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A number of coordinated behaviors are proposed for achieving specific tasks for multirobot systems. However, since most applications require more than one such behavior, one needs to be able to compose together sequences of behaviors while respecting local information flow constraints. Specifically, when the interagent communication depends on interrobot distances, these constraints translate into particular configurations that must be reached in finite time in order for the system to be able to transition between the behaviors. To this end, we develop a distributed framework based on finite-time convergence control barrier functions that enables a team of robots to adjust its configuration in order to meet the communication requirements for the different tasks. In order to demonstrate the significance of the proposed framework, we implemented a full-scale scenario where a team of eight planar robots explore an urban environment in order to localize and rescue a subject.

The cost, in terms of both time and money, of instantiating a physical testbed can be prohibitive. To help resolve this issue, the Robotarium offers a free, remotely accessible robotics lab to users around the world. Since allowing the general public to use it, hundreds of users have submitted thousands of experiments. The current and accelerating experiment submission rate poses an operational challenge that cannot be handled through manual or human supervised execution without devoting a full time operator to the platform. A solution to this problem is enable the Robotarium to operate autonomously: improving the robustness and reliability of the system while reducing required human intervention to diagnose and recover from failures. In this pursuit, the hardware, software, and algorithms deployed on the Robotarium have undergone numerous developments, including a new differential-drive robot, the use of modern virtualization techniques for the software infrastructure, and the inclusion of robust constraint-satisfaction methods for long-term safe operation. Over the past year of autonomous operation, these advances have resulted in 0.76% of the 3402 submitted remote experiments failing and requiring human intervention to recover from. This paper details these development efforts and best practices that have been learned automating a remote-access testbed to keep up with the experimental demand of a large, active, and growing userbase.

One reason why multirobot systems are preferred, in some contexts, over their single-robot counterparts is that they admit a larger spatial footprint. With multiple robots, it is possible to span a large area, which is desirable in applications such as search and rescue, environmental monitoring, and perimeter patrol [1]. However, as interrobot distances grow, so do the communication delays experienced among the robots, making precise, coordinated control hard to achieve [2]-[5].

This paper explores the expressive capabilities of a swarm of miniature mobile robots within the context of inter-robot interactions and their mapping to the so-called fundamental emotions. In particular, we investigate how motion and shape descriptors that are psychologically associated with different emotions can be incorporated into different swarm behaviors for the purpose of artistic expositions. Based on these characterizations from social psychology, a set of swarm behaviors is created, where each behavior corresponds to a fundamental emotion. The effectiveness of these behaviors is evaluated in a survey in which the participants are asked to associate different swarm behaviors with the fundamental emotions. The results of the survey show that most of the research participants assigned to each video the emotion intended to be portrayed by design. These results confirm that abstract descriptors associated with the different fundamental emotions in social psychology provide useful motion characterizations that can be effectively transformed into expressive behaviors for a swarm of simple ground mobile robots., 13 pages, 17 figures

Collisions may be harnessed as a way to improve the overall safety and navigational effectiveness of some spacecraft. However, leveraging this capability in autonomous platforms requires the abilit...

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.

Distributed control has emerged as a major focus in the systems and controls area, with multiagent robotics playing a prominent role both as a canonical instantiation of a system, where control decisions must be made by individual nodes across an information-exchange network, and as a rich source of applications [1]-[5]. These applications include environmental monitoring [6], collective materials handling [7], construction [8], disaster response [9], and precision agriculture [10].

