Dissertationen zum Thema „Control Barrier Function“

Safety constraints are ubiquitous in many robotic applications. For instance, aerial robots such as quadrotors or hexcoptors need to realize fast collision-free flight, and bipedal robots have to choose their discrete footholds properly to gain the desired friction and pressure contact forces. In this thesis, we address the safety critical control problem for fully-actuated and under-actuated mechanical systems. Since many mechanical systems evolve on nonlinear manifolds, we extend the concept of Control Barrier Function to a new concept called geometric Control Barrier Function which is specifically designed to handle safety constraints on manifolds. This type of Control Barrier Function stems from geometric control techniques and has a coordinate free and compact representation. In a similar fashion, we also extend the concept of Control Lyapunov Function to the concept of geometric Control Lyapunov Function to realize tracking on the manifolds. Based on these new geometric versions of CLF and CBF, we propose a general control design method for fully-actuated systems with both state and input constraints. In this CBF-CLF-QP control design, the control input is computed based on a state-dependent Quadratic Programming (QP) where the safety constraints are strictly enforced using geometric CBF but the tracking constraint is imposed through a type of relaxation. Through this type of relaxation, the controller could still keep the system state safe even in the cases when the reference is unsafe during some time period. For a single quadrotor, we propose the concept of augmented Control Barrier Function specifically to let it avoid external obstacles. Using this augmented CBF, we could still utilize the idea of CBF-CLF-QP controller in a sequential QP control design framework to let this quadrotor remain safe during the flight. In meantime, we also apply the geometric control techniques to the aerial transportation problem where a payload is carried by multiple quadrotors through cable suspension. This type of transportation method allows multiple quadrotors to share the payload weight, but introduces internal safety constraints at the same time. By employing both linear and nonlinear techniques, we are able to carry the payload pose to follow a pre-defined reference trajectory.

