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In the context of heterogeneous multi-robot teams deployed for executing multiple tasks, this paper develops an energy-aware framework for allocating tasks to robots in an online fashion. With a primary focus on long-duration autonomy applications, we opt for a survivability-focused approach. Towards this end, the task prioritization and execution -- through which the allocation of tasks to robots is effectively realized -- are encoded as constraints within an optimization problem aimed at minimizing the energy consumed by the robots at each point in time. In this context, an allocation is interpreted as a prioritization of a task over all others by each of the robots. Furthermore, we present a novel framework to represent the heterogeneous capabilities of the robots, by distinguishing between the features available on the robots, and the capabilities enabled by these features. By embedding these descriptions within the optimization problem, we make the framework resilient to situations where environmental conditions make certain features unsuitable to support a capability and when component failures on the robots occur. We demonstrate the efficacy and resilience of the proposed approach in a variety of use-case scenarios, consisting of simulations and real robot experiments.

When organizing robots into formations, the interplay between the underlying network topology of the team and the sensing and communication modalities available to the individual robots has a fundamental effect on what types of formations are possible. The purpose of this article is to characterize the available motions of formations in which relative angles between robots equipped with bearing-only sensors are maintained. First, infinitesimal shape-similarity, a property of frameworks for which maintaining certain angles between robots ensures that the formation is invariant to translation, rotation, and uniform scaling, is examined; the shape-similarity matrix is redeveloped, and results on its nullspace are presented. Second, triangulations, a class of frameworks, are shown to be infinitesimally shape-similar. Finally, the coupling between network topology and robot capabilities is examined through the design of a decentralized heterogeneous formation-control strategy for a class of triangulations in which all robots are equipped with bearing-only sensors and a single robot can measure distances; the formation-control strategy is demonstrated on a team of differential-drive robots.

This article is the second part of a two-part article on communication-failure-resilient architecture for distributed operation and control in smart grids with hybrid producer/consumer (prosumer) agents. Part I of this article proposed the distributed architecture and algorithmic development, while this Part II provides the corresponding algorithmic implementation, technical requirements, practical applications, and simulations. We propose a general and scalable framework for implementing resilient distributed frequency regulation (DFR) on large-scale prosumer-based power grids, such as utilities, where each prosumer represents a frequency control area. We first develop a method to obtain quasi-steady state models of prosumers from the dynamic models of generators, loads, and power lines. This model allows demonstrating the dynamic evolution of prosumers under normal conditions and during communication failures. Next, we propose a framework to implement the resilient DFR algorithm on prosumer power grids. We show that under normal conditions prosumers need to solely communicate with their neighbors to obtain optimal control actions. But, during communication failures, prosumers need to extend the communication hops to maintain system-wide stability as well as fair power sharing. The resilient DFR algorithm is demonstrated on two real-world, large-scale power grids and the results show that it can indeed complement and enhance today's Automatic Generation Control systems.

Distributed algorithms have been proposed as options to scale control propositions to the massive number of intelligent energy devices, sub-systems, and distributed energy resources being integrated into the electricity grid. Distributed algorithms rely on the communication network for exchanging information. Failures in the communication network can jeopardize distributed decision-making and in the worst-case scenario can lead to system-level stability problems. This paper proposes a communication-failure-resilient architecture for distributed operation and control in smart grids with hybrid producer/consumer (prosumer) agents. We describe the relations between system-wide performance and communication failures and identify topological conditions on the cyber-physical network, under which prosumers can perform key operating tasks, such as distributed frequency regulation through an imperfect communication network.

This paper presents a safe learning framework that employs an adaptive model learning algorithm together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique. We use the learned model in combination with control barrier certificates which constrain policies (feedback controllers) in order to maintain safety, which refers to avoiding particular undesirable regions of the state space. Under certain conditions, recovery of safety in the sense of Lyapunov stability after violations of safety due to the nonstationarity is guaranteed. In addition, we reformulate an action-value function approximation to make any kernel-based nonlinear function estimation method applicable to our adaptive learning framework. Lastly, solutions to the barrier-certified policy optimization are guaranteed to be globally optimal, ensuring the greedy policy improvement under mild conditions. The resulting framework is validated via simulations of a quadrotor, which has previously been used under stationarity assumptions in the safe learnings literature, and is then tested on a real robot, the brushbot, whose dynamics is unknown, highly complex and nonstationary., \copyright 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

