Dimos V. Dimarogonas

Panagiotis Rousseas, Dimos V. Dimarogonas

Signal Temporal Logic (STL), has recently seen extensive development, owing to its rich expressivenes for autonomous planning and control. Nevertheless, existing verification and control synthesis methods are limited with respect to the complexity and degree of nesting of the formulae. In this work, we propose a novel approach to STL based on an operator acting on reachability value functions. This constitutes a new theoretical framework for handling complex multi-nested formulae while at the same time providing tools for on-line control synthesis. In contrast to focusing on the design of STL-based reachability (or control barrier) functions, we develop operator-based nesting rules directly. Our method's expressiveness is demonstrated both theoretically, where necessary and sufficient conditions for STL formula satisfaction are extracted, as well as in simulations with complex fragments.

Martin Andreasson, Dimos V. Dimarogonas, Henrik Sandberg et al.

This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain, and a sum of nonlinear interaction functions. By using integral Lyapunov functions, we prove the stability of the proposed control protocols, and explicitly characterize the equilibrium set. We also propose a distributed proportional-integral (PI) controller for networked dynamical systems. The PI controllers successfully attenuate constant disturbances in the network. We prove that agents with single-integrator dynamics are stable for any integral gain, and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double-integrator dynamics. Throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites, power systems and building temperature control.

Sebastian van de Hoef, Karl H. Johansson, Dimos V. Dimarogonas

The problem of how to coordinate a large fleet of trucks with given itinerary to enable fuel-efficient platooning is considered. Platooning is a promising technology that enables trucks to save significant amounts of fuel by driving close together and thus reducing air drag. A setting is considered in which each truck in a fleet is provided with a start location, a destination, a departure time, and an arrival deadline from a higher planning level. Fuel-efficient plans should be computed. The plans consist of routes and speed profiles that allow trucks to arrive by their arrival deadlines. Hereby, trucks can meet on common parts of their routes and form platoons, resulting in decreased fuel consumption. We formulate a combinatorial optimization problem that combines plans involving only two vehicles. We show that this problem is hard to solve for large problem instances. Hence a heuristic algorithm is proposed. The resulting plans are further optimized using convex optimization techniques. The method is evaluated with Monte Carlo simulations in a realistic setting. We demonstrate that the proposed algorithm can compute plans for thousands of trucks and that significant fuel savings can be achieved.

Eleftherios E. Vlahakis, Arash Bahari Kordabad, Lars Lindemann et al.

Multi-agent planning under Signal Temporal Logic (STL) is often hindered by collaborative tasks that lead to computational challenges due to the inherent high dimensionality of the problem, preventing scalable synthesis with satisfaction guarantees. To address this, we formulate STL planning as an optimization program under multi-agent STL constraints and introduce a penalty-based unconstrained relaxation that can be efficiently solved via a Block-Coordinate Gradient Descent (BCGD) method, where each block corresponds to a single agent's decision variables, thereby mitigating complexity. By utilizing a quadratic penalty function defined via smooth STL semantics, we show that BCGD iterations converge to a stationary point of the penalized problem under standard regularity assumptions. To enforce feasibility, the BCGD solver is embedded within a two-layer optimization scheme: inner BCGD updates are performed for a fixed penalty parameter, which is then increased in an outer loop to progressively improve multi-agent STL robustness. The proposed framework enables scalable computations and is validated through various complex multi-robot planning scenarios.

Jana Tumova, Dimos V. Dimarogonas

We study the problem of plan synthesis for multi-agent systems, to achieve complex, high-level, long-term goals that are assigned to each agent individually. As the agents might not be capable of satisfying their respective goals by themselves, requests for other agents' collaborations are a part of the task descriptions. We consider that each agent is modeled as a discrete state-transition system and its task specification takes a form of a linear temporal logic formula, which may contain requirements and constraints on the other agent's behavior. A traditional automata-based approach to multi-agent plan synthesis from such specifications builds on centralized team planning and full team synchronization after each agents' discrete step, and thus suffers from extreme computational demands. We aim at reducing the computational complexity by decomposing the plan synthesis problem into finite horizon planning problems that are solved iteratively, upon the run of the agents. As opposed to full synchronization, we introduce an event-based synchronization that allows our approach to efficiently adapt to different time durations of different agents' discrete steps. We discuss the correctness of the solution and find assumptions, under which the proposed iterative algorithm leads to provable eventual satisfaction of the desired specifications.

Xinlei Yi, Jieqiang Wei, Dimos V. Dimarogonas et al.

In this paper, event-triggered controllers and corresponding algorithms are proposed to establish the formation with connectivity preservation for multi-agent systems. Each agent needs to update its control input and to broadcast this control input together with the relative state information to its neighbors at its own triggering times, and to receive information at its neighbors' triggering times. Two types of system dynamics, single integrators and double integrators, are considered. As a result, all agents converge to the formation exponentially with connectivity preservation, and Zeno behavior can be excluded. Numerical simulations show the effectiveness of the theoretical results.

