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Orchard Lake, MI, United States

Shaar N.S.,Massachusetts Institute of Technology | Shaar N.S.,Mathematics Works Inc. | Barbastathis G.,Singapore Alliance for Research and Technology Center | Livermore C.,Northeastern University
Journal of Microelectromechanical Systems | Year: 2015

The design, implementation, and characterization of passively aligned reconfigurable three-dimensional (3-D) microelectromechanical systems via origami folding is presented. The process integrates into a two-mask pattern all of the features necessary for actuation, aligning, and latching segments into their correct positions under the influence of a single driving force with high tolerance to magnitude inaccuracy. Lorentz force folds the two-dimensional (2-D) elements out-of-plane. Their alignment is controlled by cascaded alignment features that create an initial interaction at coarse levels of alignment and deterministically drive the system to its as-designed final position. Reversible mechanical latches engage passively, preventing unfolding when the actuation force is released. The latches are designed to be able to be unlatched for future reconfiguration, either by returning to the unlatched state or by relatching into a second state. The proposed approach was demonstrated in an SU-8 corner cube connected by thin-film gold flexural hinges. The alignment mechanism is shown to correct for up to 11° of misalignment. The latches fasten and unfasten under forces of 13.1 and 12.5~\mu N, respectively. The average angle between folded segments of the final system is measured at 90.4° as compared with the design value of 90°, with a standard deviation of 0.6°. © 1992-2012 IEEE. Source

Jiang Yu.,Mathematics Works Inc. | Jiang Z.-P.,New York University
IEEE Transactions on Automatic Control | Year: 2015

This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is solved via a new policy iteration method. The proposed method distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided, giving rise to significant computational improvement. Instead of semiglobally or locally stabilizing, the resultant control policy is globally stabilizing for a general class of nonlinear polynomial systems. Furthermore, in the absence of the a priori knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, three numerical examples are provided to validate the effectiveness of the proposed method. © 1963-2012 IEEE. Source

Zhang W.,Colorado State University | Yang L.,Colorado State University | Yang L.,CAS Institute of Automation | Cheng X.,CAS Institute of Automation | And 2 more authors.
IEEE Transactions on Vehicular Technology | Year: 2014

Rapid and accurate timing synchronization is a critical task in ultrawideband (UWB) systems. Yang and Giannakis introduced a promising algorithm, i.e., data-aided timing with dirty templates (TDT), which is known for low complexity and relaxed operation conditions in the presence of unknown time hopping and multipath channels. In this paper, we will explore the optimality of TDT. We develop a maximum-likelihood (ML) timing algorithm and obtain its optimum training sequence. It is shown that the optimum training sequence of the ML timing estimator coincides with that of the TDT algorithm. In addition, we prove that the ML algorithm can be simplified using this training sequence and that the simplified ML (SML) is equivalent to TDT. © 2013 IEEE. Source

Mckay B.,Mathematics Works Inc.
Electronic Products (Garden City, New York) | Year: 2011

Early verification with model-based design is necessary so that design problems are minimized and time-consuming hardware fixes are avoided. Early verification allows designers to quickly evaluate a variety of control strategies and optimize system behavior, identify errors early, before robot hardware is available, use simulation to test the full operating envelope, and reuse models for real-time testing. Model-based design allows designers to build a mathematical model of the control software and the physical robot, including mechanical, electrical, hydraulic, and other physical domains. These designs allow engineers to generate embedded code directly from the model to enable rapid prototyping and hardware-in-the-loop testing. In hardware-in-the-loop testing, the production controller hardware is tested against a real-time simulation of the physical robot. Source

Ouedraogo L.,Iowa State University | Kumar R.,Mathematics Works Inc.
IEEE Transactions on Automation Science and Engineering | Year: 2014

FlexRay is a communication bus (and associated protocol) that supports transmission of time-triggered and event-triggered frames. A method for determining the worst-case response-time of FlexRay frames is proposed by Pop in 2008, and is formulated as iterative sequence of Integer Linear Programming (ILP) problems. As we show, the method of Pop is conservative (overestimates the response time). We propose a new ILP formulation that computes a precise value of the worst-case response time of FlexRay frames transmitted in the dynamic segment. Furthermore, our approach is non-iterative as it requires the solving of a single ILP for computing, respectively, the delay of full bus cycles and the delay of a partial (last) bus cycle. The proposed solution is also validated by applying it to a SAE benchmark and can be used for formally guaranteeing that no message will miss its deadline during system operation. © 2013 IEEE. Source

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