Signal Temporal Logic (STL) offers an expressive formalism for describing complex high-level tasks in dynamical systems. This paper introduces a time-varying Control Barrier Function (CBF) for control-affine nonlinear stochastic systems to fulfill STL specifications. The CBFs are used in a robust optimization problem to provide a lower bound on the satisfaction probability of a given STL specification with a predetermined robustness level. We present an online control synthesis approach to minimize a performance function while having the required satisfaction guarantee. We finally provide a tractable solution to the robust optimization for STL with linear and quadratic predicate functions. To illustrate the effectiveness of the method, we apply it to a simple linear case study and to the path-planning problem for a nonlinear wheeled mobile robot.

Nowadays autonomous systems are expected to perform complex tasks that go beyond traditional control objectives such as setpoint tracking or consensus of multi-agent systems. More specifically, in a plethora of applications agents often need to collaborate with their peers in order to perform a variety of spatial tasks within strict deadlines. Spatio-temporal tasks of this form can be easily expressed in Signal Temporal Logic (STL), a predicate language that allow us to formally introduce time-constrained tasks defined as Boolean combinations of simpler subformulas involving temporal operators such as the always, eventually and until operator.

In this thesis we consider the problem of control under high-level specifications for single as well as multi-agent systems. Our work is divided in three parts. In the first part we consider spatio-temporal objectives expressed in Signal Temporal Logic and propose feedback control laws guaranteeing the satisfaction of the tasks under consideration using various levels of state information. First, motivated by multi-platoon coordination scenarios we design a nonlinear feedback control law ensuring minimal violation of a STL task involving merging and splitting of given pairs of platoons when the satisfaction of the task can not be achieved due to actuation limitations. Next, we propose a novel control barrier function to encode the satisfaction of a STL fragment involving disjunctions of selected STL tasks. As a further contribution, we propose a distributed switching feedback control law for the satisfaction of a given set of relative position-based STL tasks that is based on the prescribed performance control philosophy.

In the second part model predictive control schemes are designed for single and multi-agent systems subject to STL, input and state constraints. Contrary to state of the art, the proposed approaches encode the satisfaction of the STL tasks under consideration using continuous variables. In addition, the proposed MPC schemes are shown to be recursively feasible thanks to appropriately designed terminal ingredients while the planning horizon of the related  problems can be chosen arbitrarily small and independent of the STL task. To deal with collaborative tasks often present in multi-agent setups we present a novel approach to decompose the tasks into agent-dependent objectives allowing the design of non-cooperative control schemes that guarantee the satisfaction of the initial task with limited communication. Finally, a sequential distributed MPC scheme is proposed for coupled STL tasks offering a desired trade-off between the systems' performance and the computational complexity of previously proposed centralized approaches. The proposed scheme is solved in discrete-time yet continuous-time constraint satisfaction is ensured thanks to an appropriate tightening of the constraint sets.

Finally, in part III we consider time-invariant objectives such as safety, formation and tracking of single and multiple agents, respectively, and propose a set of feedback control laws ensuring the satisfaction of the desired objectives at all times.

Moderna autonoma system förväntas utföra komplexa uppgifter bortom traditionella reglermål såsom referensspårning och konsensus hos fler-agent-system. Många applikationer kräver att agenter samarbetar med sina kamrater för att utföra olika rumsliga uppgifter inom strikta deadlines. Spatio-temporal uppgifter av denna form kan enkelt uttryckas i Signal Temporal Logic (STL), ett predikatspråk som tillåter oss att formellt introducera tidsbegränsade uppgifter i form av booleska kombinationer av enklare underformler, vilka involverar temporala operatorer såsom alltid-, så småningom- och till dess att-operatorer.

I den här avhandlingen behandlar vi styrning under högnivå-specifikationer av system med både enstaka och flera agenter. Vårt arbete är uppdelat i tre delar. I den första delen behandlar vi spatio-temporal mål uttryckta i Signal Temporal Logic och föreslår återkopplingsreglering som garanterar att de givna målen uppnås, med hjälp av olika nivåer av tillståndsinformation. I den andra delen utformar vi modell-prediktiva reglersystem för system med enstaka och flera agenter och STL-, inmatnings- och tillståndsbegränsningar. Slutligen behandlar vi i den sista delen tidsinvarianta mål såsom säkerhet, formation och spårning av enstaka respektive flera agenter, och föreslår en uppsättning återkopplingskontrolllagar som säkerställer att de önskade målen uppnås hela tiden.

In this letter a distributed model predictive control scheme (dMPC) is proposed for a multi-agent team that is subject to a set of time-constrained spatial tasks encoded in Signal Temporal Logic (STL). Here, the agents are subject to both individual and collaborative STL tasks. In order to ensure the satisfaction of the collaborative tasks while avoiding the computational burden of a centralized problem, we propose a sequential dMPC scheme and show the recursive feasibility property of the framework given appropriately designed terminal ingredients. The resulting MPC problems are solved in discrete-time yet continuous-time satisfaction of the STL tasks is ensured with appropriate tightening of the constraint sets.