In swarm robotics systems, coordinated behaviors emerge via local interactions among the robots as well as between robots and the environment. For a swarm of robots performing a set of pre-defined tasks in an enclosed region, this paper develops a decentralized mechanism to allocate tasks to each robot by leveraging the spatial interactions occurring among the robots as they move around the domain. With the aim of achieving a desired percentage of the swarm performing each task, the developed strategy allows individual robots to switch between different tasks with a certain probability when they encounter other robots in the region. We develop an analytical model to describe the inter-robot encounters occurring in a densely packed swarm of robots using ideas from the Enskog theory of dense gases and illustrate how the swarm can leverage this model to achieve the desired allocation levels. Furthermore, the inter-robot encounters enable the robots to measure the current allocation of the swarm, which is then used to regulate the rate at which they switch between tasks. This allows the swarm to speed up or slow down the rate of transitions between tasks depending on how far the current allocation is from the desired values, ultimately facilitating uninterrupted task execution by the robots. The methods introduced in this paper illustrate how naturally occurring encounters among robots in a swarm can be used to allocate tasks to the robots in a closed-loop manner. The developed algorithm is completely decentralized and can be deployed on minimalistic robots without the need for communication or a central coordinator. The performance of the algorithm is demonstrated on a swarm of real robots.

As the size of robots decreases in multirobot systems, collisions cease to be catastrophic events that need to be avoided at all costs. This implies that less conservative, coordinated control strategies can be employed, where collisions are not only tolerated, but can potentially be harnessed as an information source. In this paper, we follow this line of inquiry by employing collisions as a sensing modality that provides information about the robots’ surroundings. We envision a collection of robots moving around with no sensors other than binary, tactile sensors that can determine if a collision occurred, and let the robots use this information to determine their locations. We apply a probabilistic localization technique based on mean-field approximations that allows each robot to maintain and update a probability distribution over all possible locations. Simulations and real multirobot experiments illustrate the feasibility of the proposed approach.

Long duration autonomy considers robots that are deployed over long time scales. As a result, the robots’ ability to operate across changing environmental conditions and perform tasks that require more time to complete than what can be supported on a single battery charge, have implications for how the control design task should be approached. By drawing inspiration from ecology, which concerns itself with the strong coupling between organism and the environment it inhabits, we encode these “survival constraints” through Boolean compositions of multiple control barrier functions, and show how this construction supports long duration autonomy in the context of persistent environmental monitoring on a team of mobile robots.

This paper presents a framework for multirobot motion planning that characterizes pairwise interactions between agents, e.g., crossing paths while en route to a destination. Mixing is identified as the number of pairwise crossings exhibited by the robot motion. Mixing patterns specified through elements of the braid group provide sufficient level of abstraction to describe interactions without concern for the geometry of the motion. Controllers are constructed explicitly reasoning about the spatial collocation of robots to execute mixing patterns, achieving rich motion in a shared space, e.g., to exchange inter-robot information. We do not focus on achieving a particular pattern, but rather on the problem of being able to execute a whole class of them (e.g., all patterns with at most $M$ pairwise interactions). The result is a hybrid system driven by symbolic inputs that are mapped onto paths, realizing desired mixing levels. Controllers derived from optimal control provide theoretical bounds on the achievable amount of mixing, satisfaction of spatio-temporal constraints, and collision-free trajectories. Designs are carried to implementation on real robot platforms.

This paper discusses the problem of making multiple robots coordinate their movements subject to energy constraints imposed by their available battery levels. This problem is instantiated in the context of energy-aware rendezvous, whereby a collection of mobile robots must decide where and when to meet, with the objective of doing so in the least amount of time, given varying available initial battery levels. As the movements of the individual robots directly affect their energy consumption, the robots must coordinate their movements in such a way that they do not run out of energy prior to the completion of the task. This problem is formulated as a constrained optimization problem, where the constraints themselves result from a lower-level optimal control problem that ensures that all of the robots have nonnegative battery levels when they meet. The energy-constrained coordination problem is solved in a distributed manner and is implemented on a team of differential-drive mobile robots.

