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Achieving stable bipedal walking on surfaces with unknown motion remains a challenging control problem due to the hybrid, time-varying, partially unknown dynamics of the robot and the difficulty of accurate state and surface motion estimation. Surface motion imposes uncertainty on both system parameters and non-homogeneous disturbance in the walking robot dynamics. In this paper, we design an adaptive ankle torque controller to simultaneously address these two uncertainties and propose a step-length planner to minimize the required control torque. Typically, an adaptive controller is used for a continuous system. To apply adaptive control on a hybrid system such as a walking robot, an intermediate command profile is introduced to ensure a continuous error system. Simulations on a planar bipedal robot, along with comparisons against a baseline controller, demonstrate that the proposed approach effectively ensures stable walking and accurate tracking under unknown, time-varying disturbances.

Arterial traffic interacts with freeway traffic, yet the two are controlled independently. Arterial traffic signals do not take into account freeway traffic and how ramps control ingress traffic and have no control over egress traffic from the freeway. This often results in long queues in either direction that block ramps and spill over to arterial streets or freeway lanes. In this paper, we propose an adaptive arterial traffic control strategy that combines traffic signal control (TSC) and dynamic speed offset (DSO) coordination using a Q-learning algorithm for a traffic network that involves a freeway segment and adjacent arterial streets. The TSC agent computes the signal cycle length and split based on observed intersection demands and adjacent freeway off-ramp queues. The DSO agent computes the relative offset and the recommended speeds of both ways between consecutive intersections based on their physical distance, intersection queues, and signal cycles. We evaluate the performance of the proposed arterial traffic control strategy using microscopic traffic simulations of an arterial corridor with seven intersections near the I-710 freeway. The proposed QL-based control significantly outperforms a fixed-time control and MAXBAND in terms of the travel time and the number of stops under low or moderate demands. In high-demand scenarios, the travel-time benefit provided by the QL-based control is reduced as it mitigates off-ramp and intersection queues, which is a necessary trade-off in our perspective. In addition, mutual benefit is obtained by implementing freeway and arterial traffic control simultaneously., Comment: submitted to TR-C

Numerous studies have shown the effectiveness of intelligent transportation system techniques such as variable speed limit (VSL), lane change (LC) control, and ramp metering (RM) in freeway traffic flow control. The integration of these techniques has the potential to further enhance the traffic operation efficiency of both freeway and adjacent arterial networks. In this regard, we propose a freeway traffic control (FTC) strategy that coordinates VSL, LC, RM actions using a Q-learning (QL) framework which takes into account arterial traffic characteristics. The signal timing and demands of adjacent arterial intersections are incorporated as state variables of the FTC agent. The FTC agent is initially trained offline using a single-section road network, and subsequently deployed online in a connected freeway and arterial simulation network for continuous learning. The arterial network is assumed to be regulated by a traffic-responsive signal control strategy based on a cycle length model. Microscopic simulations demonstrate that the fully-trained FTC agent provides significant reductions in freeway travel time and the number of stops in scenarios with traffic congestion. It clearly outperforms an uncoordinated FTC and a decentralized feedback control strategy. Even though the FTC agent does not control the arterial traffic signals, it leads to shorter average queue lengths at arterial intersections by taking into account the arterial traffic conditions in controlling freeway traffic. These results motivate a future research where the QL framework will also include the control of arterial traffic signals., Comment: 12 pages, 9 figures, 5 tables

Although the roll-streak (R-S) is fundamentally involved in the dynamics of wall-turbulence, the physical mechanism responsible for its formation and maintenance remains controversial. In this work we investigate the dynamics maintaining the R-S in turbulent Poiseuille flow at R=1650. Spanwise collocation is used to remove spanwise displacement of the streaks and associated flow components, which isolates the streamwise-mean flow R-S component and the second-order statistics of the streamwise-varying fluctuations that are collocated with the R-S. This streamwise-mean/fluctuation partition of the dynamics facilitates exploiting insights gained from the analytic characterization of turbulence in the second-order statistical state dynamics (SSD), referred to as S3T, and its closely associated restricted nonlinear dynamics (RNL) approximation. Symmetry of the statistics about the streak centerline permits separation of the fluctuations into sinuous and varicose components. The Reynolds stress forcing induced by the sinuous and varicose fluctuations acting on the R-S is shown to reinforce low- and high-speed streaks respectively. This targeted reinforcement of streaks by the Reynolds stresses occurs continuously as the fluctuation field is strained by the streamwise-mean streak and not intermittently as would be associated with streak-breakdown events. The Reynolds stresses maintaining the streamwise-mean roll arise primarily from the dominant POD modes of the fluctuations, which can be identified with the time average structure of optimal perturbations growing on the streak. These results are consistent with a universal process of R-S growth and maintenance in turbulent shear flow arising from roll forcing generated by straining turbulent fluctuations, which was identified using the S3T SSD., Comment: 33 pages, 26 figures, submitted for publication to the Journal of Fluid Mechanics

Urban Air Mobility (UAM) offers a solution to current traffic congestion by providing on-demand air mobility in urban areas. Effective traffic management is crucial for efficient operation of UAM systems, especially for high-demand scenarios. In this paper, we present a centralized traffic management framework for on-demand UAM systems. Specifically, we provide a scheduling policy, called VertiSync, which schedules the aircraft for either servicing trip requests or rebalancing in the system subject to aircraft safety margins and energy requirements. We characterize the system-level throughput of VertiSync, which determines the demand threshold at which passenger waiting times transition from being stabilized to being increasing over time. We show that the proposed policy is able to maximize throughput for sufficiently large fleet sizes. We demonstrate the performance of VertiSync through a case study for the city of Los Angeles, and show that it significantly reduces passenger waiting times compared to a first-come first-serve scheduling policy., Comment: 9 pages, 6 figures

Turbulence in wall-bounded flows is characterized by stable statistics. Although, in many turbulent systems, this stable statistical state corresponds to a stable fixed point of an associated statistical state dynamics (SSD) closed at second order, referred to as S3T, this is not the case for wall turbulence. In wall-turbulence the trajectory of the statistical state is on a transient chaotic attractor in the S3T statistical state space and the time-mean statistical state is neither a stable fixed point of this SSD nor, if it is maintained as an equilibrium, is it stable. Nevertheless, sufficiently small perturbations from the ensemble/time-mean state relax back to the mean statistical state following an effective linear dynamics. In this work, the dynamics of spanwise uniform perturbations to the time-mean flow are studied using a linear inverse model (LIM) to identify the linear operator governing the ensemble stability of the ensemble/time-mean state by obtaining the time-mean stability properties over the transient attractor of the turbulence identified by the S3T SSD. The ensemble/time-mean stability of an unstable equilibrium can be understood by noting that even when every member of an ensemble is unstable the ensemble mean may be stable with perturbations following stable dynamics. While simplifying insight into turbulent flows has been obtained by identifying and studying ensemble mean statistical states, less attention has been accorded to identifying and studying the ensemble mean dynamics. We show that in the case of wall turbulence, even though stable fixed point SSD equilibria are not available to allow the application of traditional perturbation analysis methods to identify the perturbation stability of the mean state, an effective linear stability analysis can be obtained to identify the perturbation dynamics of the ensemble/time-mean statistical state., Comment: 42 pages, 12 figures, submitted to Phys. Rev. Fluids

Ramp metering is one of the most effective tools to combat traffic congestion. In this paper, we present a ramp metering policy for a network of freeways with arbitrary number of on- and off-ramps, merge, and diverge junctions. The proposed policy is designed at the microscopic level and takes into account vehicle following safety constraints. In addition, each on-ramp operates in cycles during which it releases vehicles as long as the number of releases does not exceed its queue size at the start of the cycle. Moreover, each on-ramp dynamically adjusts its release rate based on the traffic condition. To evaluate the performance of the policy, we analyze its throughput, which is characterized by the set of arrival rates for which the queue sizes at all on-ramps remain bounded in expectation. We show that the proposed policy is able to maximize the throughput if the merging speed at all the on-ramps is equal to the free flow speed and the network has no merge junction. We provide simulations to illustrate the performance of our policy and compare it with a well-known policy from the literature., Comment: 9 pages, 5 figures. arXiv admin note: text overlap with arXiv:2207.02360

We present a compositional control synthesis method based on assume-guarantee contracts with application to correct-by-construction design of vehicular mission plans. In our approach, a mission-level specification expressed in a fragment of signal temporal logic (STL) is decomposed into predicates defined on non-overlapping time intervals. The STL predicates are then mapped to an aggregation of contracts associated with continuously differentiable time-varying control barrier functions. The barrier functions are used to constrain the lower-level control synthesis problem, which is solved via quadratic programming. Our approach can avoid the conservatism of previous methods for task-driven control based on under-approximations. We illustrate its effectiveness on a case study motivated by vehicular mission planning under safety constraints as well as constraints imposed by traffic regulations under vehicle-to-vehicle and vehicle-to-infrastructure communication., Comment: Extended version of paper accepted to appear at the 61st IEEE Conference on Decision and Control (CDC), 2022

We consider Ramp Metering (RM) at the microscopic level subject to vehicle following safety constraints for a freeway with arbitrary number of on- and off-ramps. The arrival times of vehicles to the on-ramps, as well as their destinations are modeled by exogenous stochastic processes. Once a vehicle is released from an on-ramp, it accelerates towards the free flow speed if it is not obstructed by another vehicle; once it gets close to another vehicle, it adopts a safe gap vehicle following behavior. The vehicle exits the freeway once it reaches its destination off-ramp. We design traffic-responsive RM policies that maximize the throughput. For a given routing matrix, the throughput of a RM policy is characterized by the set of on-ramp arrival rates for which the expected queue size at all the on-ramps remain bounded. The proposed RM policies work in synchronous cycles during which an on-ramp does not release more vehicles than its queue size at the beginning of the cycle. Moreover, all the policies operate under vehicle following safety constraints, where new vehicles are released only if there is sufficient gap between vehicles on the mainline at the moment of release. We provide three mechanisms under which each on-ramp: (i) pauses release for a time interval at the end of a cycle, or (ii) adjusts the release rate during a cycle, or (iii) adopts a conservative safe gap criterion for release during a cycle. All the proposed policies are reactive, meaning that they only require real-time traffic measurements without the need for demand prediction. The throughput of these policies is characterized by studying stochastic stability of the induced Markov chains, and is proven to be maximized when the merging speed at all the on-ramps equals the free flow speed. Simulations are provided to illustrate the performance of our policies and compare with a well-known RM policy from the literature., Comment: 36 pages, 15 figures, 3 tables

The safety-critical nature of adaptive cruise control (ACC) systems calls for systematic design procedures, e.g., based on formal methods or control barrier functions (CBFs), to provide strong guarantees of safety and performance under all driving conditions. However, existing approaches have mostly focused on fully verified solutions under smooth traffic conditions, with the exception of stop-and-go scenarios. Systematic methods for high-performance ACC design under safety and regulatory constraints like traffic signals are still elusive. A challenge for correct-by-construction approaches based on CBFs stems from the need to capture the constraints imposed by traffic signals, which lead to candidate time-varying CBFs (TV-CBFs) with finite jump discontinuities in bounded time intervals.

Variable Speed Limit (VSL) control has been one of the most popular techniques with the potential of smoothing traffic flow, maximizing throughput at bottlenecks, and improving mobility and safety. Despite the substantial research efforts in the application of VSL control, few studies have looked into the effect of the VSL sign distance from the point of an accident or a bottleneck. In this paper, we show that this distance has a significant impact on the effectiveness and performance of VSL control. We propose a rule-based VSL strategy that matches the outflow of the upstream VSL zone with the bottleneck capacity based on a multi-section Cell Transmission Model (CTM). Then, we consider the distance of the upstream VSL zone as a control variable and perform a comprehensive analysis of its impact on the performance of the closed-loop traffic control system based on the multi-section CTM. We develop a lower bound that this distance needs to satisfy in order to guarantee homogeneous traffic density across sections and reduce bottleneck congestion. The bound is verified analytically and demonstrated using microscopic simulation of traffic on I-710 in Southern California. The simulations are used to quantify the benefits on mobility, safety and emissions obtained by selecting the upstream VSL zone distance to satisfy the analytical lower bound. The developed lower bound is a design tool which can be used to tune and improve the performance of VSL controllers., Comment: 10 pages, 9 figures, 2 tables, submitted to T-ITS

Turbulence in the restricted nonlinear (RNL) dynamics is analyzed and compared with DNS of Poiseuille turbulence at $R=1650$. The structures are obtained by POD analysis of the two components of the flow partition used in RNL dynamics: the streamwise-mean flow and fluctuations. POD analysis of the streamwise-mean flow indicates that the dominant POD modes, in both DNS and RNL, are roll-streaks harmonic in the spanwise. However, we conclude that these POD modes do not occur in isolation but rather are Fourier components of a coherent roll-streak structure. POD analysis of the fluctuations in DNS and RNL reveals similar complex structures consisting in part of oblique waves collocated with the streak. The origin of these structures is identified by their correspondence to POD modes predicted using a stochastic turbulence model (STM). These predicted POD modes are dominated by the optimally growing structures on the streak, which the STM predicts correctly to be of sinuous oblique wave structure. This close correspondence between the roll-streak structure and the associated fluctuations in DNS, RNL and the STM implies that the self-sustaining mechanism operating in DNS is essentially the same as that in RNL, which has been previously associated with optimal perturbation growth on the streak., Comment: 31 pages, accepted by the Journal of Fluid Mechanics

We demonstrate that a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition identifies subspaces with stable Lyapunov exponents and allows the dynamics to exhibit properties of an inertial manifold, such as the synchronization of the small scales in simulations sharing the same large scales or equivalently the decay of all small scale flow states to the state uniquely determined from the large scale flow. This behaviour occurs for deviations with streamwise wavelength smaller than 130 wall units which was shown in earlier studies to correspond to the streamwise spectral peak of the cross-flow velocity components of the top Lyapunov vector of the turbulent flow.

A fundamental problem in traffic networks is driving under safety and limited physical space constraints. In this paper, we design longitudinal vehicle controllers and study the dynamics of a system of homogeneous vehicles on a single-lane ring road in order to understand the interplay of limited space, speed, and safety. Each vehicle in the system either operates in the cruise control mode or follows a vehicle ahead by keeping a safe time headway. We show that if the number of vehicles is less than a certain critical threshold, vehicles can occupy the limited space in many different configurations, i.e., different platoons of different sizes, and they converge to a uniform maximum speed while attenuating errors in the relative spacing upstream a platoon. If the number of vehicles exceeds the threshold, vehicles converge to a unique symmetric configuration and the equilibrium speed decreases as the number of vehicles increases. Next, we consider vehicle-to-vehicle (V2V) communication and show that it increases the critical number of vehicles that can travel with the maximum speed. Finally, we consider central coordination and show that the proposed controllers can force vehicles to converge to a desired configuration specified by the coordinator while maintaining safety and comfort. We demonstrate the performance of the proposed controllers via simulation., Comment: 17 pages, 13 figures; submitted to IEEE IV

Transportation networks are highly complex and the design of efficient traffic management systems is difficult due to lack of adequate measured data and accurate predictions of the traffic states. Traffic simulation models can capture the complex dynamics of transportation networks by using limited available traffic data and can help central traffic authorities in their decision-making, if appropriate input is fed into the simulator. In this paper, we design an integrated simulation-prediction system which estimates the Origin-Destination (OD) matrix of a road network using only flow rate information and predicts the behavior of the road network in different simulation scenarios. The proposed system includes an optimization-based OD matrix generation method, a Neural Network (NN) model trained to predict OD matrices via the pattern of traffic flow and a microscopic traffic simulator with a Dynamic Traffic Assignment (DTA) scheme to predict the behavior of the transportation system. We test the proposed system on the road network of the central terminal area (CTA) of the Los Angeles International Airport (LAX), which demonstrates that the integrated traffic simulation-prediction system can be used to simulate the effects of several real world scenarios such as lane closures, curbside parking and other changes. The model is an effective tool for learning the impact and possible benefits of changes in the network and for analyzing scenarios at a very low cost without disrupting the network., Comment: 19 pages. Under review

We design a coordination mechanism for truck drivers that uses pricing-and-routing schemes that can help alleviate traffic congestion in a general transportation network. We consider the user heterogeneity in Value-Of-Time (VOT) by adopting a multi-class model with stochastic Origin-Destination (OD) demands for the truck drivers. The main characteristic of the mechanism is that the coordinator asks the truck drivers to declare their desired OD pair and pick their individual VOT from a set of $N$ available options, and guarantees that the resulting pricing-and-routing scheme is Pareto-improving, i.e. every truck driver will be better-off compared to the User Equilibrium (UE) and that every truck driver will have an incentive to truthfully declare his/her VOT, while leading to a revenue-neutral (budget balanced) on average mechanism. This approach enables us to design personalized (VOT-based) pricing-and-routing schemes. We show that the Optimum Pricing Scheme (OPS) can be calculated by solving a nonconvex optimization problem. To improve computational efficiency, we propose an Approximately Optimum Pricing Scheme (AOPS) and prove that it satisfies the aforementioned properties. Both pricing-and-routing schemes are compared to the Congestion Pricing with Uniform Revenue Refunding (CPURR) scheme through extensive simulation experiments where it is shown that OPS and AOPS achieve a much lower expected total travel time and expected total monetary cost for the users compared to the CPURR scheme, without negatively affecting the rest of the network. These results demonstrate the efficiency of personalized (VOT-based) pricing-and-routing schemes., Comment: Accepted as a Journal article in Transportation Research Part C: Emerging Technologies

While linear non-normality underlies the mechanism of energy transfer from the externally driven flow to the perturbation field that sustains turbulence, nonlinearity is also known to play an essential role. The goal of this study is to better understand the role of nonlinearity in sustaining turbulence. The method used in this study is implementation in Couette flow of a statistical state dynamics (SSD) closure at second order in a cumulant expansion of the Navier-Stokes equations in which the averaging operator is the streamwise mean. The perturbations are the deviations from the streamwise mean and two mechanisms potentially contributing to maintaining these perturbations are identified. These are parametric perturbation growth arising from interaction of the perturbations with the fluctuating mean flow and transient growth of perturbations arising from nonlinear interaction between components of the perturbation field. By the method of comparing the turbulence maintained in the SSD and in the associated direct numerical simulation (DNS) in which these mechanisms have been selectively included and excluded, parametric growth is found to maintain the perturbation field of the turbulence while the more commonly invoked mechanism of transient growth of perturbations arising from scattering by nonlinear interaction is found to suppress perturbation growth. In addition to verifying that the parametric mechanism maintains the perturbations in DNS it is also verified that the Lyapunov vectors are the structures that dominate the perturbation energy and energetics in DNS. It is further verified that these vectors are responsible for maintaining the roll circulation that underlies the self-sustaining process (SSP) and in particular the maintenance of the fluctuating streak that supports the parametric perturbation growth., Comment: arXiv admin note: substantial text overlap with arXiv:1801.02093

The no-slip boundary condition results in a velocity shear forming in fluid flow near a solid surface. This shear flow supports the turbulence characteristic of fluid flow near boundaries at Reynolds numbers above $\approx1000$ by making available to perturbations the kinetic energy of the externally forced flow. Understanding the physical mechanism underlying this energy transfer poses a fundamental question. Although qualitative understanding that this transfer involves nonlinear destabilization of the roll-streak coherent structure has been established, identification of this instability has resisted analysis. The reason this instability has resisted analysis is that its analytic expression lies in the Navier-Stokes equations (NS) expressed using statistical rather than state variables. Expressing NS as a statistical state dynamics (SSD) at second order in a cumulant expansion suffices to allow analytical identification of the nonlinear roll-streak instability underlying turbulence in wall-bounded shear flow. In this nonlinear instability the turbulent perturbation field is identified by the SSD with the Lyapunov vectors of the linear operator governing perturbation evolution about the time-dependent streamwise mean flow. In this work, the implications of the predictions of SSD analysis (that this parametric instability underlies the dynamics of turbulence in Couette flow and that the perturbation structures are the associated Lyapunov vectors) are interpreted to imply new conceptual approaches to controlling turbulence. It is shown that the perturbation component of turbulence is supported on the streamwise mean flow, which implies optimal control should be formulated to suppress perturbations from the streamwise mean. It is also shown that suppressing only the top few Lyapunov vectors on the streamwise mean vectors results in laminarization. These results are verified using DNS.

Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at $R=600$ and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence., Comment: work done in the COTURB Summer Workshop 2017, submitted to J. Phys.: Conf. Series

Geophysical turbulence is observed to self-organize into large-scale flows such as zonal jets and coherent vortices. Previous studies on barotropic beta-plane turbulence have shown that coherent flows emerge out of a background of homogeneous turbulence as a bifurcation when the turbulence intensity increases and the emergence of large scale flows has been attributed to a new type of collective, symmetry breaking instability of the statistical state dynamics of the turbulent flow. In this work we extend the analysis to stratified flows and investigate turbulent self-organization in a two-layer fluid with no imposed mean north-south thermal gradient and turbulence supported by an external random stirring. We use a second order closure of the statistical state dynamics (S3T) with an appropriate averaging ansatz that allows the identification of statistical turbulent equilibria and their structural stability. The bifurcation of the statistically homogeneous equilibrium state to inhomogeneous equilibrium states comprising of zonal jets and/or large scale waves when the energy input rate of the excitation passes a critical threshold is analytically studied. The theory predicts that when the flow transitions to a statistical state with large-scale structures, these states are barotropic if the scale of excitation is larger than the deformation radius. Mixed barotropic-baroclinic states with jets and/or waves arise when the excitation is at scales shorter than the deformation radius with the baroclinic component of the flow being subdominant for low energy input rates and non-significant for higher energy input rates. The results of the S3T theory are compared to nonlinear simulations. The theory is found to accurately predict both the critical transition arameters and the scales of the emergent structures but underestimates their amplitude., Comment: submitted to the Journal of Fluid Mechanics

Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (`zonostrophic instability') which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide ranges of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the asymmetric evolution for weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability., Comment: 27 pages, 17 figures