Aaron D. Ames, Samuel Coogan, Magnus Egerstedt et al.
This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.
Smriti Chopra, Giuseppe Notarstefano, Matthew Rice et al.
In this paper, we propose a distributed version of the Hungarian Method to solve the well known assignment problem. In the context of multi-robot 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 multi-robot routing problems with "spatio-temporal" 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 "multi-robot orchestral" framework in which a team of robots cooperatively plays a piece of music on a so-called orchestral floor.
Yorai Wardi, Magnus Egerstedt
This paper considers the problem of computing the schedule of modes in a switched dynamical system, that minimizes a cost functional defined on the trajectory of the system's continuous state variable. A recent approach to such optimal control problems consists of algorithms that alternate between computing the optimal switching times between modes in a given sequence, and updating the mode-sequence by inserting to it a finite number of new modes. These algorithms have an inherent inefficiency due to their sparse update of the mode-sequences, while spending most of the computing times on optimizing with respect to the switching times for a given mode-sequence. This paper proposes an algorithm that operates directly in the schedule space without resorting to the timing optimization problem. It is based on the Armijo step size along certain Gateaux derivatives of the performance functional, thereby avoiding some of the computational difficulties associated with discrete scheduling parameters. Its convergence to local minima as well as its rate of convergence are proved, and a simulation example on a nonlinear system exhibits quite a fast convergence.
Ahmet Yasin Yazicioglu, Waseem Abbas, Magnus Egerstedt
In this paper we study the controllability of networked systems with static network topologies using tools from algebraic graph theory. Each agent in the network acts in a decentralized fashion by updating its state in accordance with a nearest-neighbor averaging rule, known as the consensus dynamics. In order to control the system, external control inputs are injected into the so called leader nodes, and the influence is propagated throughout the network. Our main result is a tight topological lower bound on the rank of the controllability matrix for such systems with arbitrary network topologies and possibly multiple leaders.
Sebastian F. Ruf, Magnus Egerstedt, Jeff S. Shamma
This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is presented, including a necessary and sufficient condition for herdability. This paper then considers the impact of the underlying graph structure of a linear system on the herdability of the system, for the case where the graph is represented as signed and directed. By classifying nodes based on the length and sign of walks from an input, we find a class of completely herdable systems as well as provide a complete characterization of nodes that can be herded in systems with an underlying graph that is a directed out-branching rooted at a single input.
Gennaro Notomista, Xiaoyi Cai, Junya Yamauchi et al.
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.
Shashwat Shivam, Ian Buckley, Yorai Wardi et al.
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.
Ruoyu Lin, Gennaro Notomista, Magnus Egerstedt
This paper develops a general framework for multi-agent control synthesis, which applies to a wide range of problems with convergence guarantees, including those with time-varying objective functions. The proposed framework achieves decentralization without inducing dynamical coupling among agents, and it naturally supports multi-objective robotics and real-time implementation. To demonstrate its generality and effectiveness, the framework is applied to solve three representative problems, namely time-varying leader-follower formation control, decentralized coverage control for time-varying density functions without approximations, which is a long-standing open problem, and safe formation navigation in a dense environment.
Riwa Karam, Ruoyu Lin, Brooks A. Butler et al.
This paper studies heterogeneous multi-team collaboration through dynamic robot allocation, where robots are treated as transferable resources. Leveraging Hamilton's rule from ecology as an altruistic decision-making mechanism, we propose a multi-team collaborative resource allocation framework with heterogeneous capabilities, transfer costs, and capability-dependent contributions. The resulting allocation problem is combinatorial and is shown to be NP-hard. To address scalability, we develop a graph neural network policy under centralized training and decentralized execution that approximates the altruistic allocations based on Hamilton's rule. The model operates over the team interaction graph and predicts robot-level transfer decisions and next robot-to-team assignments. The proposed approach is validated in a firefighting scenario through simulations and experiments, demonstrating that the learned policy achieves near-optimal performance while scaling to larger systems.
Riwa Karam, Alexander A. Nguyen, Ruoyu Lin et al.