This paper presents safety barrier certificates that ensure scalable and provably collision-free behaviors in multirobot systems by modifying the nominal controllers to formally satisfy safety constraints. This is achieved by minimizing the difference between the actual and the nominal controllers subject to safety constraints. The resulting computation of the safety controllers is done through a quadratic programming problem that can be solved in real-time and in this paper, we describe a series of problems of increasing complexity. Starting with a centralized formulation, where the safety controller is computed across all agents simultaneously, we show how one can achieve a natural decentralization whereby individual robots only have to remain safe relative to nearby robots. Conservativeness and existence of solutions as well as deadlock-avoidance are then addressed using a mixture of relaxed control barrier functions, hybrid braking controllers, and consistent perturbations. The resulting control strategy is verified experimentally on a collection of wheeled mobile robots whose nominal controllers are explicitly designed to make the robots collide.

We propose a novel algorithm to find the global optimal path in 2D environments with moving obstacles, where the optimality is understood relative to a general convex continuous running cost. By leveraging the geometric structures of optimal solutions and using gradient flows, we convert the path-planning problem into a system of finite dimensional ordinary differential equations, whose dimensions change dynamically. Then a stochastic differential equation based optimization method, called intermittent diffusion, is employed to obtain the global optimal solution. We demonstrate, via numerical examples, that the new algorithm can solve the problem efficiently.

Due to the inherently distributed and heterogeneous nature of the microgrids, distributed control can be a promising approach to improve the stability, reliability, and scalability of the microgrids compared with centralized control strategies. This paper studies the distributed reactive power sharing problem for a microgrid with connected ac inverters. Under the standard decoupling approximation for bus angle differences, the reactive power flow of each inverter is dependent on the voltage amplitudes of its neighboring inverters connected by electrical power lines. Using the Lyapunov approach, a novel distributed voltage controller with nonlinear state feedback is proposed for reactive power sharing of the microgrid. It is proved that the inverters can achieve accurate reactive power sharing under the proposed controller if the communication network of inverters is connected. Then, by introducing the sampling and holding scheme, we extend the proposed controller to the nonlinear state feedback control with event-triggered communication among inverters. The new event-triggered control approach can dramatically reduce the amount of communication of the microgrid, and significantly relax the requirement for precise real-time information transmission among the inverters. Both the proposed controllers are validated by simulations on a group of inverters with time-varying loads.

This paper proposes a general framework for determining the effect of communication delays on the convergence of certain distributed frequency regulation (DFR) protocols for prosumer-based energy systems, where prosumers are serving as balancing areas. DFR relies on iterative and distributed optimization algorithms to obtain an optimal feedback law for frequency regulation. But, it is, in general, hard to know beforehand how many iterations suffice to ensure stability. This paper develops a framework to determine a lower bound on the number of iterations required for two distributed optimization protocols. This allows prosumers to determine whether they can compute stabilizing control strategies within an acceptable time frame by taking communication delays into account. The efficacy of the method is demonstrated on two realistic power systems.

In this paper, we consider the problem of routing multiple robots to service spatially distributed requests at specified time instants. We show that such a routing problem can be formulated as a pure assignment problem. Additionally, we incorporate connectivity constraints into the problem by requiring that range-constrained robots ensure a connected information exchange network at all times. We discuss the feasibility aspects of such a spatio-temporal routing problem, and derive the minimum number of robots required to service the requests. Moreover, we explicitly construct the corresponding routes for the robots, with the total length traveled as the cost to be minimized.

An approach is presented for influencing teams of robots by means of time-varying density functions, representing rough references for where the robots should be located. A continuous-time coverage algorithm is proposed and distributed approximations are given whereby the robots only need to access information from adjacent robots. Robotic experiments show that the proposed algorithms work in practice, as well as in theory.

This paper presents an algorithm for learning the switching policy and the boundaries conditions between primitive controllers that maximize the translational movements of a complex locomoting system. The algorithm learns an optimal action for each boundary condition instead of one for each discretized state-action pair of the system, as is typically done in machine learning. The system is modeled as a hybrid system because it contains both discrete and continuous dynamics. With this hybridification of the system and with this abstraction of learning boundary-action pairs, the “curse of dimensionality” is mitigated. The effectiveness of this learning algorithm is demonstrated on both a simulated system and on a physical robotic system. In both cases, the algorithm is able to learn the hybrid control strategy that maximizes the forward translational movement of the system without the need for human involvement.