Many applications involving complex multi-task problems such as disaster relief, logistics and manufacturing necessitate the deployment and coordination of heterogeneous multi-agent systems due to the sheer number of tasks that must be executed simultaneously. A fundamental requirement for the successful coordination of such systems is leveraging the specialization of each agent within the team. This work presents a Receding Horizon Planning (RHP) framework aimed at scheduling tasks for heterogeneous multi-agent teams in a robust manner. In order to allow for the modular addition and removal of different types of agents to the team, the proposed framework accounts for the capabilities that each agent exhibits (e.g. quadrotors are agile and agnostic to rough terrain but are not suited to transport heavy payloads). An instantiation of the proposed RHP is developed and tested for a search and rescue scenario. Moreover, we present an abstracted search and rescue simulation environment, where a heterogeneous team of agents is deployed to simultaneously explore the environment, find and rescue trapped victims, and extinguish spreading fires as quickly as possible. We validate the effectiveness of our approach through extensive simulations comparing the presented framework with various planning horizons to a greedy task allocation scheme., Accepted to IFAC World Congress 2020

In this paper we address the problem of distributed estimation of spatial fields using mobile sensor networks with communication constraints. These constraints consist of a maximum communication bandwidth which limits the amount of data that can be exchanged between any two nodes of the network at each time instant. An algorithm to select the most significant data to be transferred between neighboring sensor nodes is developed starting from derived analytical error bounds. Moreover, the motion of the network nodes is controlled using a coverage control algorithm with the objective of minimizing the estimation uncertainty of each of the nodes. The resulting communication constrained distributed estimation algorithm is deployed on a team of ground mobile robots in the Robotarium, and its performance is evaluated both in terms of estimation accuracy of a simulated spatial field, and of the amount of data transferred.

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 this letter, preys with stochastic evasion policies are considered. The stochasticity adds unpredictable changes to the prey’s path for avoiding predator’s attacks. The prey’s cost function is composed of two terms balancing the unpredictability factor (by using stochasticity to make the task of forecasting its future positions by the predator difficult) and energy consumption (the least amount of energy required for performing a maneuver). The optimal probability density functions of the actions of the prey for trading-off unpredictability and energy consumption is shown to be characterized by the stationary Schrodinger’s equation.

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.

This letter presents the SlothBot, a wire-traversing robot envisioned for long-term environmental monitoring applications. The SlothBot is a solar-powered, slow-paced, energy-efficient robot—hence its name—capable of moving on a mesh of wires by switching between branching wires. Unlike ground mobile robots or aerial robots employed in environmental monitoring applications, the use of wire-traversing robots allows for longer-term deployment because of the significantly lower energy consumption. Wire traversing, coupled with the use of solar panels, facilitates the self-sustainability of the SlothBot. Locomotion and wire-switching maneuvers are performed in a fail-safe fashion, inasmuch the robot is always firmly attached to the wires, even when switching between branching wires. This is achieved by employing a two-body structure featuring an actuated decoupling mechanism. In this letter, we show the design and the motion control of the SlothBot, together with the results of long-term monitoring experiments.

Robots are entering an age of ubiquity, and to operate effectively, these systems must typically satisfy a series of constraints (e.g., collision avoidance, obeying speed limits, maintaining connectivity). In addition, modern applications hinge on the completion of particular tasks, such as driving to a certain location or monitoring a crop patch. The dichotomy between satisfying constraints and completing objectives creates a need for constraint-satisfaction frameworks that are composable with a pre-existing primary objective. Barrier functions have recently emerged as a practical and the composable method for constraint satisfaction, and prior results demonstrate a system of Boolean logic for nonsmooth barrier functions as well as a composable controller-synthesis framework; however, this prior work does not consider dynamically changing constraints (e.g., a robot sensing and avoiding an obstacle). Consequently, the main theoretical contribution of this letter extends nonsmooth barrier functions to time-varying barrier functions with jumps. In a practical instantiation of the theoretical main results, this letter revisits a classic problem by formulating a collision-avoidance framework and composing it with a nominal controller. Experimental results show the efficacy of this framework on a light detection and ranging (LIDAR)-equipped differential-drive robot in a real-time obstacle-avoidance scenario.

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.

This letter introduces integral control barrier functions (I-CBFs) as a means to enable the safety-critical integral control of nonlinear systems. Importantly, I-CBFs allow for the holistic encoding of both state constraints and input bounds in a single framework. We demonstrate this by applying them to a dynamically defined tracking controller, thereby enforcing safety in state and input through a minimally invasive I-CBF controller framed as a quadratic program.