Christos K. Verginis, Charalampos P. Bechlioulis, Dimos V. Dimarogonas et al.

In this paper, we study the longitudinal control problem for a platoon of vehicles with unknown nonlinear dynamics under both the predecessor-following and the bidirectional control architectures. The proposed control protocols are fully distributed in the sense that each vehicle utilizes feedback from its relative position with respect to its preceding and following vehicles as well as its own velocity, which can all be easily obtained by onboard sensors. Moreover, no previous knowledge of model nonlinearities/disturbances is incorporated in the control design, enhancing in that way the robustness of the overall closed loop system against model imperfections. Additionally, certain designer-specified performance functions determine the transient and steady-state response, thus preventing connectivity breaks due to sensor limitations as well as inter-vehicular collisions. Finally, extensive simulation studies and a real-time experiment conducted with mobile robots clarify the proposed control protocols and verify their effectiveness.

Christos K. Verginis, Alexandros Nikou, Dimos V. Dimarogonas

This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing graph is a static and undirected tree, in the special Euclidean group SE(3). The proposed control laws are decentralized, in the sense that each agent uses only local relative information from its neighbors to calculate its control signal, as well as robust with respect to modeling (parametric and structural) uncertainties and external disturbances. The proposed methodology guarantees the satisfaction of inter-agent distance constraints that resemble collision avoidance and connectivity maintenance properties. Moreover, certain predefined functions characterize the transient and steady state performance of the closed loop system. Finally, simulation results verify the validity and efficiency of the proposed approach.

Sebastian van de Hoef, Karl H. Johansson, Dimos V. Dimarogonas

The problem of maximizing the probability of two trucks being coordinated to merge into a platoon on a highway is considered. Truck platooning is a promising technology that allows heavy vehicles to save fuel by driving with small automatically controlled inter-vehicle distances. In order to leverage the full potential of platooning, platoons can be formed dynamically en route by small adjustments to their speeds. However, in heavily used parts of the road network, travel times are subject to random disturbances originating from traffic, weather and other sources. We formulate this problem as a stochastic dynamic programming problem over a finite horizon, for which solutions can be computed using a backwards recursion. By exploiting the characteristics of the problem, we derive bounds on the set of states that have to be explored at every stage, which in turn reduces the complexity of computing the solution. Simulations suggest that the approach is applicable to realistic problem instances.

Sebastian van de Hoef, Karl H. Johansson, Dimos V. Dimarogonas

Vehicle platooning facilitates the partial automation of vehicles and can significantly reduce fuel consumption. Mobile communication infrastructure makes it possible to dynamically coordinate the formation of platoons en route. We consider a centralized system that provides trucks with routes and speed profiles allowing them to dynamically form platoons during their journeys. For this to work, all possible pairs of vehicles that can platoon based on their location, destination, and other constraints have to be identified. The presented approach scales well to large vehicle fleets and realistic road networks by extracting features from the transport assignments of the vehicles and rules out a majority of possible pairs based on these features only. Merely a small number of remaining pairs are considered in depth by a complete and computationally expensive algorithm. This algorithm conclusively decides if platooning is possible for a pair based on the complete data associated with the two vehicles. We derive appropriate features for the problem and demonstrate the effectiveness of the approach in a simulation example.

Alexandros Nikou, Dimitris Boskos, Jana Tumova et al.

This paper presents a fully automated procedure for controller synthesis for multi-agent systems under coupling constraints. Each agent is modeled with dynamics consisting of two terms: the first one models the coupling constraints and the other one is an additional bounded control input. We aim to design these inputs so that each agent meets an individual high-level specification given as a Metric Interval Temporal Logic (MITL). First, a decentralized abstraction that provides a space and time discretization of the multi-agent system is designed. Second, by utilizing this abstraction and techniques from formal verification, we propose an algorithm that computes the individual runs which provably satisfy the high-level tasks. The overall approach is demonstrated in a simulation example conducted in MATLAB environment.

Alexandros Nikou, Dimos V. Dimarogonas

This paper addresses the problem of decentralized tube-based nonlinear Model Predictive Control (NMPC) for a class of uncertain nonlinear continuous-time multi-agent systems with additive and bounded disturbance. In particular, the problem of robust navigation of a multi-agent system to predefined states of the workspace while using only local information is addressed, under certain distance and control input constraints. We propose a decentralized feedback control protocol that consists of two terms: a nominal control input, which is computed online and is the outcome of a Decentralized Finite Horizon Optimal Control Problem (DFHOCP) that each agent solves at every sampling time, for its nominal system dynamics; and an additive state feedback law which is computed offline and guarantees that the real trajectories of each agent will belong to a hyper-tube centered along the nominal trajectory, for all times. The volume of the hyper-tube depends on the upper bound of the disturbances as well as the bounds of the derivatives of the dynamics. In addition, by introducing certain distance constraints, the proposed scheme guarantees that the initially connected agents remain connected for all times. Under standard assumptions that arise in nominal NMPC schemes, controllability assumptions as well as communication capabilities between the agents, we guarantee that the multi-agent system is ISS (Input to State Stable) with respect to the disturbances, for all initial conditions satisfying the state constraints. Simulation results verify the correctness of the proposed framework.

