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1. Birhythmic Analog Circuit Maze: A Nonlinear Neurostimulation Testbed

   https://doi.org/10.3390/e22050537  

   Jordan, Ian D. ; Park, Il Memming ( May 2020 , Entropy)

   Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesized that some symptoms originate from the inability to spontaneously transition from one attractor to another. Using external perturbations, such as electrical pulses delivered by deep brain stimulation devices, it may be possible to induce such transition out of the pathological attractors. However, the induction of transition may be non-trivial, rendering the current open-loop stimulation strategies insufficient. In order to develop next-generation neural stimulators that can intelligently learn to induce attractor transitions, we require a platform to test the efficacy of such systems. To this end, we designed an analog circuit as a model for the multistable brain dynamics. The circuit spontaneously oscillates stably on two periods as an instantiation of a 3-dimensional continuous-time gated recurrent neural network. To discourage simple perturbation strategies, such as constant or random stimulation patterns from easily inducing transition between the stable limit cycles, we designed a state-dependent nonlinear circuit interface for external perturbation. We demonstrate the existence of nontrivial solutions to the transition problem in our circuit implementation.
2. Vibrational Control in Flapping-Wing Micro-Air-Vehicles

   Taha, H ; Kiani, M ; Navarro, J ( June 2018 , American Control Conference)

   Flapping-Wing Micro-Air-Vehicles (FWMAVs) are bio-inspired air vehicles that mimic insect and bird flight. The dynamic behavior of these systems is typically described by a multi-body, multi-time-scale, nonlinear, time-varying dynamical system. Interestingly, this rich dynamics lead to unconventional stabilization mechanisms whose study essentially necessitates a mathematically rigorous analysis. In this paper, we use higherorder averaging, which is based on chronological calculus, to show that insects and their man-made counterparts (FWMAVs) exploit vibrational control to stabilize their body pitching angle. Such an unconventional stabilization cannot be captured by direct averaging. We also experimentally demonstrate such a phenomenon by constructing an experimental setup that allows for two degrees of freedom for the body; forward motion and pitching motion. We measure the response of the body pitching angle using a digital camera and an image processing algorithm at different flapping frequencies. It is found that there is a flapping frequency threshold beyond which the body pitching response is naturally (without feedback) stabilized, which conforms with the vibrational control concept. Moreover, we also construct a replica of the experimental setup with the FWMAV being replaced by a propeller revolving at constant speed, which results in a constant aerodynamic force, leaving no room for vibrational control.more »The response of the propellersetup is unstable at all frequencies, which also corroborates the fact that the observed stabilization of the FWMAV-setup at high frequencies is a vibrational stabilization phenomenon.« less
3. Tailoring the multistability of origami-inspired, buckled magnetic structures via compression and creasing

   https://doi.org/10.1039/D1MH01152A  

   Li, Yi ; Avis, Samuel J. ; Zhang, Teng ; Kusumaatmaja, Halim ; Wang, Xueju ( November 2021 , Materials Horizons)

   Origami-inspired multistable structures are gaining increasing interest because of their potential applications in fields ranging from deployable structures to reconfigurable microelectronics. The multistability of such structures is critical for their applications but is challenging to manipulate due to the highly nonlinear deformations and complex configurations of the structures. Here, a comprehensive experimental and computational study is reported to tailor the multistable states of origami-inspired, buckled ferromagnetic structures and their reconfiguration paths. Using ribbon structures as an example, a design phase diagram is constructed as a function of the crease number and compressive strain. As the crease number increases from 0 to 7, the number of distinct stable states first increases and then decreases. The multistability is also shown to be actively tuned by varying the strain from 0% to 40%. Furthermore, analyzing energy barriers for reconfiguration among the stable states reveals dynamic changes in reconfiguration paths with increasing strains. Guided by studies above, diverse examples are designed and demonstrated, from programmable structure arrays to a soft robot. These studies lay out the foundation for the rational design of functional, multistable structures.
4. Design and Assessment of Innovative Dual-Mode Rolling Isolation Systems

   https://doi.org/11244/321054  

   Hadikhan Tehrani, Mohammad ( August 2019 , The University of Oklahoma Libraries)