We consider the problem of manipulating an unknown payload using multiple agents. The objective is to find both optimal grasping positions and input forces for agents to apply so that the resulting linear and angular velocities make the rigid object track a reference. The associated optimization problem is split into force and position subproblems. The primal–dual gradient dynamics for the force subproblem can be completely decoupled into local dynamics that each agent can implement using only local measurements. The proximal gradient dynamics for the position subproblem require only local object shape information and relative positions between adjacent agents. We prove that combining the optimization dynamics for these subproblems yields an algorithm that converges to a locally optimal point for the joint force-position problem, and provide numerical simulations that demonstrate its performance on practical problems.

This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is first formulated. In this formulation, it is shown that motion coordination on a sphere is equivalent to attitude coordination on the 3-dimensional Special Orthogonal group. Then, an angle-based control barrier function that can handle a geodesic distance constraint on a spherical surface is presented. The proposed control barrier function is then extended to a relative motion case and applied to a collision avoidance problem for a rigid body network operating on a sphere. Each rigid body chooses its control input by solving a distributed optimization problem to achieve a nominal distributed motion coordination strategy while satisfying constraints for collision avoidance. The proposed collision-free motion coordination law is validated via simulation.

For multi-robot teams with heterogeneous capabilities, typical task allocation methods assign tasks to robots based on the suitability of the robots to perform certain tasks as well as the requirements of the task itself. However, in real-world deployments of robot teams, the suitability of a robot might be unknown prior to deployment, or might vary due to changing environmental conditions. This paper presents an adaptive task allocation and task execution framework which allows individual robots to prioritize among tasks while explicitly taking into account their efficacy at performing the tasks---the parameters of which might be unknown before deployment and/or might vary over time. Such a \emph{specialization} parameter---encoding the effectiveness of a given robot towards a task---is updated on-the-fly, allowing our algorithm to reassign tasks among robots with the aim of executing them. The developed framework requires no explicit model of the changing environment or of the unknown robot capabilities---it only takes into account the progress made by the robots at completing the tasks. Simulations and experiments demonstrate the efficacy of the proposed approach during variations in environmental conditions and when robot capabilities are unknown before deployment., Comment: Submitted and accepted for the 2020 IEEE International Conference on Robotics and Automation (ICRA)

The interplay between network topology and the interaction modalities of a multi-robot team fundamentally impact the types of formations that can be achieved. To explore the trade-offs between network structure and the sensing and communication capabilities of individual robots, this paper applies controller synthesis to formation control of infinitesimally shape-similar frameworks, for which maintaining the relative angles between robots ensures invariance of the framework to translation, rotation, and uniform scaling. Beginning with the development of a controller for the sole purpose of maintaining the formation, the controller-synthesis approach is introduced as a mechanism for incorporating user- designated objectives while ensuring that the formation is maintained. Both centralized and decentralized formulations of the synthesized controller are presented, the resulting sensing and communication requirements are discussed, and the method is demonstrated on a team of differential-drive robots.

This paper presents a coverage control algorithm for teams of quadcopters with downward facing visual sensors that prevents the appearance of coverage holes in-between the monitored areas while maximizing the coverage quality as much as possible. We derive necessary and sufficient conditions for preventing the appearance of holes in-between the fields of views among trios of robots. Because this condition can be expressed as logically combined constraints, control nonsmooth barrier functions are implemented to enforce it. An algorithm which extends control nonsmooth barrier functions to hybrid systems is implemented to manage the switching among barrier functions caused by the changes of the robots composing trio. The performance and validity of the proposed algorithm are evaluated in simulation as well as on a team of quadcopters.