A number of different interaction modalities have been proposed for human engagement with networked systems. In this paper, we establish formal guarantees for whether or not a given human-swarm interaction (HSI) strategy is appropriate for achieving particular multi-robot tasks, such as guiding a swarm of robots into a particular geometric configuration. In doing so, we define what it means to impose an HSI control structure on a multi-robot system. Control Lyapunov functions are used to establish feasibility for a user to achieve a particular geometric configuration with a multi-robot system under some selected HSI control structure. Several examples of multi-robot systems with unique HSI control structures are provided to illustrated the use of CLFs to establish feasibility. Additionally, we also uses these examples to illustrate how to use optimal control tools to compute three metrics for evaluating an HSI control structure: attention, effort, and scalability.

In this paper, we propose a distributed frequency regulation framework for prosumer-based electric energy systems, where a prosumer (producer-consumer) is defined as an intelligent agent which can produce, consume, and/or store electricity. Despite the frequency regulators being distributed, stability can be ensured while avoiding inter-area oscillations using a limited control effort. To achieve this, a fully distributed one-step model-predictive control protocol is proposed and analyzed, whereby each prosumer communicates solely with its neighbors in the network. The efficacy of the proposed frequency regulation framework is shown through simulations on two real-world electric energy systems of different scale and complexity. We show that prosumers can indeed bring frequency and power deviations to their desired values after small perturbations.

This paper introduces the notion of manipulability to mobile, multi-agent networks as a tool to analyze the instantaneous effectiveness of injecting control inputs at certain, so-called leader nodes in the network. Effectiveness is interpreted to characterize how the movements of the leader nodes translate into responses among the remaining follower nodes. This notion of effectiveness is a function of the interaction topologies, the agent configurations, and the particular choice of inputs used to influence the network. In fact, classic manipulability is an index used in robotics to analyze the singularity and efficiency of configurations of robot-arm manipulators. To define similar notions for leader-follower networks, we use a rigid-link approximation of the follower dynamics and, under this assumption, we prove that the instantaneous follower velocities can be uniquely determined from that of the leaders', which allows us to define a meaningful and computable manipulability index for the leader-follower networks. This paper examines the property of the proposed index in simulation and with real mobile robots, and demonstrates how the index can be used to find effective interaction topologies.

During the spring of 2013, I taught a massive open online course (MOOC), Control of Mobile Robots, to over 40,000 students worldwide. Online resources for higher education have received significant attention during the last year, but upper-level engineering classes have been virtually absent from all the major MOOC content providers(Udacity, Coursera, edX).

This paper presents a new method for injecting human inputs into mixed-initiative interactions between humans and robots. The method is based on a model-predictive control (MPC) formulation, which inevitably involves predicting the system (robot dynamics as well as human input) into the future. These predictions are complicated by the fact that the human is interacting with the robot, causing the prediction method itself to have an effect on future human inputs. We investigate and develop different prediction schemes, including fixed and variable horizon MPCs and human input estimators of different orders. Through a search-and-rescue-inspired human operator study, we arrive at the conclusion that the simplest prediction methods outperform the more complex ones, i.e., in this particular case, less is indeed more.

In this paper, we propose a distributed version of the Hungarian method to solve the well-known assignment problem. In the context of multirobot applications, all robots cooperatively compute a common assignment that optimizes a given global criterion (e.g., the total distance traveled) within a finite set of local computations and communications over a peer-to-peer network. As a motivating application, we consider a class of multirobot routing problems with “spatiotemporal” constraints, i.e., spatial targets that require servicing at particular time instants. As a means of demonstrating the theory developed in this paper, the robots cooperatively find online suboptimal routes by applying an iterative version of the proposed algorithm in a distributed and dynamic setting. As a concrete experimental test bed, we provide an interactive “multirobot orchestral” framework, in which a team of robots cooperatively plays a piece of music on a so-called orchestral floor.

The Federal Aviation Administration’s NextGen program aims to increase the capacity of the national airspace, while ensuring the safety of aircraft. This paper provides a distributed merging and spacing algorithm that maximizes the throughput at the terminal phase of flight, using information communicated between neighboring aircraft through the ADS-B framework. Aircraft belonging to a mixed fleet negotiate with each other and use dual decomposition to reach an agreement on optimal merging times, with respect to a pairwise cost, while ensuring proper interaircraft spacing for the respective aircraft types. A set of sufficient conditions on the geometry and operating conditions of merging forks is provided to identify when proper interaircraft spacing can always be achieved using the proposed algorithm for any combination of merging aircraft. Also, optimal decentralized controllers are derived for merging air traffic when operating under such conditions. The performance of the presented algorithm is verified through computer simulations.