Collaboration is a central theme in multi-robot systems as tasks and demands increasingly require capabilities that go beyond what any one individual robot possesses. Yet, despite extensive work on cooperative control and coordinated behaviors, the terminology surrounding collective multi-robot interaction remains inconsistent across research communities. In particular, cooperation, coordination, and collaboration are often treated interchangeably, without clearly articulating the differences among them. To address this gap, we propose definitions that distinguish and relate cooperation, coordination, and collaboration in multi-robot systems, highlighting the support of new capabilities in collaborative behaviors, and illustrate these concepts through representative examples. Building on this taxonomy, different frameworks for collaboration are reviewed, and technical challenges and promising future research directions are identified for collaborative multi-robot systems.
Riwa Karam, Ruoyu Lin, Brooks A. Butler et al.
This paper presents a multi-team collaboration strategy based on Hamilton's rule from ecology that facilitates resource allocation among multiple teams, where agents are considered as shared resource among all teams that must be allocated appropriately. We construct an algorithmic framework that allows teams to make bids for agents that consider the costs and benefits of transferring agents while also considering relative mission importance for each team. This framework is applied to a multi-team coverage control mission to demonstrate its effectiveness. It is shown that the necessary criteria of a mission evaluation function are met by framing it as a function of the locational coverage cost of each team with respect to agent gain and loss, and these results are illustrated through simulations.
Brooks A. Butler, Xiao Tan, Aaron D. Ames et al.
This paper presents a novel framework for ensuring safety in dynamically coupled multi-agent systems through collaborative control. Drawing inspiration from ecological models of altruism, we develop collaborative control barrier functions that allow agents to cooperatively enforce individual safety constraints under coupling dynamics. We introduce an altruistic safety condition based on the so-called Hamilton's rule, enabling agents to trade off their own safety to support higher-priority neighbors. By incorporating these conditions into a distributed optimization framework, we demonstrate increased feasibility and robustness in maintaining system-wide safety. The effectiveness of the proposed approach is illustrated through simulation in a simplified formation control scenario.
Yousef Emam, Gennaro Notomista, Paul Glotfelter et al.
Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this paper, we frame safety as a differentiable robust-control-barrier-function layer in a model-based RL framework. Moreover, we also propose an approach to modularly learn the underlying reward-driven task, independent of safety constraints. We demonstrate that this approach both ensures safety and effectively guides exploration during training in a range of experiments, including zero-shot transfer when the reward is learned in a modular way.
Farhad Farokhi, Magnus Egerstedt
In this paper, 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.
Eric Squires, Rohit Konda, Samuel Coogan et al.
This paper demonstrates that the safety override arising from the use of a barrier function can in some cases be needlessly restrictive. In particular, we examine the case of fixed-wing collision avoidance and show that when using a barrier function, there are cases where two fixed-wing aircraft can come closer to colliding than if there were no barrier function at all. In addition, we construct cases where the barrier function labels the system as unsafe even when the vehicles start arbitrarily far apart. In other words, the barrier function ensures safety but with unnecessary costs to performance. We therefore introduce model-free barrier functions which take a data driven approach to creating a barrier function. We demonstrate the effectiveness of model-free barrier functions in a collision avoidance simulation of two fixed-wing aircraft.
Gennaro Notomista, Siddharth Mayya, Yousef Emam et al.
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.
Yousef Emam, Paul Glotfelter, Sean Wilson et al.
Applications that require multi-robot systems to operate independently for extended periods of time in unknown or unstructured environments face a broad set of challenges, such as hardware degradation, changing weather patterns, or unfamiliar terrain. To operate effectively under these changing conditions, algorithms developed for long-term autonomy applications require a stronger focus on robustness. Consequently, this work considers the ability to satisfy the operation-critical constraints of a disturbed system in a modular fashion, which means compatibility with different system objectives and disturbance representations. Toward this end, this paper introduces a controller-synthesis approach to constraint satisfaction for disturbed control-affine dynamical systems by utilizing Control Barrier Functions (CBFs). The aforementioned framework is constructed by modelling the disturbance as a union of convex hulls and leveraging previous work on CBFs for differential inclusions. This method of disturbance modeling grants compatibility with different disturbance-estimation methods. For example, this work demonstrates how a disturbance learned via a Gaussian process may be utilized in the proposed framework. These estimated disturbances are incorporated into the proposed controller-synthesis framework which is then tested on a fleet of robots in different scenarios.
Yousef Emam, Gennaro Notomista, Paul Glotfelter et al.