Les systèmes dynamiques critiques pour la sécurité sont essentiels dans divers secteurs, tels que l'aérospatiale, les systèmes autonomes et les robots en santé, où des défaillances peuvent avoir des conséquences catastrophiques. Un défi majeur est la prise en compte de la dégradation des composants et des actionneurs, compromettant la sécurité et la stabilité des systèmes. Il est donc crucial d'intégrer l'état de santé du système dans la conception de la commande pour assurer une tolérance à la dégradation fonctionnelle. Ces systèmes impliquent souvent des incertitudes et des connaissances incomplètes, nécessitant des approches d'apprentissage pour assimiler les données disponibles. L'apprentissage par renforcement (RL) est une approche puissante capable de synthétiser des lois de commande optimales pour des systèmes dynamiques partiellement ou totalement inconnus. Cependant, le développement de ces approches présente des défis : la phase d'exploration nécessaire à l'apprentissage peut entraîner le système dans des régions non sûres, accélérant la dégradation des composants ; en outre, des garanties de sécurité pendant la phase opérationnelle sont cruciales pour assurer la sécurité continue du système. Le paradigme de l'apprentissage par renforcement sûr (Safe RL) vise à développer des approches RL prioritaires aux garanties de sécurité, ainsi qu'à la stabilité et l'optimalité des systèmes. Cette thèse aborde ces défis en synthétisant de nouvelles stratégies d'apprentissage de commande adaptatives aux incertitudes et à la dégradation fonctionnelle. Les contributions principales incluent :• garantir l'optimalité, la sécurité et la stabilité de la loi de commande pendant les phases d'exploration et d'exploitation du RL. En intégrant les fonctions de barrière de commande (CBFs) et les fonctions de Lyapunov de commande (CLFs) dans le cadre du RL, l'exploration sécurisée et l'exploitation stable sont assurées pour les problèmes de régulation et de suivi de trajectoire. Les CBFs définissent des régions de fonctionnement sûres, tandis que les CLFs assurent la stabilité du système. Ces fonctions guident le processus d'apprentissage, garantissant le respect des contraintes de sécurité et de stabilité;• ralentir la vitesse de dégradation en intégrant les taux de dégradation dans la conception de la commande, utilisant initialement une approche de contrôle optimal en temps discret pour les systèmes linéaires. Cela garantit que les actions de contrôle minimisent la dégradation des composants, prolongeant leur durée de vie. Pour les systèmes non linéaires, des méthodes RL sont utilisées pour résoudre le problème en temps discret et continu, fournissant des solutions adaptables aux dynamiques complexes;• proposer un nouvel algorithme de RL cyclique pour garantir la stabilité du système en cas de dégradation des actionneurs. Cet algorithme met à jour dynamiquement la loi de commande apprise, assurant une adaptation adéquate à mesure que les composants se dégradent. La nature cyclique de l'algorithme permet une réévaluation et un ajustement des lois de commande, garantissant une performance optimale continue malgré la dégradation. Ces approches ont été mises en œuvre à travers des simulations, démontrant leur efficacité dans des applications académiques
Safety-critical dynamical systems are essential in various industries, such as aerospace domain, autonomous systems, robots in healthcare area etc. where safety issues and structural or functional failure may lead to catastrophic consequences. A significant challenge in these systems is the degradation of components and actuators, which can compromise safety and stability of systems. As such, incorporating state of system's health within the control design framework is essential to ensure tolerance to functional degradation. Moreover, such system models often involve uncertainties and incomplete knowledge, especially as components degrade, altering system dynamics in a nonlinear manner, calling for development of learning approaches that envisage assimilation of available data within the control learning paradigm. However, assuring safety during the learning phase (exploration) as well as operational phase (exploitation) is of paramount importance when it comes to such dynamical systems. Traditional model-based control approaches, require precise system models, making them less effective under these conditions. In this context, Reinforcement Learning (RL) emerges as a powerful approach, capable of learning optimal control laws for partially or fully unknown dynamic systems, in the presence of input-output data (without the exact knowledge of system models). However, development and implementation of RL based approaches present their own challenges: the exploration phase, necessary for learning, can lead the system into unsafe regions and accelerate the speed of degradation; further, provable safety guarantees during the operational (exploitation) phase are equally important to ensure safety throughout the system operation. In this context, Safe Reinforcement Learning (Safe RL) paradigm targets development of RL based approaches that prioritize the safety guarantees, along with traditional stability, and optimality of systems. This thesis addresses these challenges by developing novel control learning strategies that adapt to system uncertainties and functional degradation. The main contributions of this thesis lie in proposition of novel approaches to addressing the challenges of system safety and stability, as well as decelerating the speed of degradation, thereby advancing the fields of safe RL and leading to proposition of Degradation-Tolerant Control (DTC). These contributions include:• ensuring the optimality, safety, and stability of control policy during both exploration and exploitation phases of RL. By integrating Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) within the RL framework, safe exploration and stable operation are ensured for both regulation and tracking problems. CBFs are used to define safe operating regions, while CLFs ensure that the system remains stable. These functions are incorporated into the RL algorithms to guide the learning process, ensuring that safety and stability constraints are respected;• decelerating the speed of degradation by incorporating degradation rates into control design, initially employing an optimal control approach in discrete time for linear systems. This ensures that control actions minimize the speed of degradation on system components, thereby extending their lifespan. For nonlinear systems, RL methods are employed to address the problem in both discrete and continuous time, providing adaptable solutions to complex dynamics;• proposal of a novel cyclic RL algorithm to ensure system stability under actuator degradation. This algorithm cyclically updates the learned control law, ensuring proper adaptation as system components degrade. The cyclic nature of the algorithm allows for reassessment and adjustment of control policies, ensuring continuous optimal performance despite ongoing degradation. These developed approaches were implemented through simulations, demonstrating their effectiveness in academic applications