Alexandros Filotheou, Alexandros Nikou, Dimos V. Dimarogonas

This paper addresses the problem of navigation control of a general class of 2nd order uncertain nonlinear multi-agent systems in a bounded workspace, which is a subset of $R^3$ , with static obstacles. In particular, we propose a decentralized control protocol such that each agent reaches a predefined position at the workspace, while using local information based on a limited sensing radius. The proposed scheme guarantees that the initially connected agents remain always connected. In addition, by introducing certain distance constraints, we guarantee inter-agent collision avoidance as well as collision avoidance with the obstacles and the boundary of the workspace. The proposed controllers employ a class of Decentralized Nonlinear Model Predictive Controllers (DNMPC) under the presence of disturbances and uncertainties. Finally, simulation results verify the validity of the proposed framework.

Lars Lindemann, Dimos V. Dimarogonas

Motion planning classically concerns the problem of accomplishing a goal configuration while avoiding obstacles. However, the need for more sophisticated motion planning methodologies, taking temporal aspects into account, has emerged. To address this issue, temporal logics have recently been used to formulate such advanced specifications. This paper will consider Signal Temporal Logic in combination with Model Predictive Control. A robustness metric, called Discrete Average Space Robustness, is introduced and used to maximize the satisfaction of specifications which results in a natural robustness against noise. The comprised optimization problem is convex and formulated as a Linear Program.

Sofie Andersson, Alexandros Nikou, Dimos V. Dimarogonas

This paper presents a framework for automatic synthesis of a control sequence for multi-agent systems governed by continuous linear dynamics under timed constraints. First, the motion of the agents in the workspace is abstracted into individual Transition Systems (TS). Second, each agent is assigned with an individual formula given in Metric Interval Temporal Logic (MITL) and in parallel, the team of agents is assigned with a collaborative team formula. The proposed method is based on a correct-by-construction control synthesis method, and hence guarantees that the resulting closed-loop system will satisfy the specifications. The specifications considers boolean-valued properties under real-time. Extended simulations has been performed in order to demonstrate the efficiency of the proposed controllers.

Christos K. Verginis, Alexandros Nikou, Dimos V. Dimarogonas

This paper addresses the problem of position- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in a $3$D workspace with obstacles. More specifically, we design a decentralized control protocol such that each agent achieves a predefined geometric formation with its initial neighbors, while using local information based on a limited sensing radius. The latter implies that the proposed scheme guarantees that the initially connected agents remain always connected. In addition, by introducing certain distance constraints, we guarantee inter-agent collision avoidance as well as collision avoidance with the obstacles and the boundary of the workspace. The proposed controllers employ a novel class of potential functions and do not require a priori knowledge of the dynamical model, except for gravity-related terms. Finally, simulation results verify the validity of the proposed framework.

Alexandros Nikou, Christos K. Verginis, Dimos V. Dimarogonas

This paper addresses the problem of distance- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in 3D space, under static and undirected communication topologies. More specifically, we design a decentralized model-free control protocol in the sense that each agent uses only local information from its neighbors to calculate its own control signal, without incorporating any knowledge of the model nonlinearities and exogenous disturbances. Moreover, the transient and steady state response is solely determined by certain designer-specified performance functions and is fully decoupled by the agents' dynamic model, the control gain selection, the underlying graph topology as well as the initial conditions. Additionally, by introducing certain inter-agent distance constraints, we guarantee collision avoidance and connectivity maintenance between neighboring agents. Finally, simulation results verify the performance of the proposed controllers.

Alexandros Filotheou, Alexandros Nikou, Dimos V. Dimarogonas

This paper addresses the problem of navigation control of a general class of uncertain nonlinear multi-agent systems in a bounded workspace of $\mathbb{R}^n$ with static obstacles. In particular, we propose a decentralized control protocol such that each agent reaches a predefined position at the workspace, while using only local information based on a limited sensing radius. The proposed scheme guarantees that the initially connected agents remain always connected. In addition, by introducing certain distance constraints, we guarantee inter-agent collision avoidance, as well as, collision avoidance with the obstacles and the boundary of the workspace. The proposed controllers employ a class of Decentralized Nonlinear Model Predictive Controllers (DNMPC) under the presence of disturbances and uncertainties. Finally, simulation results verify the validity of the proposed framework.