In this paper, we propose a graph-based search method to optimally allocate tasks to a team of robots given a global task specification. In particular, we define these agents as discrete transition systems. In order to allocate tasks to the team of robots, we decompose finite linear temporal logic (LTL) specifications and consider agent specific cost functions. We propose to use the stochastic optimization technique, cross entropy, to optimize over this cost function. The multi-agent task allocation cross-entropy (MTAC-E) algorithm is developed to determine both when it is optimal to switch to a new agent to complete a task and minimize the costs associated with individual agent trajectories. The proposed algorithm is verified in simulation and experimental results are included.

In this paper, we consider a two-player racing game, where an autonomous ego vehicle has to be controlled to race against an opponent vehicle, which is either autonomous or human-driven. The approach to control the ego vehicle is based on a Sensitivity-ENhanced NAsh equilibrium seeking (SENNA) method, which uses an iterated best response algorithm in order to optimize for a trajectory in a two-car racing game. This method exploits the interactions between the ego and the opponent vehicle that take place through a collision avoidance constraint. This game-theoretic control method hinges on the ego vehicle having an accurate model and correct knowledge of the state of the opponent vehicle. However, when an accurate model for the opponent vehicle is not available, or the estimation of its state is corrupted by noise, the performance of the approach might be compromised. For this reason, we augment the SENNA algorithm by enforcing Permissive RObust SafeTy (PROST) conditions using control barrier functions. The objective is to successfully overtake or to remain in the front of the opponent vehicle, even when the information about the latter is not fully available. The successful synergy between SENNA and PROST—antithetical to the notable rivalry between the two namesake Formula 1 drivers—is demonstrated through extensive simulated experiments.

This letter considers distributed flocking control on the Special Euclidean group for networked rigid bodies. The method captures the three flocking rules proposed by Reynolds: cohesion; alignment; and separation. The proposed controller is based only on relative pose (position and attitude) information with respect to neighboring rigid bodies so that it can be implemented in a fully distributed manner using only local sensors. The flocking algorithm is moreover based on pose synchronization methods for the cohesion/alignment rules and achieves safe separation distances through the application of control barrier functions. The control input for each rigid body is chosen by solving a distributed optimization problem with constraints for pose synchronization and collision avoidance. Here, the inherent conflict between cohesion and separation is explicitly handled by relaxing the position synchronization constraint. The effectiveness of the proposed flocking algorithm is demonstrated via simulation and hardware experiments.

We present an optimization framework for solving multiagent convex programs subject to inequality constraints while keeping the agents’ state trajectories private. Each agent has an objective function depending only upon its own state and the agents are collectively subject to global constraints. The agents do not directly communicate with each other but instead route messages through a trusted cloud computer. The cloud adds noise to data being sent to the agents in accordance with the framework of differential privacy and, thus, keeps each agent's state trajectory private from all other agents and any eavesdroppers. This private problem can be viewed as a stochastic variational inequality, and it is solved using a projection-based method for solving variational inequalities that resemble a noisy primal-dual gradient algorithm. Convergence of the optimization algorithm in the presence of noise is proven, and a quantifiable tradeoff between privacy and convergence is extracted from this proof. Simulation results are provided that demonstrate numerical convergence for both $\epsilon$ -differential privacy and $(\epsilon, \delta)$ -differential privacy.

This letter investigates how mobile agents with qualitatively different sensing capabilities should be organized in order to effectively cover an area. In particular, by encoding the different capabilities as different density functions in the locational cost, the result is a heterogeneous coverage control problem where the different density functions serve as a way of both abstracting and encapsulating different sensing capabilities. However, different density functions imply that mass is not conserved as the agents move and, as a result, the normal cancellations that occur across boundaries between regions of dominance in the homogeneous case no longer take place when computing the gradient of the locational cost. As a result, new terms are needed if the robots are to execute a descent flow in order to minimize the locational cost, and we show how these additional terms can be formulated as boundary-disagreement terms that are added to the standard Lloyd's algorithm. The results are implemented on real robotic platforms for a number of different use cases.