In this paper, we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies. First, when the leaders are stationary and all followers share an inertial coordinate frame, we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is fixed, we partition the (nonsymmetric) Laplacian matrix and explore its properties to derive the convergence results. When the directed network topology is switching, the commonly adopted decoupling technique based on the Kronecker product in a high-dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results. The proposed coordinate transformation technique also has potential applications in other high-dimensional distributed control scenarios and might be used to simplify the analysis of a high-dimensional system to that of a one-dimensional system when the decoupling technique based on the Kronecker product cannot be applied. Second, when the leaders are dynamic and all followers share an inertial coordinate frame, we propose a distributed tracking control algorithm without velocity measurements. When the directed network topology is fixed, we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is switching, we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high-dimensional space. We also show via some counterexamples that it is, in general, impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high-dimensional space. Simulation results are presented as a proof of concept.

This article presents a novel way of manipulating the initial conditions in the consensus equation such that a constrained agreement problem is solved across a distributed network of agents, particularly for a network represented by a tree graph. The presented method is applied to the problem of coordinating multiple pendula attached to mobile bases. The pendula should move in such a way that their motion is synchronised, which calls for a constrained optimal control problem for each pendulum as well as the constrained agreement problem across the network. Simulation results are presented that support the viability of the proposed approach as well as a hardware demonstration.

In this paper, we provide a theoretical framework for controlling graph connectivity in mobile robot networks. We discuss proximity-based communication models composed of disk-based or uniformly-fading-signal-strength communication links. A graph-theoretic definition of connectivity is provided, as well as an equivalent definition based on algebraic graph theory, which employs the adjacency and Laplacian matrices of the graph and their spectral properties. Based on these results, we discuss centralized and distributed algorithms to maintain, increase, and control connectivity in mobile robot networks. The various approaches discussed in this paper range from convex optimization and subgradient-descent algorithms, for the maximization of the algebraic connectivity of the network, to potential fields and hybrid systems that maintain communication links or control the network topology in a least restrictive manner. Common to these approaches is the use of mobility to control the topology of the underlying communication network. We discuss applications of connectivity control to multirobot rendezvous, flocking and formation control, where so far, network connectivity has been considered an assumption.

The problem of making one system ''mimic'' a motion generated by another is studied. To address this, an optimal tracking problem is introduced that, in addition to tracking, optimizes over functions that deform or ''warp'' the time axis and the output space. Parametric and nonparametric versions of the time-warped tracking problem are presented and reduced to standard Bolza problems. The output warping problem is treated for affine and piecewise affine output warping functions. Example applications are given, including that of controlling a marionette to mimic a human dancer.

In this paper, we study the problem of controlling a group of unmanned aerial vehicles (UAVs) to provide convoy protection to a group of ground vehicles. The UAVs are modeled as Dubins vehicles flying at a constant altitude with bounded turning radius. We first present time-optimal paths to provide convoy protection to stationary ground vehicles. Then, we propose a control strategy to provide convoy protection to ground vehicles moving in straight lines. The minimum number of UAVs required to provide perpetual convoy protection, in both cases, are derived.

In this paper we derive a set of constraints that are sufficient to guarantee maintained connectivity in a leader-follower multi-agent network with a proximity based communication topology. In the scenario we consider, only the leaders are aware of the global mission, which is to converge at a known destination point. Thus, the followers need to stay in contact with the group of leaders in order to reach the goal. In the paper we show that we can maintain the initial network structure, and thereby connectivity, by setting up bounds on the ratio of leaders-to-followers and on the magnitude of the goal attraction force experienced by the leaders. The results are first established for an initially complete communication graph and then extended to an incomplete graph. The results are illustrated by computer simulations.

In this paper, we present feedback control laws for an autonomous vehicle with rigidly mounted range sensors to track a desired curve. In particular, we consider a vehicle that has a group of rays around two center rays that are perpendicular to the velocity of the vehicle. Under such a sensor configuration, singularities are bound to occur in the curve tracking feedback control law when tracking concave curves. To overcome this singularity, we derive a hybrid strategy of switching between control laws when the vehicle gets close to singularities. Rigorous proof and extensive simulation results verify the validity of the proposed feedback control law.

In this work, we consider the controlled agreement problem for multi-agent networks, where a collection of agents take on leader roles while the remaining agents execute local, consensus-like protocols. Our aim is to identify reflections of graph-theoretic notions on system-theoretic properties of such systems. In particular, we show how the symmetry structure of the network, characterized in terms of its automorphism group, directly relates to the controllability of the corresponding multi-agent system. Moreover, we introduce network equitable partitions as a means by which such controllability characterizations can be extended to the multileader setting.