Pedro O. Pereira, Dimos V. Dimarogonas

In this paper we study a family of controllers that guarantees attitude synchronization for a network of elements in the unit sphere domain, i.e. $\mathcal{S}^2$. We propose distributed continuous controllers for elements whose dynamics are controllable (i.e. control with torque as command), and which can be implemented by each individual agent without the need of a common global orientation frame among the network, i.e. it requires only local information that can be measured by each individual agent from its own orientation frame. The controllers are specified according to arbitrary distance functions in $\mathcal{S}^2$, and we provide conditions on those distance functions that guarantee that i) a synchronized network of agents is locally asymptotically stable for an arbitrary network graph; ii) a synchronized network can be achieved for almost all initial conditions in a tree graph network. We also study the equilibria configurations that come with specific types of network graphs. The proposed strategies can be used in attitude synchronization of swarms of fully actuated rigid bodies, such as satellites.

Dimitris Boskos, Dimos V. Dimarogonas

The purpose of this report is to define abstractions for multi-agent systems under coupled constraints. In the proposed decentralized framework, we specify a finite or countable transition system for each agent which only takes into account the discrete positions of its neighbors. The dynamics of the considered systems consist of two components. An appropriate feedback law which guarantees that certain performance requirements (eg. connectivity) are preserved and induces the coupled constraints and additional free inputs which we exploit in order to accomplish high level tasks. In this work we provide sufficient conditions on the space and time discretization of the system which ensure that we can extract a well posed and hence meaningful finite transition system.

Peter Varnai, Dimos V. Dimarogonas

Signal temporal logic (STL) provides a user-friendly interface for defining complex tasks for robotic systems. Recent efforts aim at designing control laws or using reinforcement learning methods to find policies which guarantee satisfaction of these tasks. While the former suffer from the trade-off between task specification and computational complexity, the latter encounter difficulties in exploration as the tasks become more complex and challenging to satisfy. This paper proposes to combine the benefits of the two approaches and use an efficient prescribed performance control (PPC) base law to guide exploration within the reinforcement learning algorithm. The potential of the method is demonstrated in a simulated environment through two sample navigational tasks.

Pierre-Jean Meyer, Dimos V. Dimarogonas

This paper presents a compositional approach to specification-guided abstraction refinement for control synthesis of a nonlinear system associated with a method to over-approximate its reachable sets. Given an initial coarse partition of the state space, the control specification is given as a sequence of the cells of this partition to visit at each sampling time. The dynamics are decomposed into subsystems where some states and inputs are not observed, some states are observed but not controlled and where assume-guarantee obligations are used on the uncontrolled states of each subsystem. A finite abstraction is created for each subsystem through a refinement procedure starting from a coarse partition of the state space, then proceeding backwards on the specification sequence to iteratively split the elements of the partition whose coarseness prevents the satisfaction of the specification. Each refined abstraction is associated with a controller and it is proved that combining these local controllers can enforce the specification on the original system. The efficiency of the proposed approach compared to other abstraction methods is illustrated in a numerical example.

Jana Tumova, Dimos V. Dimarogonas

The aim of this work is to introduce an efficient procedure for discrete multi-agent planning under local complex temporal logic behavior specifications. While the first part of an agent's behavior specification constraints the agent's trace and is independent, the second part of the specification expresses the agent's tasks in terms of the services to be provided along the trace and may impose requests for the other agents' collaborations. To fight the extreme computational complexity of centralized multi-agent planning, we propose a two-phase automata-based solution, where we systematically decouple the planning procedure for the two types of specifications. At first, we only consider the former specifications in a fully decentralized way and we compactly represent each agents' admissible traces by abstracting away the states that are insignificant for the satisfaction of their latter specifications. Second, the synchronized planning procedure uses only the compact representations. The satisfaction of the overall specification is guaranteed by construction for each agent. An illustrative example demonstrating the practical benefits of the solution is included.

Leonardo J. Colombo, Dimos V. Dimarogonas

We study the problem of motion feasibility for multiagent control systems on Lie groups with collision avoidance constraints. We first consider the problem for kinematic left invariant control systems and next, for dynamical control systems given by a left-trivialized Lagrangian function. Solutions of the kinematic problem give rise to linear combinations of the control inputs in a linear subspace annihilating the collision avoidance constraints. In the dynamical problem, motion feasibility conditions are obtained by using techniques from variational calculus on manifolds, given by a set of equations in a vector space, and Lagrange multipliers annihilating the constraint force that prevents deviation of solutions from a constraint submanifold.

Alexandros Nikou, Shahab Heshmati-alamdari, Christos Verginis et al.