Multi-robot task allocation is a ubiquitous problem in robotics due to its applicability in a variety of scenarios. Adaptive task-allocation algorithms account for unknown disturbances and unpredicted phenomena in the environment where robots are deployed to execute tasks. However, this adaptivity typically comes at the cost of requiring precise knowledge of robot models in order to evaluate the allocation effectiveness and to adjust the task assignment online. As such, environmental disturbances can significantly degrade the accuracy of the models which in turn negatively affects the quality of the task allocation. In this paper, we leverage Gaussian processes, differential inclusions, and robust control barrier functions to learn environmental disturbances in order to guarantee robust task execution. We show the implementation and the effectiveness of the proposed framework on a real multi-robot system.
Priyabrata Saha, Magnus Egerstedt, Saibal Mukhopadhyay
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.
Ragesh K. Ramachandran, Pietro Pierpaoli, Magnus Egerstedt et al.
We propose a framework for resilience in a networked heterogeneous multi-robot team subject to resource failures. Each robot in the team is equipped with resources that it shares with its neighbors. Additionally, each robot in the team executes a task, whose performance depends on the resources to which it has access. When a resource on a particular robot becomes unavailable (\eg a camera ceases to function), the team optimally reconfigures its communication network so that the robots affected by the failure can continue their tasks. We focus on a monitoring task, where robots individually estimate the state of an exogenous process. We encode the end-to-end effect of a robot's resource loss on the monitoring performance of the team by defining a new stronger notion of observability -- \textit{one-hop observability}. By abstracting the impact that {low-level} individual resources have on the task performance through the notion of one-hop observability, our framework leads to the principled reconfiguration of information flow in the team to effectively replace the lost resource on one robot with information from another, as long as certain conditions are met. Network reconfiguration is converted to the problem of selecting edges to be modified in the system's communication graph after a resource failure has occurred. A controller based on finite-time convergence control barrier functions drives each robot to a spatial location that enables the communication links of the modified graph. We validate the effectiveness of our framework by deploying it on a team of differential-drive robots estimating the position of a group of quadrotors.
Shashwat Shivam, Yorai Wardi, Magnus Egerstedt et al.
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.
Yousef Emam, Siddharth Mayya, Gennaro Notomista et al.
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.
Haoyan Zhai, Magnus Egerstedt, Haomin Zhou
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport theory, the proposed method generates a graph connecting the initial and target configurations, and then finds a path over the graph using the available environmental information. The graph and path are updated iteratively when newly encountered obstacle information becomes available. The resulting method is a deterministic procedure proven to be complete, i.e., it is guaranteed to find a feasible path, when one exists, in a finite number of iterations. The method is scalable to high-dimensional problems. In addition, our method does not search the entire domain for the path, instead, the algorithm only explores a sub-region that can be described by the evolution of the Fokker-Planck equation. We demonstrate the performance of our algorithm via several numerical examples with different environments and dimensions, including high-dimensional cases.
Pietro Pierpaoli, Harish Ravichandar, Nicholas Waytowich et al.
We present a technique for learning how to solve a multi-robot mission that requires interaction with an external environment by observing an expert system executing the same mission. We define the expert system as a team of robots equipped with a library of controllers, each designed to solve a specific task, supervised by an expert policy that appropriately selects controllers based on the states of robots and environment. The objective is for an un-trained team of robots (i.e., imitator system) equipped with the same library of controllers, but agnostic to the expert policy, to execute the mission, with performances comparable to those of the expert system. From un-annotated observations of the expert system, a multi-hypothesis filtering technique is used to estimate individual controllers executed by the expert policy. Then, the history of estimated controllers and environmental states is used to train a neural network policy for the imitator system. Considering a perimeter protection scenario on a team of differential-drive robots, we show that the learned policy endows the imitator system with performances comparable to those of the expert system.
Pietro Pierpaoli, Thinh T. Doan, Justin Romberg et al.
Given a list of behaviors and associated parameterized controllers for solving different individual tasks, we study the problem of selecting an optimal sequence of coordinated behaviors in multi-robot systems for completing a given mission, which could not be handled by any single behavior. In addition, we are interested in the case where partial information of the underlying mission is unknown, therefore, the robots must cooperatively learn this information through their course of actions. Such problem can be formulated as an optimal decision problem in multi-robot systems, however, it is in general intractable due to modeling imperfections and the curse of dimensionality of the decision variables. To circumvent these issues, we first consider an alternate formulation of the original problem through introducing a sequence of behaviors' switching times. Our main contribution is then to propose a novel reinforcement learning based method, that combines Q-learning and online gradient descent, for solving this reformulated problem. In particular, the optimal sequence of the robots' behaviors is found by using Q-learning while the optimal parameters of the associated controllers are obtained through an online gradient descent method. Finally, to illustrate the effectiveness of our proposed method we implement it on a team of differential-drive robots for solving two different missions, namely, convoy protection and object manipulation.
