Random Finite Set Theory and Optimal Control of Large Collaborative Swarms

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using Model Predictive Control (MPC) to overcome the aforementioned challenges. Computationally efficient solutions are obtained via the Iterative Linear Quadratic Regulator (ILQR). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration. Then, a stochastic optimal control problem is formulated using a modified L2^2 distance. Simulation results using MPC and ILQR show that swarm intensities converge to a target destination, and the RFS control formulation can vary in the number of target destinations. ILQR also provides a more computationally efficient solution to the RFS swarm problem when compared to the MPC solution. Lastly, the RFS control solution is applied to a spacecraft relative motion problem showing the viability for this real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731

Global localization based on a rejection differential evolution filter

Autonomous systems are able to move from one point to another in a given environment because they can solve two basic problems: the localization problem and the navigation problem. The localization purpose is to determine the current pose of the autonomous robot or system and the navigation purpose is to find out a feasible path from the current pose to the goal point that avoids any obstacle present in the environment. Obviously, without a reliable localization system it is not possible to solve the navigation problem. Both problems are among the oldest problems in human travels and have motivated a considerable amount of technological advances in human history. They are also present in robot motion around the environment and have also motivated a considerable research effort to solve them in an efficient way

Measurements, Models, Systems and Design

531 s.

Mechanism of Tricalcium Silicate Hydration in the Presence of Polycarboxylate Polymers

Abstract: The early-age hydration of cement is inhibited in the presence of comb-shaped polycarboxylate ether (PCE) polymer -- a dispersant commonly added to control rheological properties of fresh cement paste. This study employs a series of microcalorimetry experiments and phase boundary nucleation and growth simulations to elucidate the effects of dosage and molecular architecture of PCE on hydration of tricalcium silicate (Ca3SiO5 or C3S in cement notation), the dominant phase in cement. Results show that PCE -- regardless of its molecular architecture -- suppresses early-age hydration of C3S. PCE-induced retardation becomes increasingly more pronounced as dosage of PCE in the paste increases. Such suppression of C3S hydration has been attributed to adsorption of PCE molecules on silicate surfaces, which inhibit topographical sites of C3S dissolution and C–S–H nucleation, and impede the post-nucleation growth of C–S–H. This study develops a correlation between molecular architecture of PCE and its ability to suppress C3S hydration through quantitative analyses of retardation effects induced by PCEs with different molecular architectures. The numerical equation, describing such correlation, offers a reliable, and, more importantly, a readily quantifiable indicator of PCE’s potential to suppress C3S hydration in relation to its dosage and molecular architecture. In the context of practical application of this study, the aforementioned numerical equation can be used to order and rank PCEs -- of various molecular architectures -- on the bases of their potentials to suppress C3S hydration, and to select ones that cause the optimum (i.e., user-desired) extent of hydration suppression

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure