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Decomposition of Human Motion into Dynamics Based Primitives with Application to Drawing Tasks + (Using tools from dynamical systems and sys … Using tools from dynamical systems and systems identiﬁcation we develop a framework for the studyof primitives for human motion, which we refer to as movemes. The objective is understanding humanmotion by decomposing it into a sequence of elementary building blocks that belong to a known alphabetof dynamical systems. In this work we address the problem of deﬁning conditions under whichcollections of signals are well-posed according to a dynamical model class M and then can generatemovemes. Based on the assumption of well-posedness, we develop segmentation and classiﬁcation algorithmsin order to reduce a complex activity into the sequence of movemes that have generated it.Using examples we show that the deﬁnition of well-posedness can be applied in practice and showanalytically that the proposed algorithms are robust with respect to noise and model uncertainty. Wetest our ideas on data sampled from ﬁve human subjects who were drawing ﬁgures using a computermouse. Our experiments show that we are able to distinguish between movemes and recognize themeven when they take place in activities containing more than one moveme at a time.)
Primitives for Human Motion: A Dynamical Approach + (Using tools from dynamical systems theory … Using tools from dynamical systems theory and systems identification theory we develop the study of primitives for human motion which we refer to as movemes. We introduce basic definitions of dynamical independence of LTI systems and segmentability of signals and, for two dimensional motions, we develop classification and segmentation algorithms. We test our ideas on data sampled from four human subjects who were engaged in a simple real-life activity including two movemes. Our experiments show that we are able to distinguish between the two movemes and recognise them even when they take place in an activity containing more than one moveme.place in an activity containing more than one moveme.)
Information Flow and Cooperative Control of Vehicle Formations + (Vehicles in formation often lack global in … Vehicles in formation often lack global information regarding the state ofall the vehicles, a deficiency which can lead to instability and poor performance. Inthis paper, we demonstrate how exchange of minimal amounts of information betweenvehicles can be designed to realize a dynamical system which supplies each vehicle witha shared reference trajectory. When the information flow law is placed in the controlloop, a separation principle is proven which guarantees stability of the formation andconvergence of the information flow law regardless of the information flow topology.gardless of the information flow topology.)
Discrete State Estimators for Systems on a Lattice + (We address the problem of estimating discr … We address the problem of estimating discrete variables in a class of deterministictransition systems where the continuous variables are available for measurement. Thissimplified scenario has practical interest, for example, in the case of decentralized multi-robotsystems. In these systems, the continuous variables represent physical quantities such as theposition and velocity of a robot, while discrete variables may represent the state of the logicalsystem that is used for control and coordination. We propose a novel approach to theestimation of discrete variables using basic lattice theory that overcomes some of the severecomplexity issues encountered in previous work. We show how to construct the proposedestimator for a multi-robot system performing a cooperative assignment task. performing a cooperative assignment task.)
On the Control of Jump Linear Markov Systems with Markov State Estimation + (We analyze a jump linear Markov system bei … We analyze a jump linear Markov system being stabilized using a zero-order hold controller. We consider the case when the Markov state is associated with the probability distribution of a measured variable. We assume that the Markov state is not known, but rather is being estimated based on the observations of the variable. We present conditions for the stability of such a system and also solve the optimal LQR control problem for the case when the state estimate update uses only the last observation value. In particular we consider a suboptimal causal version of the Viterbi estimation algorithm and show that a separtion property does not hold between the optimal control and the Markov state estimate. Some simple examples are also presented.. Some simple examples are also presented.)
Stability Analysis of Stochastically Varying Formations of Dynamic Agents + (We analyze a network of dynamic agents whe … We analyze a network of dynamic agents where thetopology of the network specifies the informationflow between the agents. We present an analysismethod for such a system for both consensus andformation stabilization problems. We consider thecase of agent dynamics being a single integrator inmore detail to show the general features introducedby the information flow. Then we show that themethod of analysis can be extended to more general cases of complicated agent dynamics, non-ideallinks for information flow, etc. We also consider thecase when the topology of the network is changingover time. The focus of the paper is on obtainingconditions for the stability of the formation thatcan be checked in a decentralized way. Some simple examples are also presented.. Some simple examples are also presented.)
Approximate Distributed Kalman Filtering in Sensor Networks with Quantifiable Performance + (We analyze the performance of an approxima … We analyze the performance of an approximate distributed Kalman filter proposedin recent work on distributed coordination. This approach todistributed estimation is novel in that it admits a systematicanalysis of its performance as various network quantities such asconnection density, topology, and bandwidth are varied. Our maincontribution is a frequency-domain characterization of thedistributed estimator's steady-state performance; this is quantified in termsof a special matrix associated with the connection topology calledthe graph Laplacian, and also the rate of message exchangebetween immediate neighbors in the communication network.te neighbors in the communication network.)
Control Over a Network: Using Actuation Buffers to Reduce Transmission Frequency + (We consider a discrete time linear feedbac … We consider a discrete time linear feedback control system with additive noise where the control signals are to be sent across a data link from the controller to the actuators. Due to network constraints it is desired to reduce the transmission frequency of the control signals. We show that by including a finite sequence of predicted control signals in each communication packet the frequency of transmission can be reduced by transmitting only when the previously sent sequence has run out. The price to pay is that the closed loop error will increase. We introduce a novel communication protocol, which we call Input Difference Transmission Scheme (IDTS), which transmits control packets when the difference between the newly computed control sequence and the predicted control sequence previously transmitted is larger than a certain thresh- old. This threshold is a design parameter and we show how the closed loop behavior varies with this threshold. Simulation results are provided to augment the theory and show how the protocol works.e theory and show how the protocol works.)
Parametric Delay-margin Maximization of Consensus Network Using Local Control Scheme + (We consider a network of identical agents … We consider a network of identical agents with arbitrary linear time-invariant (LTI) dynamics such that the network reaches consensus asymptotically. Uniform time delay is taken into account in the communication channels. The goal of this paper is to maximize the delay (so-called delay margin) that the system can tolerate before becoming unstable by implementing a low-order controller to a single agent. A parametric design method is investigated to guarantee the stability and consensusability. The set of all feasible low-order controllers based on the frequency response data is characterized by combining the argument principle and the generalized Nyquist criterion. Based on this, the algorithm of computing the delay margin is proposed for a given controlled agent. By combining all the possible margins for each controlled agent, we then can obtain the maximal delay margin for the whole network and the corresponding local controller.rk and the corresponding local controller.)
Linear System Identifiability from Distributional and Time Series Data + (We consider identifiability of linear syst … We consider identifiability of linear systems driven by white noise using a combination of distributional and time series measurements. Specifically, we assume that the system has no control inputs available and can only be observed at stationarity. The user is able to measure the full stationary state distribution as well as observe time correlations for small subsets of the state. We formulate theoretical conditions on identifiability of parameters from distributional information alone. We then give a sufficient condition and an effective necessary condition for identifiability using a combination of distributional and time series measurements. We illustrate the ideas with some simple examples as well as a biologically inspired example of a transcription and degradation process.f a transcription and degradation process.)
Robot Navigation in Dense Human Crowds: the Case for Cooperation + (We consider mobile robot navigation in den … We consider mobile robot navigation in dense human crowds. In particular, we explore two questions. Can we design a navigation algorithm that encourages humans to coop- erate with a robot? Would such cooperation improve navigation performance? We address the first question by developing a probabilistic predictive model of cooperative collision avoidance and goal-oriented behavior. Specifically, this model extends the recently introduced interacting Gaussian processes approach to the case of multiple goals and stochastic movement duration. We answer the second question by empirically validating our model in a natural environment (a university cafeteria), and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (completing 488 runs). The âmultiple goalâ interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities near 1 person/m2, while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as our planner. Furthermore, a reactive planner based on the âdynamic windowâ approachâwidely used for robotic tour guide experimentsâfails for crowd densities above 0.55 people/m2. We conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.nt robot navigation in dense human crowds.)
Optimal Control with Weighted Average Costs and Temporal Logic Specifications + (We consider optimal control for a system s … We consider optimal control for a system subject to temporal logic constraints. We minimize a weighted average cost function that generalizes the commonly used average cost function from discrete-time optimal control. Dynamic programming algorithms are used to construct an optimal trajectory for the system that minimizes the cost function while satisfying a temporal logic specification. Constructing an optimal trajectory takes only polynomially more time than constructing a feasible trajectory. We demonstrate our methods on simulations of autonomous driving and robotic surveillance tasks.us driving and robotic surveillance tasks.)
Bootstrapping bilinear models of robotic sensorimotor cascades + (We consider the bootstrapping problem, whi … We consider the bootstrapping problem, which consists in learning a model of the agent's sensors and actuators starting from zero prior informa- tion, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a simple bioplausible control strategy. The convergence proper- ties of learning and control are demonstrated with extensive simulations and by analytical arguments.e simulations and by analytical arguments.)
Receding Horizon Control of Multi-Vehicle Formations: A Distributed Implementation + (We consider the control of dynamically dec … We consider the control of dynamically decoupledsubsystems whose state vectors are coupled in the costfunction of a finite horizon optimal control problem. For agiven cost structure, we generate distributed optimal controlproblems for each subsystem and establish that a distributedreceding horizon implementation is asymptotically stabilizing.The communication requirements at each recedinghorizon update include the exchange of the previous optimalcontrol trajectory between subsystems with coupling inthe cost function. The key requirements for stability are thateach distributed optimal control not deviate too far from theprevious one, and that the receding horizon updates happensufficiently fast. A simulation example of multi-vehicleformation stabilization is provided.hicle formation stabilization is provided.)
Distributed Receding Horizon Control with Applications to Multi-Vehicle Formation Stabilization + (We consider the control of interacting sub … We consider the control of interacting subsystems whose dynamics and constraintsare uncoupled, but whose state vectors are coupled non-separably in a single centralizedcost function of a finite horizon optimal control problem. For a given centralizedcost structure, we generate distributed optimal control problems for each subsystemand establish that the distributed receding horizon implementation is asymptoticallystabilizing. The communication requirements between subsystems with coupling in thecost function are that each subsystem obtain the previous optimal control trajectory ofthose subsystems at each receding horizon update. The key requirements for stabilityare that each distributed optimal control not deviate too far from the previous optimalcontrol, and that the receding horizon updates happen sufficiently fast. The theory isapplied in simulation for stabilization of a formation of vehicles. stabilization of a formation of vehicles.)
Multi-dimensional state estimation in adversarial environment + (We consider the estimation of a vector sta … We consider the estimation of a vector state based on m measurements that can be potentially manipulated by an adversary. The attacker is assumed to have limited resources and can only manipulate up to l of the m measurements. However, it can the compromise measurements arbitrarily. The problem is formulated as a minimax optimization, where one seeks to construct an optimal estimator that minimizes the âworst-caseâ error against all possible manipulations by the attacker and all possible sensor noises. We show that if the system is not observable after removing 2l sensors, then the worst-case error is infinite, regardless of the estimation strategy. If the system remains observable after removing arbitrary set of 2l sensor, we prove that the optimal state estimation can be computed by solving a semidefinite programming problem. A numerical example is provided to illustrate the effectiveness of the proposed state estimator.ctiveness of the proposed state estimator.)
Risk-aware motion planning for automated vehicle among human-driven cars + (We consider the maneuver planning problem … We consider the maneuver planning problem for automated vehicles when they share the road with human- driven cars and interact with each other using a finite set of maneuvers. Each maneuver is calculated considering input constraints, actuator disturbances and sensor noise, so that we can use a maneuver automaton to perform high-level planning that is robust against low-level effects. In order to model the behavior of human-driven cars in response to the intent of the automated vehicle, we use control improvisation to build a probabilistic model. To accommodate for potential mismatches between the learned human model and human driving behaviors, we use a conditional value-at-risk objective function to obtain the optimal policy for the automated vehicle. We demonstrate through simulations that our motion planning framework allows an automated vehicle to exploit human behaviors with different levels of robustness.viors with different levels of robustness.)
A bio-plausible design for visual attitude stabilization + (We consider the problem of attitude stabil … We consider the problem of attitude stabilization using exclusively visual sensory input, and we look for a solution which can satisfy the constraints of a ``bio-plausible'' computation. We obtain a PD controller which is a bilinear form of the goal image, and the current and delayed visual input. Moreover, this controller can be learned using classic neural networks algorithms. The structure of the resulting computation, derived from general principles by imposing a bilinear computation, has striking resemblances with existing models for visual information processing in insects (Reichardt Correlators and lobula plate tangential cells). We validate the algorithms using faithful simulations of the fruit fly visual input.simulations of the fruit fly visual input.)
Consensus Seeking Using Multi-Hop Relay Protocol + (We consider the problem of average consens … We consider the problem of average consensus seeking in networked multi-agent systems. Based on local information and a simple distributed algorithm, states of all agents automatically converge to the average value of the initial conditions, where the convergence speed is determined by the algebraic connectivity of the underlying communication network. In order to achieve an average consensus quickly, we propose a new type of consensus protocol, multi-hop relay protocol, in which each agent expands its knowledge by employing multi-hop communication links. We explicitly show that multi-hop relay protocol increases the convergence speed without physically changing the network topology. Moreover, accumulated delays along communication links are discussed. We show that, for multi-hop relay protocol, the faster the protocol converges, the more sensitive it is to the delay. This tradeoff is identified when we investigate the stable delay margin using frequency sweep method.delay margin using frequency sweep method.)
Data Transmission over Networks for Estimation and Control + (We consider the problem of controlling a l … We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal LQG controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network mentioned above. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the more commonly used viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network.measure of the reliability of the network.)
Distributed Power Allocation for Vehicle Management Systems + (We consider the problem of designing distr … We consider the problem of designing distributed control protocols -for aircraft vehicle management systems- that cooperatively allocate electric power while meeting certain higher level goals and requirements, and dynamically reacting to the changes in the internal system state and external environment. A decentralized control problem is posed where each power distribution unit is equipped with a controller that implements a local protocol to allocate power to a certain subset of loads. We use linear temporal logic as the specification language for describing correct behaviors of the system (e.g., safe operating conditions) as well as the admissible dynamic behavior of the environment due to, for example, wind gusts and changes in system health. We start with a global specification and decompose it into local ones. These decompositions allow the protocols for each local controller to be separately synthe- sized and locally implemented while guaranteeing the global specifications to hold. Through a design example, we show that by refining the interface rules between power distribution units, it is possible to reduce the total power requirement.ble to reduce the total power requirement.)
Risk-Averse Planning Under Uncertainty + (We consider the problem of designing polic … We consider the problem of designing policies for partially observable Markov decision processes (POMDPs) with dynamic coherent risk objectives. Synthesizing risk-averse optimal policies for POMDPs requires infinite memory and thus undecidable. To overcome this difficulty, we propose a method based on bounded policy iteration for designing stochastic but finite state (memory) controllers, which takes advantage of standard convex optimization methods. Given a memory budget and optimality criterion, the proposed method modifies the stochastic finite state controller leading to sub-optimal solutions with lower coherent risk.ptimal solutions with lower coherent risk.)
Risk-Averse Decision Making Under Uncertainty + (We consider the problem of designing polic … We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigationumerical experiments on a rover navigatio)
Constrained risk-averse Markov decision processes + (We consider the problem of designing polic … We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.lue-at-risk (EVaR) coherent risk measures.)
Dynamic State Estimation in Distributed Aircraft Electric Control Systems via Adaptive Submodularity + (We consider the problem of estimating the … We consider the problem of estimating the discrete state of an aircraft electric system under a distributed control architecture through active sensing. The main idea is to use a set of controllable switches to reconfigure the system in order to gather more information about the unknown state. By adaptively making a sequence of reconfiguration decisions with uncertain outcome and by correlating the measurements and prior information to make the next decision, we aim to reduce the uncertainty. A greedy strategy is developed that maximizes the one-step expected uncertainty reduction. By exploiting recent results on adaptive submodularity, we give theoretical guarantees on the worst-case performance of the greedy strategy. We apply the proposed method in a fault de- tection scenario where the discrete state captures possible faults in various circuit components. In addition, simple abstraction rules are proposed to alleviate state space explosion and to scale up the strategy. Finally, the efficiency of the proposed method is demonstrated empirically on different circuits.strated empirically on different circuits.)

(We consider the problem of estimating the subset of test conditions unde)

Efficient local validation of partially ordered models via Baysian directed sampling + (We consider the problem of estimating the … We consider the problem of estimating the subset of test conditions under which a simplified model—or set of simplified models—accurately approximates the behavior of a true system. We approach the problem by proposing a compact set of possible test conditions, and an unknown but samplable continous validity function over that set that quantifies the accuracy of the model under each possible condition. We propose a novel Bayes estimator that optimally directs function sampling to greedily minimize the expected posterior misclassification rate of the valid set, which we call minimum posterior misclassification sampling (GP-MPM), and we show that the the method can be extended to approximate the valid sets of a partially ordered set of models, with sample complexity growing sublinearly with the number of models. In testing against a safety-focused model, we show that the algorithm’s estimated valid set approaches the true valid set much more quickly than undirected sampling, even with small sample sizes.ed sampling, even with small sample sizes.)
Motion planning in observations space with learned diffeomorphism models + (We consider the problem of planning motion … We consider the problem of planning motions in observations space, based on learned models of the dynamics that associate to each action a diffeomorphism of the observations domain. For an arbitrary set of diffeomorphisms, this problem must be formulated as a generic search problem. We adapt established algorithms of the graph search family. In this scenario, node expansion is very costly, as each node in the graph is associated to an uncertain diffeomorphism and corresponding predicted observations. We describe several improvements that ameliorate performance: the introduction of better image similarities to use as heuristics; a method to reduce the number of expanded nodes by preliminarily identifying redundant plans; and a method to pre-compute composite actions that make the search efficient in all directions.ke the search efficient in all directions.)
A bio-plausible design for visual pose stabilization + (We consider the problem of purely visual p … We consider the problem of purely visual pose stabilization (also known as servoing) of a second-order rigid- body system with six degrees of freedom: how to choose forces and torques, based on the current view and a memorized goal image, to steer the pose towards a desired one. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. This particular computational structure has several numerically favorable characteristics (sparse, local, and parallel), and thus permits an efficient engineering implementation. We show results of the control law tested on an indoor helicopter platform.w tested on an indoor helicopter platform.)
A bootstrappable bio-plausible design for visual pose stabilization + (We consider the problem of purely visual p … We consider the problem of purely visual pose stabilization of a second-order rigid-body system: how to choose forces and torques, based on the visual input alone, such that the view converges to a memorized goal image. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. Moreover, the control laws can be ``bootstrapped'' (learned unsupervisedly) from experience, which further substantiate the bio-plausibility of such computation. the bio-plausibility of such computation.)
Specifying and Analyzing Networked and Layered Control Systems Operating on Multiple Clocks + (We consider the problem of reasoning about … We consider the problem of reasoning about networked and layered control systems using assume-guarantee specifications. As these systems are formed by the interconnection of components that operate under various clocks, we introduce a new logic, Multiclock Logic (MCL), to be able to express the requirements of components form the point of view of their local clocks. Specifying components locally promotes independent design and component reuse. We carry out a contract-based analysis of a control system implemented via two control algorithms (model predictive control and feedback linearization) running on their own processors and clocks. Then we implement each of the contracts to build a system. The system performs as desired when the requirements derived from our system-level analysis are respected. Violating the constraints required by the contract-based analysis of the system leads to error.sed analysis of the system leads to error.)
Temporal Logic Control of Switched Affine Systems with an Application in Fuel Balancing + (We consider the problem of synthesizing hi … We consider the problem of synthesizing hier- archical controllers for discrete-time switched affine systems subject to exogenous disturbances that guarantee that the trajectories of the system satisfy a high-level specification expressed as a linear temporal logic formula. Our method builds upon recent results on temporal logic planning and embedded controller synthesis. First, the control problem is lifted to a discrete level by constructing a finite transition system that abstracts the behavior of the underlying switched system. At the discrete level, we recast the problem as a two player temporal logic game by treating the environment driven switches as adversaries. The solution strategy for the game (i.e. the discrete plan) is then implemented at the continuous level by solving finite-horizon optimal control problems that establish reachability between discrete states and that compensate the effects of continuous disturbances. We also extend the earlier work by making efficient use of propositions in the temporal logic formula to drive the abstraction procedure and to facilitate the computation of continuous input at implementation time.An aircraft fuel system example is formulated; and solved using the proposed method. This sample problem demonstrates the applicability of the abstraction procedure and correct-by-construction controllers to regulate the fuel levels in multiple tanks during interesting operations like aerial refueling.eresting operations like aerial refueling.)
Distributed Synthesis of Control Protocols for Smart Camera Networks + (We consider the problem of synthesizing co … We consider the problem of synthesizing control protocols for smart camera networks where the goal is to guarantee that certain linear temporal logic (LTL) specifications related to a given surveillance task are met. We first present a centralized control architecture for assigning pan-tilt-zoom (PTZ) cameras to targets so that the specification is met for any admissible behavior of the targets. Then, in order to alleviate the computational complexity associated with LTL synthesis and to enable implementation of local control protocols on individual PTZ cameras, we propose a distributed synthe- sis methodology. The main idea is to decompose the global specification into local specifications for each PTZ camera. A thorough design example is presented to illustrate the steps of the proposed procedure.trate the steps of the proposed procedure.)
Hot-swapping robot task goals in reactive formal synthesis + (We consider the problem of synthesizing ro … We consider the problem of synthesizing robot controllers to realize a task that unpredictably changes with time. Tasks are formally expressed in the GR(1) fragment of temporal logic, in which some of the variables are set by an adversary. The task changes by the addition or removal of goals, which occurs online (i.e., at run-time). We present an algorithm for mending control strategies to realize tasks after the addition of goals, while avoiding global re-synthesis of the strategy. Experiments are presented for a planar surveillance task in which new regions of interest are incrementally added. Run-times are empirically shown to be extremely favorable compared to re-synthesizing from scratch. We also present an algorithm for mending control strategies for the removal of goals. While in this setting the original strategy is still feasible (as we prove), our algorithm provides a more satisfying solution by âtightening loose ends.â Both algorithms are shown to yield so-called reach annotations, and thus the control strategies are easily amenable to other algorithms concerning incremental synthesis, e.g., as in previous work by the authors for robot navigation in uncertain environments.obot navigation in uncertain environments.)
Equilibrium Controllability for a Class of Mechanical Systems + (We define a notion of controllability for … We define a notion of controllability for mechanical systems which determinesthe configurations which are accessible from a given configuration. Wederive sufficient conditions for this notion of controllability in terms ofthe given inputs, their Lie brackets, and their covariant derivatives.brackets, and their covariant derivatives.)
Real Time Trajectory Generation for Differentially Flat Systems with Unstable Zero Dynamics + (We define the real time trajectory generat … We define the real time trajectory generation problem to be how to generate,possibly with some delay, a full state space and input trajectory in realtime from an output trajectory that is given online, while allowing atradeoff between stability and performance. Wepropose two algorithms that solve the real time trajectory generationproblem for flat systems with zero dynamics, and discuss some interestingproperties. We explicitly address the tradeoff between stability andperformance. The algorithms are validated in simulations and experimentswith a thrust vectored ducted fan aircraft.ith a thrust vectored ducted fan aircraft.)
A two-state ribosome and protein model can robustly capture the chemical reaction dynamics of gene expression + (We derive phenomenological models of gene … We derive phenomenological models of gene expression from a mechanistic description of chemical reactions using an automated model reduction method. Using this method, we get analytical descriptions and computational performance guarantees to compare the reduced dynamics with the full models. We develop a new two-state model with the dynamics of the available free ribosomes in the system and the protein concentration. We show that this new two-state model captures the detailed mass-action kinetics of the chemical reaction network under various biologically plausible conditions on model parameters. On comparing the performance of this model with the commonly used mRNA transcript-protein dynamical model for gene expression, we analytically show that the free ribosome and protein model has superior error and robustness performance.superior error and robustness performance.)
Discrete Function Approximation: Numerical Tools for Nonlinear Control + (We describe a method for discrete represen … We describe a method for discrete representation of continuous functions and show howthis may be used for typical computations in nonlinear control desi gn. The methodinvolves representing functions by their values and finitely many derivatives at discreteset of points on the domain. We propose a grid structure based on a hierarchy ofrectangular boxes that provides flexibility in placing grid points densely in some regionsand sparsely in the other. The grids possess enough structure to facilitate easyinterpolation schemes based on piecewise polynomials. We illustrate the method using asimple example where we compute the feedback linearizing output of a system.e feedback linearizing output of a system.)
Coarse analysis of multiscale systems: diffuser flows, charged particle motion, and connections to averaging theory + (We describe a technique for the efficient … We describe a technique for the efficient computation of the dominant-scale dynamics of a fluid system when only a high-fidelity simulation is available. Such a technique is desirable when governing equations for the dominant scales are unavailable, when model reduction is impractical, or when the original high-fidelity computation is expensive. We adopt the coarse analysis framework proposed by I. G. Kevrekidis (Comm. Math. Sci. 2003), where a computational superstructure is designed to use short-time, high-fidelity simulations to extract the dominant features for a multi- scale system. We apply this technique to compute the dominant features of the compressible flow through a planar diffuser. We apply the proper orthogonal decomposition to classify the dominant and subdominant scales of diffuser flows. We derive a suitable coarse pro jective Adams-Bashforth time integration routine and apply it to compute averaged diffuser flows. The results include accu- rate tracking of the dominant-scale dynamics for a range of parameter values for the computational superstructure. These results demonstrate that coarse analysis methods are useful for solving fluid flow problems of a multiscale nature. In order to elucidate the behavior of coarse analysis techniques, we make comparisons to averaging theory. To this end, we derive governing equations for the average motion of charged particles in a magnetic field in a number of different settings. First, we apply a novel procedure, inspired by WKB theory and Whitham averaging, to average the variational principle. The resulting equations are equivalent to the guiding center equations for charged particle motion; this marks an instance where averaging and variational principles commute. Secondly, we apply Lagrangian averaging techniques, previously applied in fluid mechanics, to derive averaged equations. Making comparisons to the WKB/Whitham-style derivation allows for the necessary closure of the Lagrangian averaging formulation. We also discuss the Hamiltonian setting and show that averaged Hamiltonian systems may be derivable using concepts from coarse analysis. Finally, we apply a prototypical coarse analysis procedure to the system of charged particles and generate tra jectories that resemble guiding center tra jectories. We make connections to perturbation theory to derive guidelines for the design of coarse analysis techniques and comment on the prototypical coarse analysis application.on the prototypical coarse analysis application.)
Lagrangian Mechanics and Carangiform Locomotion + (We describe the interaction of a rigid bod … We describe the interaction of a rigid body and its incompressible fluid environmentwith reduced Euler-Lagrange equations on the appropriate Cartesian product manifold. Wepropose a modification to the planar form of these equations to accomodate control inputsconsistent with a model for carangiform swimming. Initial Lie algebraic analysis of theresulting control system suggests its usefulness in predicting efficacious gaits forpiscimimetic robots.efficacious gaits for piscimimetic robots.)
Extremal Properties of Complex Networks + (We describe the structure of connected gra … We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks. the form and properties of such networks.)
Networks with the Smallest Average Distance and the Largest Average Clustering + (We describe the structure of the graphs wi … We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance, ignoring their average clustering. The form of these graphs is shown with analytical arguments. Finally, we measure the sensitivity to rewiring of this architecture with respect to the clustering coefficient, and we devise a method to make these networks more robust with respect to vertex removal.ore robust with respect to vertex removal.)
Synthesis of Distributed Longitudinal Control 1 Protocols for a Platoon of Autonomous Vehicles + (We develop a framework for control protoco … We develop a framework for control protocol syn- thesis for a platoon of autonomous vehicles subject to temporal logic specifications. We describe the desired behavior of the platoon in a set of linear temporal logic formulas, such as collision avoidance, close spacing or comfortability. The problem of decomposing a global specification for the platoon into distributed specification for each pair of adjacent vehicles is hard to solve. We use the invariant specifications to tackle this problem and the decomposition is proved to be scalable.. Based on the specifications in Assumption/Guarantee form, we can construct a two-player game (between the vehicle and its closest leader) locally to automatically synthesize a controller protocol for each vehicle. Simulation example for a distributed vehicles control problem is also shown.ed vehicles control problem is also shown.)
Optimal Control of Non-deterministic Systems for a Computationally Efficient Fragment of Temporal Logic + (We develop a framework for optimal control … We develop a framework for optimal control policy synthesis for non-deterministic transition systems subject to temporal logic specifications. We use a fragment of temporal logic to specify tasks such as safe navigation, response to the environment, persistence, and surveillance. By restricting specifications to this fragment, we avoid a potentially doubly-exponential automaton construction. We compute feasible con- trol policies for non-deterministic transition systems in time polynomial in the size of the system and specification. We also compute optimal control policies for average, minimax (bottleneck), and average cost-per-task-cycle cost functions. We highlight several interesting cases when these can be computed in time polynomial in the size of the system and specification. Additionally, we make connections between computing optimal control policies for an average cost-per-task-cycle cost function and the generalized traveling salesman problem. We give simulation results for motion planning problems.tion results for motion planning problems.)
Automaton-Guided Controller Synthesis for Nonlinear Systems with Temporal Logic + (We develop a method for the control of dis … We develop a method for the control of discrete-time nonlinear systemssubject to temporal logic specifications. Our approach uses a coarseabstraction of the system and an automaton representing the temporal logicspecification to guide the search for a feasible trajectory. This decomposesthe search for a feasible trajectory into a series of constrainedreachability problems. Thus, one can create controllers for any system forwhich techniques exist to compute (approximate) solutions to constrainedreachability problems. Representative techniques include sampling-basedmethods for motion planning, reachable set computations for linear systems,and graph search for finite discrete systems. Our approach avoids theexpensive computation of a discrete abstraction, and its implementation isamenable to parallel computing. We demonstrate our approach with numericalexperiments on temporal logic motion planning problems with high-dimensional(10+ states) continuous systems.mensional (10+ states) continuous systems.)
Addressable, “Packet-Based” Intercellular Communication through Plasmid Conjugation + (We develop a system for implementing “pack … We develop a system for implementing “packet-based” intercellular communication in an engineered bacterial population via conjugation. Our system uses gRNA-based identification markers that allow messages to be addressed to specific strains via Cas9-mediated cleavage of messages sent to the wrong recipient, which we show reduces plasmid transfer by four orders of magnitude. Integrase-mediated editing of the address on the message plasmid allows cells to dynamically update the message’s recipients in vivo. As a proof-of-concept demonstration of our system, we propose a linear path scheme that would propagate a message sequentially through the strains of a population in a defined order.trains of a population in a defined order.)
Classification of Human Motion into Dynamics Based Primitives with Application to Drawing Tasks + (We develop the study of primitives of huma … We develop the study of primitives of human motion, which we refer to as movemes. The idea is to understand human motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet of dynamical systems. Where do these dynamic primitives come from in practice? How can we construct an alphabet of movemes from human data? In this paper we address these issues. We define conditions under which collections of signals are well-posed according to a dynamical model class M and thus can generate movemes. Using examples from human drawing data, we show that the definition of well-posedness can be applied in practice so to establish if sets of actions, reviewed as signals in time, can define movemes.d as signals in time, can define movemes.)
Reasoning over Test Specifications using Assume-Guarantee Contracts + (We establish a framework to reason about t … We establish a framework to reason about test campaigns described formally. First, we introduce the notion of a test structure — an object that carries i) the formal specifications of the system under test, and ii) the test objective, which is specified by a test engineer. We build on test structures to define test campaigns and specifications for the tester. Secondly, we use the algebra of assume-guarantee contracts to reason about constructing tester specifications, comparing test struc- tures and test campaigns, and combining and splitting test structures. Using the composition operator, we characterize the conditions on the constituent tester specifications and test objectives for feasibly combin- ing test structures. We illustrate the different applications of the quotient operator to split the test objective, the system into subsystems, or both. Finally, we illustrate test executions corresponding to the combined and split test structures in a discrete autonomous driving example and an aircraft formation-flying example. We anticipate that reasoning over test specifications would aid in generating optimal test campaigns. aid in generating optimal test campaigns.)
Optimal LQG Control Across a Packet-Dropping Link + (We examine optimal Linear Quadratic Gaussi … We examine optimal Linear Quadratic Gaussian control for a system in which communication betweenthe sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend thefamiliar LQG separation principle to this problem that allows us to solve this problem using a standardLQR state-feedback design, along with an optimal algorithm for propagating and using the informationacross the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter atthe sensor side of the link, and a switched linear filter at the controller side. Our design does not assumeany statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern.Further, the solution is appealing from a practical point of view because it can be implemented as asmall modification of an existing LQG control design.ication of an existing LQG control design.)
Optimal LQG control across packet-dropping links + (We examine two special cases of the problem of optimal linear quadratic Gaussian control of a system whose state is being measured by sensors that communicate with the controller over packet-dropping links. We pose the problem as an)
Protein degradation in a TX-TL cell-free expression system using ClpXP protease + (We explored the possibility of supplementi … We explored the possibility of supplementing an in vitro S30-based Escherichia coli expression system (or âTX-TLâ) with ClpXP, an AAA+ protease pair that selectively degrades tagged proteins, to provide finely-tuned degradation. The mechanism of ClpXP degradation has been extensively studied both in vitro and in vivo. However, it has not been characterized for use in synthetic circuits -- metrics such as toxicity, ATP usage, degradation variation over time, and cellular loading need to be determined. In particular, TX-TL in batch mode is known to be resource limited, and ClpXP is known to require significant amounts of ATP to unfold different protein targets. We find that ClpXPâs protein degradation dynamics is dependent on protein identity, but can be determined experimentally. Degradation follows Michaels- Menten kinetics, and can be fine tuned by ClpX or ClpP concentration. Added purified ClpX is also not toxic to TX-TL reactions. Therefore, ClpXP provides a controllable way to introduce protein degradation and dynamics into synthetic circuits in TX-TL.NOTE: This is a technical report for future inclusion in work pending submission, review, and publication. Therefore, this work has not been peer-reviewed and is presented as-is.s not been peer-reviewed and is presented as-is.)

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