With the development and integration of cyber-physical and safety-critical systems, control systems are expected to achieve tasks that include logic rules, receptive decision-making, safety constraints, and so forth. For example, in a persistent surveillance application, an unmanned aerial vehicle might be required to "take photos of areas A and B infinitely often, always avoid unsafe region C, and return to the charging point when the battery level goes low." One possible design approach to achieve such complex specifications is automata-based planning using formal verification algorithms. Central to the existing formal verification of continuous-time systems is the notion of abstraction, which consists of partitioning the state space into cells, and then formulating a certain control problem on each cell. The control problem is characterized as finding a state feedback to make all the closed-loop trajectories starting from one cell reach and enter a consecutive cell in finite time without intruding any other cells. This essentially abstracts the continuous system into a finite-state transition graph. The complex specifications can thus be checked against the simple transition model using formal verification tools, which yields a sequence of cells to visit consecutively. While control algorithms have been developed in the literature for linear systems associated with a polytopic partitioning of the state space, the partitioning and control problem for systems on a curved space is a relatively unexplored research area. In this thesis, we consider $ SO (3) $ and $ \ mathbb {S} ^ 2 $, the two most commonly encountered manifolds in mechanical systems, and propose several approaches to address the partitioning and control problem that in principle could be generalized to other manifolds. Chapter 2 proposes a discretization scheme that consists of sampling point generation and cell construction. Each cell is constructed as a ball region around a sampling point with an identical radius. Uniformity measures for the sampling points are proposed. As a result, the $SO(3)$ manifold is discretized into interconnected cells whose union covers the whole space. A graph model is naturally built up based on the cell adjacency relations. This discretization method, in general, can be extended to any Riemannian manifold. To enable the cell transitions, two reference trajectories are constructed corresponding to the cell-level plan. We demonstrate the results by solving a constrained attitude maneuvering problem with arbitrary obstacle shapes. It is shown that the algorithm finds a feasible trajectory as long as it exists at that discretization level. In Chapter 3, the 2-sphere manifold is considered and discretized into spherical polytopes, an analog of convex polytopes in the Euclidean space. Moreover, with the gnomonic projection, we show that the spherical polytopes can be naturally mapped into Euclidean polytopes and the dynamics on the manifold locally transform to a simple linear system via feedback linearization. Based on this transformation, the control problems then can be solved in the Euclidean space, where many control schemes exist with safe cell transition guarantee. This method serves as a special case that solves the partition-and-control problem by transforming the states and dynamics on manifold to Euclidean space in local charts. In Chapter 4, we propose a notion of high-order barrier functions for general control affine systems to guarantee set forward invariance by checking their higher order derivatives. This notion provides a unified framework to constrain the transient behavior of the closed-loop trajectories, which is essential in the cell-transition control design. The asymptotic stability of the forward invariant set is also proved, which is highly favorable for robustness with respect to model perturbations. We revisit the cell transition problem in Chapter 2 and show that even with a simple stabilizing nominal controller, the proposed high-order barrier function framework provides satisfactory transient performance.

QC 20201012

Neste trabalho é proposta a determinação do ponto de Máximo Carregamento (PMC) em sistemas elétricos de potência por meio do método da Função Lagrangiana Barreira Modificada (FLBM), uma variante do método de Pontos Interiores (PI). Também por meio do método da FLBM, busca-se determinar qual é a barra, para cada sistema, que apresenta a maior sensibilidade em relação ao fator de carregamento, ou seja, qual seria a primeira barra que deveria sofrer corte de carga a fim de aumentar a margem de carregamento do sistema e, assim, evitar o colapso de tensão. Para comprovação dos resultados obtidos por meio do método da FLBM utiliza-se a técnica de Análise de Sensibilidade (AS). A formulação do problema tem como restrições de igualdade as equações de balanço de potência do sistema elétrico e como restrições de desigualdade os limites de tensões nas barras, assim como os limites de geração de potência reativa nas barras com controle da referida potência. Estudos de casos foram realizados em um sistema de 3 barras e nos sistemas IEEE 14, 57, 118 e 300 barras; tais estudos demonstraram a robustez e a eficiência dos algoritmos propostos.
This work proposes the determination of the Maximum Loading Point (MLP) in electric power system via Lagrangian Modified Barrier Function (LMBF) method, a variant of Interior Point (IP). The LMBF method is also used to determine which bus, for each system, has the highest sensitivity of load factor, i.e., which bus would be the first to have load shedding in order to increase the loading margin system and thus prevent voltage collapse. To validate this approach, the Sensitivity Analysis (SA) technique was used for the confirmation of the results obtained by the LMBF method. The formulation of the problem considered the equations of power balance of the electrical system equality constraints, and the buses voltage magnitude limits, as well as the limits of reactive power control at the buses of that power inequality constraints. Case studies were conducted in a system of 3 buses and IEEE systems 14, 57, 118 and 300 buses, demonstrating the robustness and efficiency of the proposed algorithms.

