge. An automated evaluation shows that Bagel outperforms utterance class LM baselines on this domain. A human evaluation of 600 resynthesized dialogue extracts shows that Bagel's FLM output produces utterances comparable to a handcrafted baseline, whereas the perceptron classifier performs worse. Interestingly, human judges find the system sampling from the n-best list to be more natural than a system always returning the first-best utterance. The judges are also more willing to interact with the n-best system in the future. These results suggest that capturing the large variation found in human language using data-driven methods is beneficial for dialogue interaction. In this paper, we propose three criteria for efficient sample selection in case of data stream regression problems within an online active learning context. The selection becomes important whenever the target values, which guide the update of the regressors as well as the implicit model structures, are costly or time-consuming to measure and also in case when very fast models updates are required to cope with stream mining real-time demands. Reducing the selected samples as much as possible while keeping the predictive accuracy of the models on a high level is, thus, a central challenge. This should be ideally achieved in unsupervised and single-pass manner. Our selection criteria rely on three aspects: 1) the extrapolation degree combined with the model's nonlinearity degree , which is measured in terms of a new specific homogeneity criterion among adjacent local approximators; 2) the uncertainty in model outputs, which can be measured in terms of confidence intervals using so-called adaptive local error bars — we integrate a weighted localization of an incremental noise level estimator and propose formulas for online merging of local error bars; 3) the uncertainty in model parameters, which is estimated by the so-called A-optimality criterion, which relies on the Fisher information matrix. The selection criteria are developed in combination with evolving generalized Takagi–Sugeno (TS) fuzzy models (containing rules in arbitrarily rotated position), as it could be shown in previous publications that these outperform conventional evolving TS models (containing axis-parallel rules). The results based on three high-dimensional real-world streaming problems show that a model update based on only 10 –20 selected samples can still achieve similar accumulated model errors over time to the case when performing a full model update on all samples. This can be achieved with a negligible sensitivity on the size of the active learning latency buffer. Random sampling with the same percentages of samples selected, however, achieved much higher error rates. Hence, the intelligence in our sample selection concept leads to an economic balance between model accuracy and measurement as well computational costs for model updates.