This paper presents a fully automated procedure for controller synthesis for a general class of multi-agent systems under coupling constraints. Each agent is modeled with dynamics consisting of two terms: the first one models the coupling constraints and the other one is an additional bounded control input. We aim to design these inputs so that each agent meets an individual high-level specification given as a Metric Interval Temporal Logic (MITL). Furthermore, the connectivity of the initially connected agents, is required to be maintained. First, assuming a polyhedral partition of the workspace, a novel decentralized abstraction that provides controllers for each agent that guarantee the transition between different regions is designed. The controllers are the solution of a Robust Optimal Control Problem (ROCP) for each agent. Second, by utilizing techniques from formal verification, an algorithm that computes the individual runs which provably satisfy the high-level tasks is provided. Finally, simulation results conducted in MATLAB environment verify the performance of the proposed framework.

Soulaimane Berkane, Andrea Bisoffi, Dimos V. Dimarogonas

For a vehicle moving in an $n$-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded spherical region. The proposed hybrid control algorithm switches between two modes of operation: stabilization (motion-to-goal) and avoidance (boundary-following). The geometric construction of the flow and jump sets of the hybrid controller, exploiting a hysteresis region, guarantees robust switching (chattering-free) between the stabilization and avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for a 3-dimensional scenario.

Christos K. Verginis, Charalampos P. Bechlioulis, Dimos V. Dimarogonas et al.

In this paper, we consider the two dimensional (2-D) predecessor-following control problem for a platoon of unicycle vehicles moving on a planar surface. More specifically, we design a decentralized kinematic control protocol, in the sense that each vehicle calculates its own control signal based solely on local information regarding its preceding vehicle, by its on-board camera, without incorporating any velocity measurements. Additionally, the transient and steady state response is a priori determined by certain designer-specified performance functions and is fully decoupled by the number of vehicles composing the platoon and the control gains selection. Moreover, collisions between successive vehicles as well as connectivity breaks, owing to the limited field of view of cameras, are provably avoided. Finally, an extensive simulation study is carried out in the WEBOTS realistic simulator, clarifying the proposed control scheme and verifying its effectiveness.

Alexandros Nikou, Jana Tumova, Dimos V. Dimarogonas

This paper presents a fully automated procedure for controller synthesis for multi-agent systems under the presence of uncertainties. We model the motion of each of the $N$ agents in the environment as a Markov Decision Process (MDP) and we assign to each agent one individual high-level formula given in Probabilistic Computational Tree Logic (PCTL). Each agent may need to collaborate with other agents in order to achieve a task. The collaboration is imposed by sharing actions between the agents. We aim to design local control policies such that each agent satisfies its individual PCTL formula. The proposed algorithm builds on clustering the agents, MDP products construction and controller policies design. We show that our approach has better computational complexity than the centralized case, which traditionally suffers from very high computational demands.

Mehran Zareh, Dimos V. Dimarogonas, Mauro Franceschelli et al.

In this paper consensus in second-order multi-agent systems with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded inter-sampling intervals. It is assumed that each agent has exact knowledge of its own state at any time instant. The considered local interaction rule is PD-type. Sufficient conditions for stability of the consensus protocol to a time-invariant value are derived based on LMIs. Such conditions only require the knowledge of the connectivity of the graph modeling the network topology. Numerical simulations are presented to corroborate the theoretical results.

Mehran Zareh, Dimos V. Dimarogonas, Mauro Franceschelli et al.

In this paper consensus in second-order multi-agent systems with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded inter-sampling intervals. It is assumed that each agent has exact knowledge of its own state at all times. The considered local interaction rule is PD-type. The characterization of the convergence properties exploits a Lyapunov-Krasovskii functional method, sufficient conditions for stability of the consensus protocol to a time-invariant value are derived. Numerical simulations are presented to corroborate the theoretical results.

Tommaso Zaccherini, Siyuan Liu, Dimos V. Dimarogonas

This paper addresses decentralized control of large-scale heterogeneous multi-agent systems subject to bounded external disturbances and limited communication, with the objective of satisfying cooperative Signal Temporal Logic (STL) specifications. The considered specifications involve spatiotemporal tasks that require collaboration among multiple agents, including agents beyond direct communication neighborhoods. To address the communication constraints, a $k$-hop Prescribed Performance State Observer ($k$-hop PPSO) is designed to enable each agent to estimate the states of agents up to $k$ communication hops away using only information from $1$-hop neighbors, while guaranteeing predefined performance bounds on the estimation errors. The estimation error bounds are explicitly incorporated into a reformulation of the spatial robustness of the STL specifications, yielding robustness measures that account for worst-case estimation uncertainty. Based on the modified robustness, a decentralized continuous-time feedback control law is designed to guarantee satisfaction of the STL specifications in the presence of bounded disturbances and estimation errors. The proposed framework provides formal correctness guarantees using only local information and limited communication. Numerical simulations illustrate the theoretical results.

Christos K. Verginis, Dimos V. Dimarogonas

This paper addresses the problem of decentralized abstractions for multiple mobile manipulators with 2nd order dynamics. In particular, we propose decentralized controllers for the navigation of each agent among predefined regions of interest in the workspace, while guaranteeing at the same time inter-agent collision avoidance and connectivity maintenance for a subset of initially connected agents. In that way, the motion of the coupled multi-agent system is abstracted into multiple finite transition systems for each agent, which are then suitable for the application of temporal logic-based high level plans. The proposed methodology is decentralized, since each agent uses local information based on limited sensing capabilities. Finally, simulation studies verify the validity of the approach.