   Loss of operation or devastating damage to buildings and industrial structures, as well as equipment housed in them, has been observed due to earthquake-induced vibrations. A common source of operational downtime is due to the performance reduction of vital equipment, which are sensitive to the total transmitted acceleration. A well-known method of protecting such equipment is seismic isolation of the equipment itself (or a group of equipment), as opposed to the entire structure due to the lower cost of implementation. The first objective of this dissertation is assessing a rolling isolation system (RIS) based on existing design guidelines for telecommunications equipment. A discrepancy is observed between the required response spectrum (RRS) and the one and only accelerogram recommended in the guideline. Several filters are developed to generate synthetic accelerograms that are compatible with the RRS. The generated accelerograms are used for probabilistic assessment of a RIS that is acceptable per the guideline. This assessment reveals large failure probability due to displacement demands in excess of the displacement capacity of the RIS. When the displacement demands on an isolation system are in excess of its capacity, impacts result in spikes in transmitted acceleration. Therefore, the second objective of this dissertation ismore »to design impact prevention/mitigation mechanisms. A dual-mode system is proposed where the behavior changes when the displacement exceeds a predefined threshold. A new piecewise optimal control approach is developed and applied to find the best possible mechanism for the region beyond the threshold. By utilizing the designed curves obtained from the proposed optimal control procedure, a Kelvin-Voigt device is tuned for illustrative purposes. On the other hand, the preference for protecting equipment decreases as the earthquake intensity increases. In extreme seismic loading, the response mitigation of the primary structure (i.e., life safety and collapse prevention) is of greater concern than protecting isolated equipment. Therefore, the third objective of this dissertation is to develop an innovative dual-mode system that can behave as equipment isolation under low to moderate seismic loading and passively transition to behave as a vibration absorber for the primary structure under extreme seismic loading. To reduce the computational cost of simulating a large linear elastic structure with nonlinear attachments (i.e., equipment isolation with cubic hardening nonlinearity), a reduced order modeling method is introduced that can capture the behavior of such nonlinear coupled systems. The method is applied to study the feasibility of dual-mode vibration isolation/absorber. To this end, nonlinear transmissibility curves for the roof displacement and isolated mass total acceleration are developed from the steady-state responses of dual-mode systems using the harmonic balanced method. The final objective of this dissertation is to extend the reduced order modeling method developed for linear elastic structure with nonlinear attachment to inelastic structures (without attachments). The new inelastic model condensation (IMC) method uses the modal properties of the full structural model (in the elastic range) to construct a linear reduced order model in conjunction with a hysteresis model to capture the hysteretic inter-story restoring forces. The parameters of these hysteretic forces are easily tuned, in order to fit the inelastic behavior of the condensed structure to that of the full model under a variety of simple loading scenarios. The fidelity of structural models condensed in this way is demonstrated via simulation for different ground motion intensities on three different building structures with various heights. The simplicity, accuracy, and efficiency of this approach could significantly alleviate the computational burden of performance-based earthquake engineering.« less
5. Manipulating deformable objects by interleaving prediction, planning, and control

   https://doi.org/10.1177/0278364920918299  

   McConachie, Dale ; Dobson, Andrew ; Ruan, Mengyao ; Berenson, Dmitry ( July 2020 , The International Journal of Robotics Research)

   We present a framework for deformable object manipulation that interleaves planning and control, enabling complex manipulation tasks without relying on high-fidelity modeling or simulation. The key question we address is when should we use planning and when should we use control to achieve the task? Planners are designed to find paths through complex configuration spaces, but for highly underactuated systems, such as deformable objects, achieving a specific configuration is very difficult even with high-fidelity models. Conversely, controllers can be designed to achieve specific configurations, but they can be trapped in undesirable local minima owing to obstacles. Our approach consists of three components: (1) a global motion planner to generate gross motion of the deformable object; (2) a local controller for refinement of the configuration of the deformable object; and (3) a novel deadlock prediction algorithm to determine when to use planning versus control. By separating planning from control we are able to use different representations of the deformable object, reducing overall complexity and enabling efficient computation of motion. We provide a detailed proof of probabilistic completeness for our planner, which is valid despite the fact that our system is underactuated and we do not have a steering function. We thenmore »demonstrate that our framework is able to successfully perform several manipulation tasks with rope and cloth in simulation, which cannot be performed using either our controller or planner alone. These experiments suggest that our planner can generate paths efficiently, taking under a second on average to find a feasible path in three out of four scenarios. We also show that our framework is effective on a 16-degree-of-freedom physical robot, where reachability and dual-arm constraints make the planning more difficult.« less