We study the problem of controlling multi-agent systems under a set of signal temporal logic tasks. Signal temporal logic is a formalism that is used to express time and space constraints for dynamical systems. Recent methods to solve the control synthesis problem for single-agent systems under signal temporal logic tasks are, however, subject to a high computational complexity. Methods for multi-agent systems scale at least linearly with the number of agents and induce even higher computational burdens. We propose a computationally-efficient control strategy to solve the multi-agent control synthesis problem that results in a robust satisfaction of a set of signal temporal logic tasks. In particular, a decentralized feedback control law is proposed that is based on time-varying control barrier functions. The obtained control law is discontinuous and formal guarantees are provided by nonsmooth analysis. Simulations show the efficacy of the presented method.
We develop a novel decentralized control method for a network of perturbed linear systems with dynamical couplings subject to Signal Temporal Logic (STL) specifications. We first transform the STL requirements into set containment problems and then we develop controllers to solve these problems. Our approach is based on treating the couplings between subsystems as disturbances, which are bounded sets that the subsystems negotiate in the form of parametric assume-guarantee contracts. The set containment requirements and parameterized contracts are added to the subsystems' constraints. We introd…
The cooperative control of the connected and automated vehicle (CAV) is recognized as an effective approach to alleviate traffic congestion and improve traffic safety, especially for on-ramp bottlenecks. However, in the mixed traffic, the uncertainty of human-driven vehicles (HDVs) makes the on-ramp merging control for CAVs more challenging. This paper proposes a decentralized optimal control method to address the merging control problem of CAVs at highway on-ramps in the mixed traffic. We first formulate the optimal merging control problem, which includes the constraints of safety and vehicle…
Capability-Aware Heterogeneous Control Barrier Functions for Decentralized Multi-Robot Safe Navigation
Department of Computer Science and Engineering, Texas A&M University（德克萨斯A&M大学计算机科学与工程系）；Department of Computer Science, University of Illinois Chicago（伊利诺伊大学芝加哥分校计算机科学系）
Massachusetts Institute of Technology（麻省理工学院）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；California Institute of Technology（加州理工学院）
We study the multi-agent safe control problem where agents should avoid collisions to static obstacles and collisions with each other while reaching their goals. Our core idea is to learn the multi-agent control policy jointly with learning the control barrier functions as safety certificates. We propose a novel joint-learning framework that can be implemented in a decentralized fashion, with generalization guarantees for certain function classes. Such a decentralized framework can adapt to an arbitrarily large number of agents. Building upon this framework, we further improve the scalability …
We propose control barrier functions (CBFs) for a family of dynamical systems to satisfy a broad fragment of Signal Temporal Logic (STL) specifications, which may include subtasks with nested temporal operators or conflicting requirements (e.g., achieving multiple subtasks within the same time interval). The proposed CBFs take into account the actuation limits of the dynamical system as well as a feasible sequence of subtasks, and they define time-varying feasible sets of states the system must always stay inside. We show some theoretical results on the correctness of the proposed method. We i…
We present a compositional control synthesis method based on assume-guarantee contracts with application to correct-by-construction design of vehicular mission plans. In our approach, a mission-level specification expressed in a fragment of signal temporal logic (STL) is decomposed into predicates defined on non-overlapping time intervals. The STL predicates are then mapped to an aggregation of contracts associated with continuously differentiable time-varying control barrier functions. The barrier functions are used to constrain the lower-level control synthesis problem, which is solved via q…
Temporal logic has been widely used to express complex task specifications for cyber-physical systems (CPSs). One way to synthesize a controller for CPS under temporal logic constraints is to first abstract the CPS as a discrete transition system, and then apply formal methods. This approach, however, is computationally demanding and its scalability suffers due to the curse of dimensionality. In this paper, we propose a control barrier function (CBF) approach to abstraction-free control synthesis under a linear temporal logic (LTL) constraint. We first construct the deterministic Rabin automat…
For a class of spatio-temporal tasks defined by a fragment of Signal Temporal Logic (STL), we construct a nonsmooth time-varying control barrier function (CBF) and develop a controller based on a set of simple optimization problems. Each of the optimization problems invokes constraints that allow to exploit the piece-wise smoothness of the CBF for optimization additionally to the common gradient constraint in the context of CBFs. In this way, the conservativeness of the control approach is reduced in those points where the CBF is nonsmooth. Thereby, nonsmooth CBFs become applicable to time-var…