Dans cette thèse, nous nous attaquons aux défis de la localisation des systèmes multi-robots, en nous concentrant sur la localisation coopérative dans des formations non infiniment rigides avec des contraintes de détection. Nos contributions introduisent un cadre dans lequel les objectifs éventuellement conflictuels du maintien de la connectivité, de l'exécution des tâches et de l'acquisition d'informations sont "médiés" à l'aide d'un programme quadratique et des fonctions de barrière de contrôle et du formalisme de la fonction de Lyapunov de contrôle. Une autre contribution de cette thèse concerne la localisation active distribuée de cibles mobiles multiples par un groupe de robots volants utilisant des mesures basées sur des caméras, tout en accommodant d'autres tâches si la redondance du système le permet. Dans ce cas également, la formulation du problème utilise un programme quadratique et des fonctions de barrière de contrôle. En nous appuyant sur la fonction de barrière de contrôle et le cadre du programme quadratique, nous identifions et abordons les limites de l'état actuel de la technique, en particulier en ce qui concerne les fonctions de barrière de contrôle distribuées. Nos modifications aboutissent à un contrôleur qui converge vers la solution optimale centralisée. Enfin, nous présentons une méthodologie d'observation comme une nouvelle contribution, facilitant la localisation coopérative d'un système multi-robots dans un cadre commun en utilisant des mesures relatives au cadre du corps
In this thesis, we tackle challenges in the localization of multi-robot systems, focusing on cooperative localization in non-infinitesimally rigid formations with sensing constraints. Our contributions introduce a framework in which the possibly conflicting goals of connectivity maintenance, task execution and the information acquisition are "mediated" using a quadratic program and the control barrier functions and control Lyapunov function formalism. Another contribution of this thesis addresses distributed active localization of multiple moving targets by a group of flying robots using camera-based measurements, while accommodating other tasks if system redundancy permits. Also in this case, the problem formulation utilizes a quadratic program and control barrier functions. Building on the control barrier function and quadratic program framework, we identify and address limitations in the existing state of the art, particularly in distributed control barrier functions. Our modifications result in a controller that converges to the centralized optimal solution. Lastly, we present an observer methodology as a novel contribution, allowing cooperative localization of a multi-robot system in a common frame using body-frame relative measurements

Scale modeling has been commonly used for architectural acoustics but use in other noise control areas is nominal. Acoustic scale modeling theory is first reviewed and then feasibility for small-scale applications, such as is common in the electronics industry, is investigated. Three application cases are used to examine the viability. In the first example, a scale model is used to determine the insertion loss of a rectangular barrier. In the second example, the transmission loss through parallel tubes drilled through a cylinder is measured and results are compared to a 2.85 times scale model with good agreement. The third example is a rectangular cuboid with a smaller cylindrical well bored into it. A point source is placed above the cuboid. The transfer function was measured between positions on the top of the cylinder and inside of the cylindrical well. Treatments were then applied sequentially including a cylindrical barrier around the well, a membrane cover over the opening, and a layer of sound absorption over the well. Results are compared between the full scale and a 5.7 times scale model and correlation between the two is satisfactory.

Este trabalho propõe um novo modelo e uma nova abordagem para resolução do problema de fluxo de potência ótimo reativo com variáveis de controle discretas e restrições de atuação de dispositivos de controle de tensão. Matematicamente, esse problema é formulado como um problema de programação não linear com variáveis contínuas e discretas e restrições de complementaridade, cuja abordagem para resolução proposta neste trabalho se baseia na resolução de uma sequência de problemas modificados pelo algoritmo da função Lagrangiana barreira modificada-penalidade-discreto. Nessa abordagem, o problema original é modificado da seguinte forma: 1) as variáveis discretas são tratadas como contínuas por funções senoidais incorporadas na função objetivo do problema original; 2) as restrições de complementaridade são transformadas em restrições de desigualdade equivalentes; e 3) as restrições de desigualdade são transformadas em restrições de igualdade a partir do acréscimo de variáveis de folga não negativas. Para resolver o problema modificado, a condição de não negatividade das variáveis de folga é tratada por uma função barreira modificada com extrapolação quadrática. O problema modificado é transformado em um problema Lagrangiano, cuja solução é determinada a partir da aplicação das condições necessárias de otimalidade. No algoritmo da função Lagrangiana barreira modificada-penalidade-discreto, uma sequência de problemas modificados é resolvida até que todas as variáveis do problema modificado associadas às variáveis discretas do problema original assumam valores discretos. Para demonstrar a eficácia do modelo proposto e a robustez dessa abordagem para resolução de problemas de fluxo de potência ótimo reativo, foram realizados testes com os sistemas elétricos IEEE de 14, 30, 57 e 118 barras e com o sistema equivalente CESP 440 kV de 53 barras. Os resultados mostram que a abordagem para resolução de problemas de programação não linear proposta é eficaz no tratamento de variáveis discretas e restrições de complementaridade.
This work proposes a novel model and a new approach for solving the reactive optimal power flow problem with discrete control variables and voltage-control actuation constraints. Mathematically, such problem is formulated as a nonlinear programming problem with continuous and discrete variables and complementarity constraints, whose proposed resolution approach is based on solving a sequence of modified problems by the discrete penalty-modified barrier Lagrangian function algorithm. In this approach, the original problem is modified in the following way: 1) the discrete variables are treated as continuous by sinusoidal functions incorporated into the objective function of the original problem; 2) the complementarity constraints are transformed into equivalent inequality constraints; and 3) the inequality constraints are transformed into equality constraints by the addition of non-negative slack variables. To solve the modified problem, the non-negativity condition of the slack variables is treated by a modified barrier function with quadratic extrapolation. The modified problem is transformed into a Lagrangian problem, whose solution is determined by the application of the first-order necessary optimality conditions. In the discrete penalty- modified barrier Lagrangian function algorithm, a sequence of modified problems is successively solved until all the variables of the modified problem that are associated with the discrete variables of the original problem assume discrete values. The efectiveness of the proposed model and the robustness of this approach for solving reactive optimal power flow problems were verified with the IEEE 14, 30, 57 and 118-bus test systems and the 440 kV CESP 53-bus equivalent system. The results show that the proposed approach for solving nonlinear programming problems successfully handles discrete variables and complementarity constraints.