Alexandros Nikou, Dimos V. Dimarogonas

This paper deals with the problem of time-constrained navigation of a robot modeled by uncertain nonlinear non-affine dynamics in a bounded workspace of $\mathbb{R}^n$. Initially, we provide a novel class of robust feedback controllers that drive the robot between Regions of Interest (RoI) of the workspace. The control laws consists of two parts: an on-line controller which is the outcome of a Finite Horizon Optimal Control Problem (FHOCP); and a backstepping feedback law which is tuned off-line and guarantees that the real trajectory always remains in a bounded hyper-tube centered along the nominal trajectory of the robot. The proposed controller falls within the so-called tube-based Nonlinear Model Predictive control (NMPC) methodology. Then, given a desired high-level specification for the robot in Metric Interval Temporal Logic (MITL), by utilizing the aforementioned controllers, a framework that provably guarantees the satisfaction of the formula is provided. The proposed framework can handle the rich expressiveness of MITL in both safety and reachability specifications. Finally, the proposed framework is validated by numerical simulations.

Lars Lindemann, Dimos V. Dimarogonas

Control systems that satisfy temporal logic specifications have become increasingly popular due to their applicability to robotic systems. Existing control methods, however, are computationally demanding, especially when the problem size becomes too large. In this paper, a robust and computationally efficient model predictive control framework for signal temporal logic specifications is proposed. We introduce discrete average space robustness, a novel quantitative semantic for signal temporal logic, that is directly incorporated into the cost function of the model predictive controller. The optimization problem entailed in this framework can be written as a convex quadratic program when no disjunctions are considered and results in a robust satisfaction of the specification. Furthermore, we define the predicate robustness degree as a new robustness notion. Simulations of a multi-agent system subject to complex specifications demonstrate the efficacy of the proposed method.

Lukas Vogel, Andrea Carron, Eleftherios E. Vlahakis et al.

We propose a stochastic model predictive control (MPC) framework for linear systems subject to joint-in-time chance constraints under unknown disturbance distributions. Unlike existing approaches that rely on parametric or Gaussian assumptions, or require expensive offline computation, the method uses conformal prediction to construct finite-sample confidence regions for the system's error trajectories with minimal computational effort. These probabilistic sets enable relaxation of the joint-in-time chance constraints into a deterministic closed-loop formulation based on indirect feedback, ensuring recursive feasibility and chance constraint satisfaction. Further, we extend to the output feedback setting and establish analogous guarantees from output measurements alone, given access to noise samples. Numerical examples demonstrate the effectiveness and advantages compared to existing approaches.

Pedro O. Pereira, Dimitris Boskos, Dimos V. Dimarogonas

In this paper, we study attitude synchronization for elements in the unit sphere of R3 and for elements in the 3D rotation group, for a network with switching topology. The agents angular velocities are assumed to be the control inputs, and a switching control law for each agent is devised that guarantees synchronization, provided that all elements are initially contained in a given region, unknown to the network. The control law is decentralized and it does not require a common orientation frame among all agents. We refer to synchronization of unit vectors in R3 as incomplete synchronization, and of 3D rotation matrices as complete synchronization. Our main contribution lies on showing that these two problems can be analyzed under a common framework, where all elements' dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension.

Pierre-Jean Meyer, Dimos V. Dimarogonas

This paper deals with the control synthesis problem for a continuous nonlinear dynamical system under a Linear Temporal Logic (LTL) formula. The proposed solution is a top-down hierarchical decomposition of the control problem involving three abstraction layers of the problem, iteratively solved from the coarsest to the finest. The LTL planning is first solved on a small transition system only describing the regions of interest involved in the LTL formula. For each pair of consecutive regions of interest in the resulting accepting path satisfying the LTL formula, a discrete plan is then constructed in the partitioned workspace to connect these two regions while avoiding unsafe regions. Finally, an abstraction refinement approach is applied to synthesize a controller for the dynamical system to follow each discrete plan. The second main contribution, used in the third abstraction layer, is a new monotonicity-based method to over-approximate the finite-time reachable set of any continuously differentiable system. The proposed framework is demonstrated in simulation for a motion planning problem of a mobile robot modeled as a disturbed unicycle.

Nana Wang, Pelin Sekercioglu, Dimos V. Dimarogonas

We address the problem of interaction topology identification in open multi-agent systems (OMAS) with dynamic node sets and fast switching interactions. In such systems, new agents join and interactions change rapidly, resulting in intervals with short dwell time and rendering conventional segment-wise estimation and clustering methods unreliable. To overcome this, we propose a projection-based dissimilarity measure derived from a consistency property of local least-squares operators, enabling robust mode clustering. Aggregating intervals within each cluster yields accurate topology estimates. The proposed framework offers a systematic solution for reconstructing the interaction topology of OMAS subject to fast switching. Finally, we illustrate our theoretical results via numerical simulations.