Yousef Emam, Paul Glotfelter, Magnus Egerstedt
The Robotarium, a remotely accessible swarm-robotics testbed, has provided free, open access to robotics and controls research for hundreds of users in thousands of experiments. This high level of usage requires autonomy in the system, which mainly corresponds to constraint satisfaction in the context of users' submissions. In other words, in case that the users' inputs to the robots may lead to collisions, these inputs must be altered to avoid these collisions automatically. However, these alterations must be minimal so as to preserve the users' objective in the experiment. Toward this end, the system has utilized barrier functions, which admit a minimally invasive controller-synthesis procedure. However, barrier functions are yet to be robustified with respect to unmodeled disturbances (e.g., wheel slip or packet loss) in a manner conducive to real-time synthesis. As such, this paper formulates robust barrier functions for a general class of disturbed control-affine systems that, in turn, is key for the Robotarium to operate fully autonomously (i.e., without human supervision). Experimental results showcase the effectiveness of this robust formulation in a long-term experiment in the Robotarium.
Pietro Pierpaoli, Anqi Li, Mohit Srinivasan et al.
A number of coordinated behaviors have been proposed for achieving specific tasks for multi-robot 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 inter-agent communication depends on inter-robot 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.
Eric Squires, Pietro Pierpaoli, Rohit Konda et al.
This paper considers how to ensure that a system of fixed wing Unmanned Aerial Vehicles (UAVs) can avoid collisions. To do so we develop a novel method for creating a barrier function, which is similar to a Lyapunov function and can be used to ensure that a system can stay safe for all future times. After introducing the general approach, it is shown how to ensure that collision avoidance for two vehicles can be guaranteed for all future times. The construction is then extended to the case of arbitrarily many vehicles by addressing how to satisfy multiple safety objectives simultaneously. We do this while ensuring output actuator commands are within specified limits. Because this formulation requires communication of control values and may therefore reduce throughput of other important messages, we then show how to reformulate the solution without this significant communication overhead while still ensuring safety is maintained and actuator limits are respected. We validate the theoretical developments of this paper in the simulator SCRIMMAGE with a simulation of 20 UAVs that maintain safe distances from each other even though their nominal paths would otherwise cause a collision.
Anqi Li, Ching-An Cheng, Byron Boots et al.
Robotic systems often need to consider multiple tasks concurrently. This challenge calls for controller synthesis algorithms that fulfill multiple control specifications while maintaining the stability of the overall system. In this paper, we decompose multi-objective tasks into subtasks, where individual subtask controllers are designed independently and then combined to generate the overall control policy. In particular, we adopt Riemannian Motion Policies (RMPs), a recently proposed controller structure in robotics, and, RMPflow, its associated computational framework for combining RMP controllers. We re-establish and extend the stability results of RMPflow through a rigorous Control Lyapunov Function (CLF) treatment. We then show that RMPflow can stably combine individually designed subtask controllers that satisfy certain CLF constraints. This new insight leads to an efficient CLF-based computational framework to generate stable controllers that consider all the subtasks simultaneously. Compared with the original usage of RMPflow, our framework provides users the flexibility to incorporate design heuristics through nominal controllers for the subtasks. We validate the proposed computational framework through numerical simulation and robotic implementation.
María Santos, Magnus Egerstedt
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.
Gennaro Notomista, Siddharth Mayya, Seth Hutchinson et al.
For a team of heterogeneous robots executing multiple tasks, we propose a novel algorithm to optimally allocate tasks to robots while accounting for their different capabilities. Motivated by the need that robot teams have in many real-world applications of remaining operational for long periods of time, we allow each robot to choose tasks taking into account the energy consumed by executing them, besides the global specifications on the task allocation. The tasks are encoded as constraints in an energy minimization problem solved at each point in time by each robot. The prioritization of a task over others -- effectively signifying the allocation of the task to that particular robot -- occurs via the introduction of slack variables in the task constraints. Moreover, the suitabilities of certain robots towards certain tasks are also taken into account to generate a task allocation algorithm for a team of robots with heterogeneous capabilities. The efficacy of the developed approach is demonstrated both in simulation and on a team of real robots.