In this letter, we consider the problem of rendering robotic tasks persistent by ensuring that the robots' energy levels are never depleted, which means that the tasks can be executed over long time horizons. This process is referred to as the persistification of the task. In particular, the state of each robot is augmented with its battery level so that the desired persistent behavior can be encoded as the forward invariance of a set such that the robots never deplete their batteries. Control barrier functions are employed to synthesize controllers that ensure that this set is forward invariant and, therefore, that the robotic task is persistent. As an application, this letter considers the persistification of a robotic sensor coverage task in which a group of robots has to cover an area of interest. The successful persistification of the coverage task is shown in simulation and on a team of mobile robots.

In this paper, we investigate the effect of insufficient time-scale separation between inner and the outer loops in networked, cascaded systems. First, a qualitative model is developed where the stability of a cascaded system is analyzed in terms of the gains acting at the outer and inner loops. Next, interconnected cascaded systems are considered, which represent networks congested by data sent by multiple clients. Then, the effect of the number of clients for the performance is examined through the scalable stability notion, which guarantees positively lower-bounded convergence rates with respect to the number of clients.

This paper concerns optimal mode-scheduling in autonomous switched-mode hybrid dynamical systems, where the objective is to minimize a cost-performance functional defined on the state trajectory as a function of the schedule of modes. The controlled variable, namely the modes’ schedule, consists of the sequence of modes and the switchover times between them. We propose a gradient-descent algorithm that adjusts a given mode-schedule by changing multiple modes over time-sets of positive Lebesgue measures, thereby avoiding the inefficiencies inherent in existing techniques that change the modes one at a time. The algorithm is based on steepest descent with Armijo step sizes along Gâteaux differentials of the performance functional with respect to schedule-variations, which yields effective descent at each iteration. Since the space of mode-schedules is infinite dimensional and incomplete, the algorithm’s convergence is proved in the sense of Polak’s framework of optimality functions and minimizing sequences. Simulation results are presented, and possible extensions to problems with dwell-time lower-bound constraints are discussed.

This paper concerns an output-tracking technique based on a standalone integrator with variable gain. The control algorithm, recently proposed by the authors, appears to have a wide scope in linear and nonlinear systems while aiming at simple and efficient computations in the loop. For a class of memoryless systems it resembles a Newton-Raphson flow for solving the loop equation, but it is applicable to a broader class of dynamical systems. Furthermore, the technique is suitable for tracking constant as well as time-dependent reference signals, and its convergence performance is robust with respect to computational errors in the loop. The objective of this paper is to test the technique on a control problem arising in multi-agent systems. Specifically, we are motivated by regulating trajectories of follower agents by a lead agent in a platoon or swarm of multi-agent networks connected by the graph Laplacian. We study a particular example, which is challenging from the standpoint of control, with the aim of identifying the limits of the technique and investigating their possible extensions.

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.

Recently, significant gains have been made in our understanding of multi-robot systems, and such systems have been deployed in domains as diverse as precision agriculture, flexible manufacturing, e...

As multi-agent systems become more wide-spread and versatile, the ability to satisfy multiple system-level constraints grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet such constraints by guaranteeing forward invariance of desirable sets. However, satisfying multiple constraints typically implies formulating multiple barrier functions, which would be ameliorated if the barrier functions could be composed together as Boolean logic formulas. The use of max and min operators, which yields nonsmooth functions, represents one path to accomplish Boolean compositions of barrier functions, and this letter extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. We validate our results by deploying Boolean compositions of nonsmooth barrier functions onto a team of mobile robots.

We present a framework for asynchronously solving convex optimization problems over networks of agents which are augmented by the presence of a centralized cloud computer. This framework uses a Tikhonov-regularized primal-dual approach in which the agents update the system's primal variables and the cloud updates its dual variables. To minimize coordination requirements placed upon the system, the times of communications and computations among the agents are allowed to be arbitrary, provided they satisfy mild conditions. Communications from the agents to the cloud are likewise carried out without any coordination in their timing. However, we require that the cloud keeps the dual variable's value synchronized across the agents, and a counterexample is provided that demonstrates that this level of synchrony is indeed necessary for convergence. Convergence rate estimates are provided in both the primal and dual spaces, and simulation results are presented that demonstrate the operation and convergence of the proposed algorithm.