Farhad Mehdifar, Charalampos P. Bechlioulis, Dimos V. Dimarogonas

This paper proposes a funnel control method under time-varying hard and soft output constraints. First, an online funnel planning scheme is designed that generates a constraint consistent funnel, which always respects hard (safety) constraints, and soft (performance) constraints are met only when they are not conflicting with the hard constraints. Next, the prescribed performance control method is employed for designing a robust low-complexity funnel-based controller for uncertain nonlinear Euler-Lagrangian systems such that the outputs always remain within the planned constraint consistent funnels. Finally, the results are verified with a simulation example of a mobile robot tracking a moving object while staying in a box-constrained safe space.

Pelin Sekercioglu, Nana Wang, Angela Fontan et al.

We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian. Topology identification relies on an edge-based formulation of the network and adaptive control protocols through the design of a persistently excited auxiliary network. Our approach guarantees the simultaneous identification and synchronization of the unknown signed network and establishes uniform semiglobal practical asymptotic stability of the estimation errors. Numerical simulations validate our theoretical results.

Farhad Mehdifar, Lars Lindemann, Charalampos P. Bechlioulis et al.

This paper introduces a novel control framework to address the satisfaction of multiple time-varying output constraints in uncertain high-order MIMO nonlinear control systems. Unlike existing methods, which often assume that the constraints are always decoupled and feasible, our approach can handle coupled time-varying constraints even in the presence of potential infeasibilities. First, it is shown that satisfying multiple constraints essentially boils down to ensuring the positivity of a scalar variable, representing the signed distance from the boundary of the time-varying output-constrained set. To achieve this, a single consolidating constraint is designed that, when satisfied, guarantees convergence to and invariance of the time-varying output-constrained set within a user-defined finite time. Next, a novel robust and low-complexity feedback controller is proposed to ensure the satisfaction of the consolidating constraint. Additionally, we provide a mechanism for online modification of the consolidating constraint to find a least violating solution when the constraints become mutually infeasible for some time. Finally, simulation examples of trajectory and region tracking for a mobile robot validate the proposed approach.

Panagiotis Rousseas, Haejoon Lee, Dimos V. Dimarogonas et al.

Control synthesis under constraints is at the forefront of research on autonomous systems, in part due to its broad application from low-level control to high-level planning, where computing control inputs is typically cast as a constrained optimization problem. Assessing feasibility of the constraints and selecting among subsets of feasible constraints is a challenging yet crucial problem. In this work, we provide a novel theoretical analysis that yields necessary and sufficient conditions for feasibility assessment of linear constraints and based on this analysis, we develop novel methods for feasible constraint selection in the context of control of autonomous systems. Through a series of simulations, we demonstrate that our algorithms achieve performance comparable to state-of-the-art methods while offering improved computational efficiency. Importantly, our analysis provides a novel theoretical framework for assessing, analyzing and handling constraint infeasibility.

Alexandros Nikou, Shahab Heshmati-alamdari, Dimos V. Dimarogonas

This paper deals with the design and experimental validation of a state-of-the art tube-based Model Predictive Control (MPC) for achieving time-constrained tasks. Given the uncertain nonlinear dynamics of the robot as well as a high-level task written in Metric Interval Temporal Logic (MITL), the goal is to design a feedback control law that guarantees the satisfaction of the task. The workspace is divided into Regions of Interest (RoI) and contains also unsafe regions (obstacles) that the robot should not visit. The feedback control law consists of two terms: a control input which is the outcome of a Finite Horizon Optimal Control (FHOCP); and a state feedback law that guarantees that the nominal trajectories are bounded within a tube centered along the nominal trajectories. The aforementioned control law guarantees that the robot is safely navigated through the RoI within certain time bounds. The proposed framework can handle the rich expressiveness of MITL and is experimentally tested with a Nexus mobile robot in our lab facilities. The experimental results show that the proposed framework is promising for solving real-life robotic as well as industrial problems.

Christos K. Verginis, Dimos V. Dimarogonas

This paper presents a novel control strategy for the coordination of a multi-agent system subject to high-level goals expressed as linear temporal logic formulas. In particular, each agent, which is modeled as a sphere with 2nd order dynamics, has to satisfy a given local temporal logic specification subject to connectivity maintenance and inter-agent collision avoidance. We propose a novel continuous control protocol that guarantees navigation of one agent to a goal point, up to a set of collision-free initial configurations, while maintaining connectivity of the initial neighboring set and avoiding inter-agent collisions. Based on that, we develop a hybrid switching control strategy that ensures that each agent satisfies its temporal logic task. Simulation results depict the validity of the proposed scheme.