Gennaro Notomista, Magnus Egerstedt
In this paper we propose a control framework that enables robots to execute tasks persistently, i.e., over time horizons much longer than robots' battery life. This is achieved by ensuring that the energy stored in the batteries of the robots is never depleted. This is framed as a set invariance constraint in an optimization problem whose objective is that of minimizing the difference between the robots' control inputs and nominal control inputs corresponding to the task that is to be executed. We refer to this process as the persistification of a robotic task. Forward invariance of subsets of the state space of the robots is turned into a control input constraint by using control barrier functions. The solution of the formulated optimization problem with energy constraints ensures that the robotic task is persistent. To illustrate the operation of the proposed framework, we consider two tasks whose persistent execution is particularly relevant: environment exploration and environment surveillance. We show the persistification of these two tasks both in simulation and on a team of wheeled mobile robots on the Robotarium.
Gennaro Notomista, Siddharth Mayya, Anirban Mazumdar et al.
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 employing a vibration-based locomotion strategy.
Siddharth Mayya, Gennaro Notomista, Dylan Shell et al.
In robot swarms operating under highly restrictive sensing and communication constraints, individuals may need to use direct physical proximity to facilitate information exchange. However, in certain task-related scenarios, this requirement might conflict with the need for robots to spread out in the environment, e.g., for distributed sensing or surveillance applications. This paper demonstrates how a swarm of minimally-equipped robots can form high-density robot aggregates which coexist with lower robot densities in the domain. We envision a scenario where a swarm of vibration-driven robots---which sit atop bristles and achieve directed motion by vibrating them---move somewhat randomly in an environment while colliding with each other. Theoretical techniques from the study of far-from-equilibrium collectives and statistical mechanics clarify the mechanisms underlying the formation of these high and low density regions. Specifically, we capitalize on a transformation that connects the collective properties of a system of self-propelled particles with that of a well-studied molecular fluid system, thereby inheriting the rich theory of equilibrium thermodynamics. This connection is a formal one and is a relatively recent result in studies of motility induced phase separation; it is previously unexplored in the context of robotics. Real robot experiments as well as simulations illustrate how inter-robot collisions can precipitate the formation of non-uniform robot densities in a closed and bounded region.
Anqi Li, Mustafa Mukadam, Magnus Egerstedt et al.
In many applications, multi-robot systems are required to achieve multiple objectives. For these multi-objective tasks, it is oftentimes hard to design a single control policy that fulfills all the objectives simultaneously. In this paper, we focus on multi-objective tasks that can be decomposed into a set of simple subtasks. Controllers for these subtasks are individually designed and then combined into a control policy for the entire team. One significant feature of our work is that the subtask controllers are designed along with their underlying manifolds. When a controller is combined with other controllers, their associated manifolds are also taken into account. This formulation yields a policy generation framework for multi-robot systems that can combine controllers for a variety of objectives while implicitly handling the interaction among robots and subtasks. To describe controllers on manifolds, we adopt Riemannian Motion Policies (RMPs), and propose a collection of RMPs for common multi-robot subtasks. Centralized and decentralized algorithms are designed to combine these RMPs into a final control policy. Theoretical analysis shows that the system under the control policy is stable. Moreover, we prove that many existing multi-robot controllers can be closely approximated by the framework. The proposed algorithms are validated through both simulated tasks and robotic implementations.
Sebastian F Ruf, Magnus Egerstedt, Jeff S. Shamma
We consider the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. First a number of foundational results on herdability of a continuous time, linear time invariant system are presented. These show that the herdability of a linear system can be determined based on certain matrices, such as the controllability matrix, which arise in the study of controllability of linear systems. Second, the relationship between the sign pattern of the underlying graph structure of a system and the herdability properties of the system is investigated. In doing so the notion of sign herdability is introduced which captures classes of systems whose sign pattern determines their herdability. We identify a set of conditions, first on the sign pattern of the controllability matrix and then on the underlying graph structure, that ensure that the system is sign herdable.
