arXiv subjects

Dimos V. Dimarogonas

Publications and source records attributed to Dimos V. Dimarogonas.

At least 127 records · Page 7Linked to original sources

arXiv2021

Event-Triggered Tracking Control of Networked and Quantized Control Systems

This paper studies the tracking control problem of networked and quantized control systems under both multiple networks and event-triggered mechanisms. Multiple networks are to connect the plant and reference system with decentralized controllers to guarantee their information transmission, whereas event-triggered mechanisms are to reduce the information transmission via multiple networks. In this paper, all networks are independent and asynchronous and have local event-triggered mechanisms, which are based on local measurements and determine whether the local measurements need to be transmitted. We first implement an emulation-based approach to develop a novel hybrid model for tracking control of networked and quantized control systems. Next, sufficient conditions are derived and decentralized event-triggered mechanisms are designed to ensure the tracking performance. Finally, a numerical example is given to illustrate the obtained results.

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arXiv2021

Higher Order Convergent Control Barrier Functions for Leader-Follower Multi-Agent Systems under STL Tasks

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 satisfaction of STL tasks independent of the agents' initial conditions.

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arXiv2021

Reactive and Risk-Aware Control for Signal Temporal Logic

The deployment of autonomous systems in uncertain and dynamic environments has raised fundamental questions. Addressing these is pivotal to build fully autonomous systems and requires a systematic integration of planning and control. We first propose reactive risk signal interval temporal logic (ReRiSITL) as an extension of signal temporal logic (STL) to formulate complex spatiotemporal specifications. Unlike STL, ReRiSITL allows to consider uncontrollable propositions that may model humans as well as random environmental events such as sensor failures. Additionally, ReRiSITL allows to incorporate risk measures, such as (but not limited to) the Conditional Value-at-Risk, to measure the risk of violating certain spatial specifications. Second, we propose an algorithm to check if an ReRiSITL specification is satisfiable. For this purpose, we abstract the ReRiSITL specification into a timed signal transducer and devise a game-based approach. Third, we propose a reactive planning and control framework for dynamical control systems under ReRiSITL specifications.

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arXiv2021

Safe-by-Design Control for Euler-Lagrange Systems

Safety-critical control is characterized as ensuring constraint satisfaction for a given dynamical system. Recent developments in zeroing control barrier functions (ZCBFs) have provided a framework for ensuring safety of a superlevel set of a single constraint function. Euler-Lagrange systems represent many real-world systems including robots and vehicles, which must abide by safety-regulations, especially for use in human-occupied environments. These safety regulations include state constraints (position and velocity) and input constraints that must be respected at all times. ZCBFs are valuable for satisfying system constraints for general nonlinear systems, however their construction to satisfy state and input constraints is not straightforward. Furthermore, the existing barrier function methods do not address the multiple state constraints that are required for safety of Euler-Lagrange systems. In this paper, we propose a methodology to construct multiple, non-conflicting control barrier functions for Euler-Lagrange systems subject to input constraints to satisfy safety regulations, while concurrently taking into account robustness margins and sampling-time effects. The proposed approach consists of a sampled-data controller and an algorithm for barrier function construction to enforce safety (i.e satisfy position and velocity constraints). The proposed method is validated in simulation on a 2-DOF planar manipulator.

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arXiv2021

High-order Barrier Functions: Robustness, Safety and Performance-Critical Control

In this paper, we propose a notion of high-order (zeroing) barrier functions that generalizes the concept of zeroing barrier functions and guarantees set forward invariance by checking their higher order derivatives. The proposed formulation guarantees asymptotic stability of the forward invariant set, which is highly favorable for robustness with respect to model perturbations. No forward completeness assumption is needed in our setting in contrast to existing high order barrier function methods. For the case of controlled dynamical systems, we relax the requirement of uniform relative degree and propose a singularity-free control scheme that yields a locally Lipschitz control signal and guarantees safety. Furthermore, the proposed formulation accounts for "performance-critical" control: it guarantees that a subset of the forward invariant set will admit any existing, bounded control law, while still ensuring forward invariance of the set. Finally, a non-trivial case study with rigid-body attitude dynamics and interconnected cell regions as the safe region is investigated.