Kevin Jamsahar, Adrian Wiltz, Maria Charitidou et al.

This work presents a modular, Python-based simulator that simplifies the evaluation of novel vehicle control and coordination algorithms in complex traffic scenarios while keeping the implementation overhead low. It allows researchers to focus primarily on developing the control and coordination strategies themselves, while the simulator manages the setup of complex road networks, vehicle configuration, execution of the simulation and the generation of video visualizations of the results. It is thereby also well-suited to support control education by allowing instructors to create interactive exercises providing students with direct visual feedback. Thanks to its modular architecture, the simulator remains easily customizable and extensible, lowering the barrier for conducting advanced simulation studies in vehicle and traffic control research.

Farhad Mehdifar, Mani H. Dhullipalla, Charalampos P. Bechlioulis et al.

This paper addresses the problem of collaboratively satisfying long-term spatial constraints in multi-agent systems. Each agent is subject to spatial constraints, expressed as inequalities, which may depend on the positions of other agents with whom they may or may not have direct communication. These constraints need to be satisfied asymptotically or after an unknown finite time. The agents' objective is to collectively achieve a formation that fulfills all constraints. The problem is initially framed as a centralized unconstrained optimization, where the solution yields the optimal configuration by maximizing an objective function that reflects the degree of constraint satisfaction. This function encourages collaboration, ensuring agents help each other meet their constraints while fulfilling their own. When the constraints are infeasible, agents converge to a least-violating solution. A distributed consensus-based optimization scheme is then introduced, which approximates the centralized solution, leading to the development of distributed controllers for single-integrator agents. Finally, simulations validate the effectiveness of the proposed approach.

Xiaoyu Liu, Dimos V. Dimarogonas, Changxin Liu et al.

This paper presents a novel distributed model predictive control (MPC) formulation without terminal cost and a corresponding distributed synthesis approach for distributed linear discrete-time systems with coupled constraints. The proposed control scheme introduces an explicit stability condition as an additional constraint based on relaxed dynamic programming. As a result, contrary to other related approaches, system stability with the developed controller does not rely on designing a terminal cost. A distributed synthesis approach is then introduced to handle the stability constraint locally within each local agent. To solve the underlying optimization problem for distributed MPC, a violation-free distributed optimization approach is developed, using constraint tightening to ensure feasibility throughout iterations. A numerical example demonstrates that the proposed distributed MPC approach ensures closed-loop stability for each feasible control sequence, with each agent computing its control input in parallel.

Yushan Li, Jiabao He, Julien M. Hendrickx et al.

This paper develops a feedback-based method to preserve the topology privacy of consensus protocols in network systems. The key idea is to intentionally violate topology identifiability conditions, thereby preventing unique or accurate recovery of the true topology from available observations, while preserving the intended consensus behavior. This problem is challenging because the feedback magnitude directly reflects the privacy level of edges, while it is strongly coupled with the consensus convergence and constrained by local communications at each node. To begin with, we derive the feedback conditions of both partial and full observation cases, where the topology unsolvability from observation data is characterized in the former, and the solution space that enforces topology inaccuracy from data is constructed in the latter. Then, we propose a novel distributed topology modification design under limited privacy budgets, and establish the performance guarantees through a controllable tradeoff between the consensus deviation and the topology privacy. Finally, we develop a low-complexity heuristic algorithm to achieve optimal privacy preservation on existing edges. Comparative simulations validate the effectiveness and outperformance of the proposed preservation design.

Georgios Mitsos, Dimos V. Dimarogonas, Siyuan Liu

This paper presents a secure-by-construction planning and control framework for multi-agent systems subject to linear temporal logic (LTL) specifications. The framework protects sensitive information from a passive intruder with partial observations of the agents' motion. Security in multi-agent coordination is captured by two notions that prevent the intruder from inferring whether a secret task has been executed and from identifying the agent responsible for its execution. The proposed framework incorporates the security constraints directly into the LTL synthesis procedure by constructing a secure finite transition system that removes all paths violating these constraints. Standard LTL synthesis is then applied to this secure abstraction to generate discrete plans, which are then refined into dynamically feasible continuous trajectories. This synthesis procedure provides formal guarantees that the resulting behavior of the multi-agent system satisfies both the global LTL specification and the security constraints. The effectiveness of the proposed framework is demonstrated through a two-drone case study.

Panagiotis Rousseas, Dimos V. Dimarogonas

In this work, a novel method for planar task and motion planning based on hybrid modeling is proposed. By virtue of a discrete variable which models local constraint satisfaction and enables local feasibility analysis, the proposed control architecture unifies planning with control design. Concurrently, control barrier functions are designed on a transformed disk version of the original nonconvex and geometrically complex robotic workspace, thus amending the issue of deadlocks. Simulations of the proposed method indicate effective handling of multiple overlapping spatio-temporal tasks even in the face of input saturation.