A successful defensive strategy in ice hockey games is often designed empirically by an experienced professional. The majority of previous work on automating the strategy focuses on analyzing spatial data to decide the most optimal formation and action but cannot generalize the system to real games with real-time capabilities. We propose a novel control logic for generating real-time ice hockey defensive motion based on a control barrier function (CBF) and coverage control to extend our antecessors' logic that succeeds in duplicating ideal formations for specific scenes. To this end, we first …
In this work we formulate the satisfaction of a (syntactically co-safe) linear temporal logic specification on a physical plant through a recent hybrid dynamical systems formalism. In order to solve this problem, we introduce an extension to such a hybrid system framework of the so-called eventuality property, which matches suitably the condition for the satisfaction of such a temporal logic specification. The eventuality property can be established through barrier certificates, which we derive for the considered hybrid system framework. Using a hybrid barrier certificate, we propose a solutio…
Patching Control Lyapunov Barrier Functions for Temporal Logic Specifications with Bounded Controls
Massachusetts Institute of Technology（麻省理工学院）；University of Waterloo（滑铁卢大学）；MacLean Engineering & Marketing Co. Limited（麦克林工程与营销有限公司）；Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
We consider the problem of guaranteeing that the transient voltages and currents stay within prescribed bounds in Direct Current (DC) microgrids, when the controller does not have access to accurate system dynamics due to the load being unknown and/or time-varying. To achieve this, we propose an optimization based controller design using control barrier functions. We show that the proposed controller has a decentralized structure and is robust with respect to the uncertainty in the precise values of the system parameters, such as the load.
Recent work has shown that stabilizing an affine control system to a desired state while optimizing a quadratic cost subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In our own recent work, we defined High Order CBFs (HOCBFs) for systems and constraints with arbitrary relative degrees. In this paper, in order to accommodate initial states that do not satisfy the state constraints and constraints with arbitrary relative degree, we generalize HOCBFs to High Order Cont…
We develop a probabilistic control algorithm, $\texttt{GTLProCo}$, for swarms of agents with heterogeneous dynamics and objectives, subject to high-level task specifications. The resulting algorithm not only achieves decentralized control of the swarm but also significantly improves scalability over state-of-the-art existing algorithms. Specifically, we study a setting in which the agents move along the nodes of a graph, and the high-level task specifications for the swarm are expressed in a recently-proposed language called graph temporal logic (GTL). By constraining the distribution of the s…
Motivated by the recent interest in cyber-physical and autonomous robotic systems, we study the problem of dynamically coupled multi-agent systems under a set of signal temporal logic tasks. In particular, the satisfaction of each of these signal temporal logic tasks depends on the behavior of a distinct set of agents. Instead of abstracting the agent dynamics and the temporal logic tasks into a discrete domain and solving the problem therein or using optimization-based methods, we derive collaborative feedback control laws. These control laws are based on a decentralized control barrier funct…
The paper considers the problem of controlling Connected and Automated Vehicles (CAVs) traveling through a three-entry roundabout so as to jointly minimize both the travel time and the energy consumption while providing speed-dependent safety guarantees, as well as satisfying velocity and acceleration constraints. We first design a systematic approach to dynamically determine the safety constraints and derive the unconstrained optimal control solution. A joint optimal control and barrier function (OCBF) method is then applied to efficiently obtain a controller that optimally track the unconstr…
Robust Decentralized Abstractions for Multiple Mobile Manipulators
ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology（林奈 ACCESS 中心，电气工程学院，KTH 皇家理工学院）；KTH Center for Autonomous Systems（KTH 自主系统中心）
This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discrete-time dynamics. The temporal logic specification is given in safe-LTL_F, a fragment of linear temporal logic over traces of finite length. The interaction of the CPS with the adversary is modeled as a two-player zero-sum discrete-time dynamic stochastic game with the CPS as defender. We formulate a dynamic programming based approach to determine a stationary defender policy that maximized the p…
Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNet
Amazon Robotics（亚马逊机器人）；Department of Mechanical Engineering（机械工程系）；Worcester Polytechnic Institute（沃斯堡技术学院）；Department of Electrical and Computer Engineering and the Department of Computer Science（电气与计算机工程系和计算机科学系）