Cette thèse porte sur la commande des systèmes non linéaires soumis à des contraintes non différentiables ou non convexes. L'objectif est de pouvoir réaliser une commande permettant de considérer tout type de contraintes évaluables en temps réel.Pour répondre à cet objectif, la commande prédictive a été utilisée en ajoutant des fonctions barrières à la fonction de coût. Un algorithme d'optimisation sans gradient a permis de résoudre ce problème d'optimisation. De plus, une formulation permettant de garantir la stabilité et la robustesse vis-à-vis de perturbations a été proposée dans le cadre des systèmes linéaires. La démonstration de la stabilité repose sur les ensembles invariants et la théorie de Lyapunov.Dans le cas des systèmes non linéaires, les réseaux de neurones dynamiques ont été utilisés comme modèle de prédiction pour la commande prédictive. L'apprentissage de ces réseaux ainsi que les observateurs non linéaires nécessaires à leur utilisation ont été étudiés. Enfin, notre étude s'est portée sur l'amélioration de la prédiction par réseaux de neurones en présence de perturbations.La méthode de synthèse de correcteurs présentée dans ces travaux a été appliquée à l’évitement d’obstacles par un véhicule autonome
This PhD thesis deals with the control of nonlinear systems subject to nondifferentiable or nonconvex constraints. The objective is to design a control law considering any type of constraints that can be online evaluated.To achieve this goal, model predictive control has been used in addition to barrier functions included in the cost function. A gradient-free optimization algorithm has been used to solve this optimization problem. Besides, a cost function formulation has been proposed to ensure stability and robustness against disturbances for linear systems. The proof of stability is based on invariant sets and the Lyapunov theory.In the case of nonlinear systems, dynamic neural networks have been used as a predictor for model predictive control. Machine learning algorithms and the nonlinear observers required for the use of neural networks have been studied. Finally, our study has focused on improving neural network prediction in the presence of disturbances.The synthesis method presented in this work has been applied to obstacle avoidance by an autonomous vehicle