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.

We present a new method for learning control law that stabilizes an unknown nonlinear dynamical system at an equilibrium point. We formulate a system identification task in a self-supervised learning setting that jointly learns a controller and corresponding stable closed-loop dynamics hypothesis. The input-output behavior of the unknown dynamical system under random control inputs is used as the supervising signal to train the neural network-based system model and the controller. The proposed method relies on the Lyapunov stability theory to generate a stable closed-loop dynamics hypothesis and corresponding control law. We demonstrate our method on various nonlinear control problems such as n-link pendulum balancing and trajectory tracking, pendulum on cart balancing, and wheeled vehicle path following., Comment: Copyright 2021 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

This paper concerns an application of a recently-developed nonlinear tracking technique to trajectory control of autonomous vehicles at traffic intersections. The technique uses a flow version of the Newton-Raphson method for controlling a predicted system-output to a future reference target. Its implementations are based on numerical solutions of ordinary differential equations, and it does not specify any particular method for computing its future reference trajectories. Consequently it can use relatively simple algorithms on crude models for computing the target trajectories, and more-accurate models and algorithms for trajectory control in the tight loop. We demonstrate this point at an extant predictive traffic planning-and-control method with our tracking technique. Furthermore, we guarantee safety specifications by applying to the tracking technique the framework of control barrier functions., Comment: to be published in Proc.21st IFAC World Congress, Berlin, Germany, July 12-17,2020

In this paper we present a study of a specific class of vibration-driven robots: the brushbots. In a bottom-up fashion, we start by deriving dynamic models of the brushes and we discuss the conditions under which these models can be employed to describe the motion of brushbots. Then, we present two designs of brushbots: a fully-actuated platform and a differential-drive-like one. The former is employed to experimentally validate both the developed theoretical models and the devised motion control algorithms. Finally, a coordinated-control algorithm is implemented on a swarm of differential-drive-like brushbots in order to demonstrate the design simplicity and robustness that can be achieved by employing a vibration-based locomotion strategy.

In this paper, we study the problem of navigating quadcopters through a sequence of hoops. The specification may be given directly or indirectly via a linear temporal logic (LTL) formula. We approach this problem in three phases. First, we introduce a planner that generates a path through a given sequence of hoops. Second, we augment our planner to leverage a given specification in linear temporal logic (LTL) and generate a sequence that satisfies this specification. Third, we implement cross-entropy optimization on this planner to enhance trajectory performance where quadcopter trajectories are modified within the solution space to optimize over a cost function. We implement this planner as a novel interaction modality between users and quadcopters on the Robotarium. Simulation and experimental results are provided.

Recent advances in the capabilities of autonomous underwater vehicles suggest their growing utility in support of oceanographic inquiry. Towards developing autonomous systems to aid in monitoring and exploration of the polar, under-ice environment, this paper examines multi-vehicle teams consisting of autonomous profilers, a class of low-cost autonomous underwater vehicles that can only actuate their depth. Existing research on the under-ice environment documents the existence of depth-dependent ocean currents, which can be opportunistically leveraged to coordinate the motion of a team of autonomous profilers. As such, this paper proposes a backstepping control strategy that enables teams of autonomous profilers to execute established networked control algorithms; the backstepping controllers are examined through simulation and deployment on a team of differential-drive robots.