Siddharth Mayya, Pietro Pierpaoli, Magnus Egerstedt
In densely-packed robot swarms operating in confined regions, spatial interference -- which manifests itself as a competition for physical space -- forces robots to spend more time navigating around each other rather than performing the primary task. This paper develops a decentralized algorithm that enables individual robots to decide whether to stay in the region and contribute to the overall mission, or vacate the region so as to reduce the negative effects that interference has on the overall efficiency of the swarm. We develop this algorithm in the context of a distributed collection task, where a team of robots collect and deposit objects from one set of locations to another in a given region. Robots do not communicate and use only binary information regarding the presence of other robots around them to make the decision to stay or retreat. We illustrate the efficacy of the algorithm with experiments on a team of real robots.
Gennaro Notomista, Magnus Egerstedt
In this paper we present a reformulation--framed as a constrained optimization problem--of multi-robot tasks which are encoded through a cost function that is to be minimized. The advantages of this approach are multiple. The constraint-based formulation provides a natural way of enabling long-term robot autonomy applications, where resilience and adaptability to changing environmental conditions are essential. Moreover, under certain assumptions on the cost function, the resulting controller is guaranteed to be decentralized. Furthermore, finite-time convergence can be achieved, while using local information only, and therefore preserving the decentralized nature of the algorithm. The developed control framework has been tested on a team of ground mobile robots implementing long-term environmental monitoring.
Mohit Srinivasan, Samuel Coogan, Magnus Egerstedt
In this paper, a method to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent dynamical systems is proposed. Finite time convergence to a desired set in the state space is guaranteed under the existence of a suitable finite time convergence control barrier function. In addition, these barrier functions also guarantee forward invariance once the system converges to the desired set. This allows us to formulate a theoretical framework which synthesizes controllers for the multi-agent system. These properties also enable us to solve the reachability problem in continuous time by formulating a theorem on the composition of multiple finite time convergence control barrier functions. This approach is more flexible than existing methods and also allows for a greater set of feasible control laws. Linear temporal logic is used to specify complex task specifications that need to be satisfied by the multi-agent system. With this solution methodology, a control law is synthesized that satisfies the given temporal logic task specification. Robotic experiments are provided which were performed on the Robotarium multi-robot testbed at Georgia Tech.
Pietro Pierpaoli, Dominique Sauter, Magnus Egerstedt
Teams of networked autonomous agents have been used in a number of applications, such as mobile sensor networks and intelligent transportation systems. However, in such systems, the effect of faults and errors in one or more of the sub-systems can easily spread throughout the network, quickly degrading the performance of the entire system. In consensus-driven dynamics, the effects of faults are particularly relevant because of the presence of unconstrained rigid modes in the transfer function of the system. Here, we propose a two-stage technique for the identification and accommodation of a biased-measurements agent, in a network of mobile robots with time invariant interaction topology. We assume these interactions to only take place in the form of relative position measurements. A fault identification filter deployed on a single observer agent is used to estimate a single fault occurring anywhere in the network. Once the fault is detected, an optimal leader-based accommodation strategy is initiated. Results are presented by means of numerical simulations and robot experiments.
Gennaro Notomista, Magnus Egerstedt
In this paper we consider the coverage control problem for a team of wire-traversing robots. The two-dimensional motion of robots moving in a planar environment has to be projected to one-dimensional manifolds representing the wires. Starting from Lloyd's descent algorithm for coverage control, a solution that generates continuous motion of the robots on the wires is proposed. This is realized by means of a Continuous Onto Wires (COW) map: the robots' workspace is mapped onto the wires on which the motion of the robots is constrained to be. A final projection step is introduced to ensure that the configuration of the robots on the wires is a local minimizer of the constrained locational cost. An algorithm for the continuous constrained coverage control problem is proposed and it is tested both in simulation and on a team of mobile robots.
Paul Glotfelter, Magnus Egerstedt
When designing control strategies for differential-drive mobile robots, one standard tool is the consideration of a point at a fixed distance along a line orthogonal to the wheel axis instead of the full pose of the vehicle. This abstraction supports replacing the non-holonomic, three-state unicycle model with a much simpler two-state single-integrator model (i.e., a velocity-controlled point). Yet this transformation comes at a performance cost, through the robot's precision and maneuverability. This work contains derivations for expressions of these precision and maneuverability costs in terms of the transformation's parameters. Furthermore, these costs show that only selecting the parameter once over the course of an application may cause an undue loss of precision. Model Predictive Control (MPC) represents one such method to ameliorate this condition. However, MPC typically realizes a control signal, rather than a parameter, so this work also proposes a Parametric Model Predictive Control (PMPC) method for parameter and sampling horizon optimization. Experimental results are presented that demonstrate the effects of the parameterization on the deployment of algorithms developed for the single-integrator model on actual differential-drive mobile robots.