Constraints in input, output, and states are evident in most of the practical systems. Explicitly incorporating these constraints into the control design process leads to its superior performance in general. Therefore, considering different types of constraints, several robust constrained adaptive nonlinear control designs are proposed in this thesis for different classes of uncertain nonlinear. In the first part of this thesis, a barrier Lyapunov function (BLF) based state constrained adaptive control design is presented for two different classes of uncertain nonlinear systems, known as nonlinear systems with relative degree one and Euler-Lagrange systems. In adaptive control synthesis, a neural network-based approximated system dynamics is constructed to approximate the model uncertainties of the system, and then a tracking controller is designed to achieve the desired tracking response. The weights of the neural network are updated using a Lyapunov stable weight update rule. It is shown that the closed-loop states of the system both remain bounded within the imposed constraints as well as asymptotically converge to a predefined domain. In the second part of this thesis, error transformation based state-constrained adaptive control design is proposed for generic second-order nonlinear systems with state and input constraints, model uncertainties, and external disturbances. A new error transformation is proposed to enforce state constraints; Nussbaum gain is used to impose desired input constraints, and radial basis function neural networks (RBFNNs) are utilized to approximate modeling uncertainties. In this control design philosophy, first, imposed constraints are converted into error constraints and then, using the proposed error transformation, the constrained system is transformed into equivalent unconstrained system. Next, a stable adaptive controller is designed for the unconstrained system, which indirectly establishes the stability of the constrained system without violation of imposed constraints. The closed-loop stability of the system is proven using the Lyapunov stability theory. In the third part of this thesis, an adaptive controller is derived for a feedback linearizable MIMO nonlinear system subjected to time-varying output constraints, input constraints, unknown control directions, modeling uncertainties, and external disturbances. In the control design, another novel error transformation is used to enforce time-varying output constraints, and Nussbaum gain is used to handle input constraints and unknown control directions. One of the features of the proposed adaptive controller is that only a single variable is required to approximate the uncertainties of the whole system, consequently minimizing the computational requirement. Another feature of the proposed controller is that zero error tracking is achieved in presence of unstructured uncertainties and external disturbances. The aforementioned control designs are scalable and can be reduced into output-constrained control and unconstrained control by changing the nature of error dependent controller gain matrices. Controllers can also be used to constrain the closed-loop error of the system directly, thereby minimizing error transients. Furthermore, proposed controllers give flexibility to impose independent constraints on the desired component of the system states and lead to easy on-board implementable closed-form control solutions. A two-link robot manipulator problem and other benchmark problems are used to demonstrate the effectiveness of the proposed control designs by performing extensive simulation results. In the last part of this thesis, a real-life application problem is selected, where the objective is to effectively control a hypersonic flight vehicle during its cruise. The problem is quite challenging as it demands narrow bounds on both input and state in the presence of large modeling uncertainties. The control objective is achieved by using the proposed BLF based constrained adaptive controller. A three-loop architecture is proposed to synthesis this adaptive flight controller, which ensures that the vehicle velocity, attitude and angular body rates remain bounded within the prescribed bounds. The proposed adaptive control leads to quick learning of the unknown function in the system dynamics with much lesser transients. It also ensures that the imposed state constraints are not violated at any point of time. Effectiveness of the control design is illustrated by carrying out a large number of Monte-Carlo like randomized high fidelity six-degree-of-freedom (Six-DOF) simulation studies for a winged-cone hypersonic vehicle. The Six-DOF model was constructed by collecting the necessary aerodynamic and inertial data of the vehicle found scattered in various literature and integrating those into the air-frame equations of motion. Simulation results show that the proposed controller is quite robust to effectively control the vehicle in the presence of significant modeling uncertainties.

In this thesis we modified a sampling-based motion planning algorithm to improve sampling efficiency. First, we modify the RRT* motion planning algorithm with a local motion planner that guarantees collision-free state trajectories without explicitly checking for collision with obstacles. The control trajectories are generated by solving a sequence of quadratic programs with Control Barrier Functions (CBF) constraints. If the control trajectories satisfy the CBF constraints, the state trajectories are guaranteed to stay in the free subset of the state space. Second, we use a stochastic optimization algorithm to adapt the sampling density function of RRT* to increase the probability of sampling in promising regions in the configuration space. In our approach, we use the nonparametric generalized cross-entropy (GCE) method is used for importance sampling, where a subset of the sampled RRT* trajectories is incrementally exploited to adapt the density function. The modified algorithms, the Adaptive CBF-RRT* and the CBF-RRT*, are demonstrated with numerical examples using the unicycle dynamics. The Adaptive CBF-RRT* has been shown to yield paths with lower cost with fewer tree vertexes than the CBF-RRT*.
2022-03-27T00:00:00Z

Finding safe trajectories for multiagent autonomous systems can be difficult, especially as multiple robots and obstacles are added to the system. Control barrier functions (CBFs) have been effective in addressing this problem. Although the use of CBFs for guaranteeing safe operation is well established, there is no standard software implementation to simplify the integration of these techniques into robotic systems. We present a CBF Toolbox to fill this void. Although the CBF Toolbox can be used to ensure safety based on local control decisions, it may not be sufficient to guide a robots to their goals in certain environments. In these cases, path planning algorithms are required. We present one such algorithm, which is the multiagent extension of the CBF guided rapidly-exploring random trees (CBF-RRT) to demonstrate how the CBF Toolbox can be applied. This work addresses the theory behind the CBF Toolbox, as well as presenting examples of how it is applied to multiagent systems. Examples are shown for its use in both simulation and hardware experiments. Details are provided on CBF guided rapidly-exploring random trees (CBF-RRT), and its application to multiagent systems with multiagent CBF-RRT (MA-CBF-RRT) that streamlines safe path planning for teams of robots.