When deploying autonomous agents in unstructured environments over sustained periods of time, adaptability and robustness oftentimes outweigh optimality as a primary consideration. In other words, safety and survivability constraints play a key role and in this paper, we present a novel, constraint-learning framework for control tasks built on the idea of constraints-driven control. However, since control policies that keep a dynamical agent within state constraints over infinite horizons are not always available, this work instead considers constraints that can be satisfied over some finite time horizon T > 0, which we refer to as limited-duration safety. Consequently, value function learning can be used as a tool to help us find limited-duration safe policies. We show that, in some applications, the existence of limited-duration safe policies is actually sufficient for long-duration autonomy. This idea is illustrated on a swarm of simulated robots that are tasked with covering a given area, but that sporadically need to abandon this task to charge batteries. We show how the battery-charging behavior naturally emerges as a result of the constraints. Additionally, using a cart-pole simulation environment, we show how a control policy can be efficiently transferred from the source task, balancing the pole, to the target task, moving the cart to one direction without letting the pole fall down., 11 pages, 4 figures; published in Automatica

In this paper, we present a solution to the problem of coordinating multiple robots across a communication channel that experiences delays. The proposed approach leverages control barrier functions in order to ensure that the multi-robot system remains dissipative. This is achieved by encoding the dissipativity-preserving condition as a set invariance constraint. This constraint is then included in an optimization problem, whose objective is that of modifying, in a minimally invasive fashion, the nominal input to the robots. The formulated optimization problem is decentralized in the sense that, in order to be solved, it does not require the individual robots to have access to global information. Moreover, thanks to its convexity, each robot can solve it using fast and efficient algorithms. The effectiveness of the proposed control framework is demonstrated through the implementation of a formation control algorithm in presence of delays on a team of mobile robots.

For multi-agent systems, it is common to encode the task as an optimization problem with two distinctly different solution methodologies - one is to directly apply control inputs as optimization updates, the other is to solve the optimization problem through communications before applying actual control inputs. This reveals an important trade-off between communication and execution overhead for control of multiagent systems. To formally study this trade-off, we restrict our consideration to a class of commonly studied multi-agent problems where the objective function is the sum of a set of edge potential functions. The gradient descent algorithm and Newton's method are viewed as the proxy for the pure execution and the pure communication strategy, respectively. We propose an algorithm based on truncated Newton's method that provides tunable levels of trade-off between communication and execution efforts. Theoretical results on the convergence rate of the purposed algorithm are studied for the consensus problem under different trade-off strategies. The performance of the proposed algorithm is validated through simulation.

This paper concerns applications of a recently-developed output-tracking technique to trajectory control of autonomous vehicles. The technique is based on three principles: Newton-Raphson flow for solving algebraic equations,output prediction, and controller speedup. Early applications of the technique, made to simple systems of an academic nature,were implemented by simple algorithms requiring modest computational efforts. In contrast, this paper tests it on commonly-used dynamic models to see if it can handle more complex control scenarios. Results are derived from simulations as well as a laboratory setting, and they indicate effective tracking convergence despite the simplicity of the control algorithm., Comment: Accepted in ECC conference

The sensing modalities available to individual agents in a multi-robot team have a significant effect on what the team can accomplish. Previous work on infinitesimal shape-similarity has shown that maintaining relative angles between robots equipped with bearing-only sensors can render a formation of these robots invariant to translation, rotation, and uniform scaling; however, previous work has not proposed decentralized control strategies for exploiting this invariance. To address this deficiency, this paper proposes a decentralized formation control strategy for assembled triangulations, a class of infinitesimally shape-similar formations. Heterogeneous in terms of sensing and control, a decentralized formation control strategy is developed in which one robot sets the position of the formation, a robot capable of measuring bearings and distances controls the scale and heading, and the remaining robots maintain the assembled triangulation. The asymptotic controllers that compose the formation control strategy of this work are implemented on a team of differential-drive robots.

This paper presents a coverage control strategy for teams of quadcopters that ensures that no area is left unsurveyed in between the fields of view of the visual sensors mounted on the quadcopters. We present a locational cost that quantifies the team’s coverage performance according to the sensors’ performance function. Moreover, the cost function penalizes overlaps between the fields of view of the different sensors, with the objective of increasing the area covered by the team. A distributed control law is derived for the quadcopters so that they adjust their position and zoom according to the direction of ascent of the cost. Control barrier functions are implemented to ensure that, while executing the gradient ascent control law, no holes appear in between the fields of view of neighboring robots. The performance of the algorithm is evaluated in simulated experiments.