Motoya Ohnishi, Li Wang, Gennaro Notomista et al.
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.
Li Wang, Evangelos A. Theodorou, Magnus Egerstedt
To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach.
Siddharth Mayya, Magnus Egerstedt
In multi-robot systems where a central decision maker is specifying the movement of each individual robot, a communication failure can severely impair the performance of the system. This paper develops a motion strategy that allows robots to safely handle critical communication failures for such multi-robot architectures. For each robot, the proposed algorithm computes a time horizon over which collisions with other robots are guaranteed not to occur. These safe time horizons are included in the commands being transmitted to the individual robots. In the event of a communication failure, the robots execute the last received velocity commands for the corresponding safe time horizons leading to a provably safe open-loop motion strategy. The resulting algorithm is computationally effective and is agnostic to the task that the robots are performing. The efficacy of the strategy is verified in simulation as well as on a team of differential-drive mobile robots.
Li Wang, Aaron D. Ames, Magnus Egerstedt
Safety Barrier Certificates that ensure collision-free maneuvers for teams of differential flatness-based quadrotors are presented in this paper. Synthesized with control barrier functions, the certificates are used to modify the nominal trajectory in a minimally invasive way to avoid collisions. The proposed collision avoidance strategy complements existing flight control and planning algorithms by providing trajectory modifications with provable safety guarantees. The effectiveness of this strategy is supported both by the theoretical results and experimental validation on a team of five quadrotors.
Daniel Pickem, Paul Glotfelter, Li Wang et al.
This paper describes the Robotarium -- a remotely accessible, multi-robot research facility. The impetus behind the Robotarium is that multi-robot testbeds constitute an integral and essential part of the multi-robot research cycle, yet they are expensive, complex, and time-consuming to develop, operate, and maintain. These resource constraints, in turn, limit access for large groups of researchers and students, which is what the Robotarium is remedying by providing users with remote access to a state-of-the-art multi-robot test facility. This paper details the design and operation of the Robotarium and discusses the considerations one must take when making complex hardware remotely accessible. In particular, safety must be built into the system already at the design phase without overly constraining what coordinated control programs users can upload and execute, which calls for minimally invasive safety routines with provable performance guarantees.
Li Wang, Aaron Ames, Magnus Egerstedt
This paper presents a formal framework for collision avoidance in multi-robot systems, wherein an existing controller is modified in a minimally invasive fashion to ensure safety. We build this framework through the use of control barrier functions (CBFs) which guarantee forward invariance of a safe set; these yield safety barrier certificates in the context of heterogeneous robot dynamics subject to acceleration bounds. Moreover, safety barrier certificates are extended to a distributed control framework, wherein neighboring agent dynamics are unknown, through local parameter identification. The end result is an optimization-based controller that formally guarantees collision free behavior in heterogeneous multi-agent systems by minimally modifying the desired controller via safety barrier constraints. This formal result is verified in simulation on a multi-robot system consisting of both cumbersome and agile robots, is demonstrated experimentally on a system with a Magellan Pro robot and three Khepera III robots.
Li Wang, Aaron D. Ames, Magnus Egerstedt
Compositional barrier functions are proposed in this paper to systematically compose multiple objectives for teams of mobile robots. The objectives are first encoded as barrier functions, and then composed using AND and OR logical operators. The advantage of this approach is that compositional barrier functions can provably guarantee the simultaneous satisfaction of all composed objectives. The compositional barrier functions are applied to the example of ensuring collision avoidance and static/dynamical graph connectivity of teams of mobile robots. The resulting composite safety and connectivity barrier certificates are verified experimentally on a team of four mobile robots.
A. Yasin Yazicioglu, Waseem Abbas, Magnus Egerstedt
In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely the leaders. Our main result relates the controllability of such systems to the graph distances between the agents. More specifically, we present a graph topological lower bound on the rank of the controllability matrix. This lower bound is tight, and it is applicable to systems with arbitrary network topologies, coupling weights, and number of leaders. An algorithm for computing the lower bound is also provided. Furthermore, as a prominent application, we present how the proposed bound can be utilized to select a minimal set of leaders for achieving controllability, even when the coupling weights are unknown.