We discuss an online decentralized decision making problem where the agents are coupled with affine inequality constraints. Alternating Direction Method of Multipliers (ADMM) is used as the computation engine and we discuss the convergence of the algorithm in an online setting. To be specific, when decisions have to be made sequentially with a fixed time step, there might not be enough time for the ADMM to converge before the scenario changes and the decision needs to be updated. In this case, a suboptimal solution is employed and we analyze the optimality gap given the convergence condition. …
We address the problem of optimally controlling Connected and Automated Vehicles (CAVs) arriving from two multi-lane roads and merging at multiple points where the objective is to jointly minimize the travel time and energy consumption of each CAV subject to speed-dependent safety constraints, as well as speed and acceleration constraints. This problem was solved in prior work for two single-lane roads. A direct extension to multi-lane roads is limited by the computational complexity required to obtain an explicit optimal control solution. Instead, we propose a general framework that converts …
This paper is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of control sub-barrier certificates of subsystems, enabling one to construct control barrier certificates of interconnected systems by employing some max-type small-gain conditions. The main goal is to synthesize hybrid controllers enforcing com…
The paper presents a methodology for temporal logic verification of continuous-time switched stochastic systems. Our goal is to find the lower bound on the probability that a complex temporal property is satisfied over a finite time horizon. The required temporal properties of the system are expressed using a fragment of linear temporal logic, called safe-LTL with respect to finite traces. Our approach combines automata-based verification and the use of barrier certificates. It relies on decomposing the automaton associated with the negation of specification into a sequence of simpler reachabi…
This paper presents control strategies based on time-varying convergent higher order control barrier functions for a class of leader-follower multi-agent systems under signal temporal logic (STL) tasks. Each agent is assigned a local STL task which may be dependent on the behavior of agents involved in other tasks. The leader has knowledge on the associated tasks and controls the performance of the subgroup involved agents. Robust solutions for the task satisfaction, based on the leader's accessibility to the follower agents' states are suggested. Our approach finds solutions to guarantee the …
We investigate a multi-agent planning problem, where each agent aims to achieve an individual task while avoiding collisions with others. We assume that each agent's task is expressed as a Time-Window Temporal Logic (TWTL) specification defined over a 3D environment. We propose a decentralized receding horizon algorithm for online planning of trajectories. We show that when the environment is sufficiently connected, the resulting agent trajectories are always safe (collision-free) and lead to the satisfaction of the TWTL specifications or their finite temporal relaxations. Accordingly, deadloc…
In this paper, we study formal synthesis of control policies for partially observed jump-diffusion systems against complex logic specifications. Given a state estimator, we utilize a discretization-free approach for formal synthesis of control policies by using a notation of control barrier functions without requiring any knowledge of the estimation accuracy. Our goal is to synthesize an offline control policy providing (potentially maximizing) a lower bound on the probability that the trajectories of the partially observed jump-diffusion system satisfy some complex specifications expressed by…
We address the problem of optimally controlling Connected and Automated Vehicles (CAVs) arriving from four multi-lane roads at an intersection where they conflict in terms of safely crossing (including turns) with no collision. The objective is to jointly minimize the travel time and energy consumption of each CAV while ensuring safety. This problem was solved in prior work for single-lane roads. A direct extension to multiple lanes on each road is limited by the computational complexity required to obtain an explicit optimal control solution. Instead, we propose a general framework that first…
Cooperative Decentralized Multi-agent Control under Local LTL Tasks and Connectivity Constraints
ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology（ACCESS林奈中心，电气工程学院，皇家理工学院）；KTH Centre for Autonomous Systems（KTH自主系统中心）
Decentralized Abstractions and Timed Constrained Planning of a General Class of Coupled Multi-Agent Systems
ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology（瑞典皇家理工学院电气工程学院 ACCESS 林奈中心）；KTH Center for Autonomous Systems（KTH 自主系统中心）；Control Systems Lab, Department of Mechanical Engineering, National Technical University of Athens（雅典国立技术大学机械工程系控制系统实验室）
This paper presents a control strategy based on a new notion of time-varying fixed-time convergent control barrier functions (TFCBFs) for a class of coupled multi-agent systems under signal temporal logic (STL) tasks. In this framework, each agent is assigned a local STL task regradless of the tasks of other agents. Each task may be dependent on the behavior of other agents which may cause conflicts on the satisfaction of all tasks. Our approach finds a robust solution to guarantee the fixed-time satisfaction of STL tasks in a least violating way and independent of the agents' initial conditio…