In this work we consider the problem of control under Signal Temporal Logic specifications (STL) that depend on relative position information among neighboring agents. In particular, we consider STL tasks for given pairs of agents whose satisfaction is translated into a set of setpoint output tracking problems with transient and steady-state constraints. Contrary to existing work the proposed framework does not require initial satisfaction of the funnel constraints but can ensure their satisfaction within a pre-specified finite time. Given a tree topology in which agents sharing a STL task form an edge, we show that the resulting control laws ensure the satisfaction of the STL task as well as boundedness of all closed loop signals using only local information.

In this work we consider the problem of control under Signal Temporal Logic specifications (STL) that depend on relative position information among neighboring agents. In particular, we consider STL tasks for given pairs of agents whose satisfaction is translated into a set of setpoint output tracking problems with transient and steady-state constraints. Contrary to existing work the proposed framework does not require initial satisfaction of the funnel constraints but can ensure their satisfaction within a pre-specified finite time. Given a tree topology in which agents sharing a STL task form an edge, we show that the resulting control laws ensure the satisfaction of the STL task as well as boundedness of all closed loop signals using only local information.

In this work we pursue the problem of distributed distance-based formation control with prescribed transient and steady state behavior under connectivity and collision avoidance constraints. In addition to the distance-based formation a subset of agents is enforced to reach a desired distance from a dynamic virtual leader with bounded velocity under prescribed transient and steady state constraints while preserving connectivity with the virtual leader and a desired safety distance. We show that the aforementioned objectives can be ensured when the communication graph is an undirected tree and a single agent has access to the virtual leader's state information. Under these conditions we propose a model-free control law for known nonlinear systems as also an adaptive controller when the nonlinear dynamics of the agents are considered unknown and approximated using neural networks. Simulation results verify the effectiveness of the proposed controller both for known and unknown dynamics.

In this work we consider the control problem of systems that are subject to disjunctions of Signal Temporal Logic (STL) tasks. Motivated by existing approaches encoding the STL tasks utilizing time-varying control barrier functions (CBFs), we propose a continuously differentiable function for encoding the STL constraints that is defined as the composition of a smooth approximator of the max operator and a set of functions ensuring the satisfaction of the corresponding STL tasks with a desired robustness, and derive conditions for the choice of the class K function (when the latter is considered to be linear) to ensure that the proposed function is a CBF. Then, a control law ensuring the satisfaction of the STL task is found as a solution to a computationally efficient QP.

Signal Temporal Logic (STL) has been found an expressive language for describing complex, time-constrained tasks in several robotic applications. Existing methods encode such specifications by either using integer constraints or by employing set invariance techniques. While in the first case this results in MILP control problems, in the latter case designer-specific choices may induce conservatism in the robot's performance and the satisfaction of the task. In this paper a continuous-time receding horizon control scheme (RHS) is proposed that exploits the trade-off between task satisfaction and performance costs such as actuation and state costs, traditionally considered in RHS schemes. The satisfaction of the STL tasks is encoded using time-varying control barrier functions (CBFs) that are designed online, thus avoiding the integer expressions that are often used in literature. The recursive feasibility of the proposed scheme is guaranteed by the satisfaction of a time-varying terminal constraint that ensures the satisfaction of the task with pre-determined robustness. The effectiveness of the method is illustrated in a multi-robot simulation scenario.

Multiple robots are increasingly being considered in a variety of tasks requiring continuous surveillance of a dynamic area, examples of which are environmental monitoring, and search and rescue missions. Motivated by these applications, in this paper we consider the multi-robot persistent coverage control problem over a grid environment. The goal is to ensure a desired lower bound on the coverage level of each cell in the grid, that is decreasing at a given rate for unoccupied cells. We consider a finite set of candidate poses for the agents and introduce a directed graph with nodes representing their admissible poses. We formulate a persistent coverage control problem as a MILP problem that aims to maximize the coverage level of the cells over a finite horizon. To solve the problem, we design a receding horizon scheme (RHS) and prove its recursive feasibility property by introducing a set of time-varying terminal constraints to the problem. These terminal constraints ensure that the agents are always able to terminate their plans in pre-determined closed trajectories. A two-step method is proposed for the construction of the closed trajectories, guaranteeing the satisfaction of the coverage level lower bound constraint, when the resulting closed trajectories are followed repeatedly. Due to the special structure of the problem, agents are able to visit every cell in the grid repeatedly within a worst-case visitation period. Finally, we provide a computational time analysis of the problem for different simulated scenarios and demonstrate the performance of the RHS problem by an illustrative example.

Control barrier functions (CBFs) have been recently considered for ensuring safety of nonlinear input-affine systems by means of appropriately designed controllers rendering a desired superlevel set of the CBF function forward invariant. In this work, we consider the safety control problem for nonlinear input-affine systems with multiple time-varying input delays. In order to ensure safety, we first design a set of predictors that estimate the state of the system at different future times by utilizing the control laws designed to ensure safety of the delay-free system. Under the assumption of perfect estimation of the future states, we show that under the designed controller, the closed-loop performance of the systems with and without the input delays is the same by the time the input with the largest delay acts on the system with delays for the first time.