This paper concerns a particular aspect of the optimal control problem for switched systems that change modes whenever the state intersects certain switching surfaces. These surfaces are assumed to be parameterized by a finite dimensional switching parameter, and the optimization problem we consider is that of minimizing a given cost-functional with respect to the switching parameter under the assumption that the initial state of the system is not a priori known. We approach this problem from two different vantage points by first minimizing the worst possible cost over the given set of initial states using results from min–max optimization. The second approach is based on a sensitivity analysis in which variational arguments give the derivative of the switching parameters with respect to the initial conditions.

In this paper, we address the problem of adaptively enriching motion description languages for multi-modal control by systematically enlarging the set of available modes. This problem is formulated as an optimal control problem, where new modes are designed by combining recurring mode string fragments into smooth, new “meta-modes”, and variational arguments are employed to derive optimality conditions for this construction.

In this article, we introduce the MODEbox tool for automatically producing hybrid, multimodal control programs from data. In particular, given an I/O string, four distinct operational units are introduced. The application of the MODEbox tool is illustrated on two different examples involving robots and ants.

In this paper, we solve an optimal control problem using the calculus of variation. The system under consideration is a switched autonomous delay system that undergoes jumps at the switch- ing times. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. Optimality conditions involving analytic expressions for the partial derivatives of a given cost function with respect to the control variables are derived using the calculus of variation. A locally optimal impulsive control strategy can then be found using a numerical gradient descent algorithm.

Periodic smoothing splines appear for example as generators of closed, planar curves, and in this paper they are constructed using a controlled two point boundary value problem in order to generate the desired spline function. The procedure is based on minimum norm problems in Hilbert spaces and a suitable Hilbert space is defined together with a corresponding linear affine variety that captures the constraints. The optimization is then reduced to the computationally stable problem of finding the point in the constraint variety closest to the data points.

This paper presents a neural network model for the stencil printing process (SPP) in surface-mount technology (SMT) manufacturing of printed circuit boards (PCBs). A practical model description that decomposes the overall steady-state process in independently modeled subspaces is provided. The neural network model can be updated in real-time procuring a method to control the process by dynamically searching the optimal set point of the control variables. The optimization is performed by minimizing the weighted mean squared error with respect to the desired solder brick height or volume; furthermore, in the case when multiple solutions exist, the set point that yields the lowest variance is used. The process simulator is mainly suitable for offline testing and debugging of more complex closed-loop control algorithms for the SPP optimization providing a common and realistic framework for algorithm performance evaluation. An important consideration in this paper is based on the fact that the estimation of the sampled moments of the probability distributions is made using a statistically significant number of data samples from each board, for each component type, for each printing direction, and for each pad orientation.

In this paper, we present a multi-pronged approach to the “Learning from Example” problem. In particular, we present a framework for integrating learning into a standard, hybrid navigation strategy, composed of both plan-based and reactive controllers. Based on the classification of colors and textures as either good or bad, a global map is populated with estimates of preferability in conjunction with the standard obstacle information. Moreover, individual feedback mappings from learned features to learned control actions are introduced as additional behaviors in the behavioral suite. A number of real-world experiments are discussed that illustrate the viability of the proposed method. © 2007 Wiley Periodicals, Inc.

Optimal switch-time control is an area that investigates how best to switch between different control modes. In this paper we present an algorithm for solving the optimal switch-time control problem for single-switch, linear systems where the state of the system is only partially known through the outputs. A method is presented that both guarantees that the current switch time remains optimal as the state estimates evolve, and that ensures this in a computationally feasible manner, thus rendering the method applicable to real-time applications. An extension is moreover considered where constraints on the switch time provide the observer with sufficient time to settle. The viability of the proposed method is illustrated through a number of examples.

This paper presents a solution to the problem of constructing control programs, i.e. sequences of control modes, from a given motion alphabet. In particular, techniques are developed that enable reinforcement learning to act directly at the mode level, and hence make learning applicable to continuous time control systems in a straightforward manner. Moreover, given such a control program, the issue of improving the system performance through the addition of new control laws is addressed as an optimal control problem. In fact, this is achieved through an optimal combination of recurring mode strings. A number of examples are provided that illustrate the viability of the proposed methods.