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arXiv2021

KDF: Kinodynamic Motion Planning via Geometric Sampling-based Algorithms and Funnel Control

We integrate sampling-based planning techniques with funnel-based feedback control to develop KDF, a new framework for solving the kinodynamic motion-planning problem via funnel control. The considered systems evolve subject to complex, nonlinear, and uncertain dynamics (aka differential constraints). Firstly, we use a geometric planner to obtain a high-level safe path in a user-defined extended free space. Secondly, we develop a low-level funnel control algorithm that guarantees safe tracking of the path by the system. Neither the planner nor the control algorithm use information on the underlying dynamics of the system, which makes the proposed scheme easily distributable to a large variety of different systems and scenarios. Intuitively, the funnel control module is able to implicitly accommodate the dynamics of the system, allowing hence the deployment of purely geometrical motion planners. Extensive computer simulations and experimental results with a 6-DOF robotic arm validate the proposed approach.

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arXiv2021

Fixed-Time Convergent Control Barrier Functions for Coupled Multi-Agent Systems Under STL Tasks

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 condition in the presence of undesired violation effects of the neighbor agents. Particularly, the robust performance of the task satisfactions can be adjusted in a user-specified way.

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arXiv2021

Robust approximate symbolic models for a class of continuous-time uncertain nonlinear systems via a control interface

Discrete abstractions have become a standard approach to assist control synthesis under complex specifications. Most techniques for the construction of a discrete abstraction for a continuous-time system require time-space discretization of the concrete system, which constitutes property satisfaction for the continuous-time system non-trivial. In this work, we aim at relaxing this requirement by introducing a control interface. Firstly, we connect the continuous-time uncertain concrete system with its discrete deterministic state-space abstraction with a control interface. Then, a novel stability notion called $η$-approximate controlled globally practically stable, and a new simulation relation called robust approximate simulation relation are proposed. It is shown that the uncertain concrete system, under the condition that there exists an admissible control interface such that the augmented system (composed of the concrete system and its abstraction) can be made $η$-approximate controlled globally practically stable, robustly approximately simulates its discrete abstraction. The effectiveness of the proposed results is illustrated by two simulation examples.

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arXiv2021

Distributed motion coordination for multi-robot systems under LTL specifications

This paper investigates the online motion coordination problem for a group of mobile robots moving in a shared workspace, each of which is assigned a linear temporal logic specification. Based on the realistic assumptions that each robot is subject to both state and input constraints and can have only local view and local information, a fully distributed multi-robot motion coordination strategy is proposed. For each robot, the motion coordination strategy consists of three layers. An offline layer pre-computes the braking area for each region in the workspace, the controlled transition system, and a so-called potential function. An initialization layer outputs an initially safely satisfying trajectory. An online coordination layer resolves conflicts when one occurs. The online coordination layer is further decomposed into three steps. Firstly, a conflict detection algorithm is implemented, which detects conflicts with neighboring robots. Whenever conflicts are detected, a rule is designed to assign dynamically a planning order to each pair of neighboring robots. Finally, a sampling-based algorithm is designed to generate local collision-free trajectories for the robot which at the same time guarantees the feasibility of the specification. Safety is proven to be guaranteed for all robots at any time. The effectiveness and the computational tractability of the resulting solution is verified numerically by two case studies.

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arXiv2021

Signal Temporal Logic Task Decomposition via Convex Optimization

In this paper we focus on the problem of decomposing a global Signal Temporal Logic formula (STL) assigned to a multi-agent system to local STL tasks when the team of agents is a-priori decomposed to disjoint sub-teams. The predicate functions associated to the local tasks are parameterized as hypercubes depending on the states of the agents in a given sub-team. The parameters of the functions are, then, found as part of the solution of a convex program that aims implicitly at maximizing the volume of the zero level-set of the corresponding predicate function. Two alternative definitions of the local STL tasks are proposed and the satisfaction of the global STL formula is proven when the conjunction of the local STL tasks is satisfied.

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arXiv2021

Barrier Function-based Collaborative Control of Multiple Robots under Signal Temporal Logic Tasks

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 function condition that results in discontinuous control laws, as opposed to a centralized condition resembling the single-agent case. The benefits of our approach are inherent robustness properties typically present in feedback control as well as satisfaction guarantees for continuous-time multi-agent systems. More specifically, time-varying control barrier functions are used that account for the semantics of the signal temporal logic tasks at hand. For a certain fragment of signal temporal logic tasks, we further propose a systematic way to construct such control barrier functions. Finally, we show the efficacy and robustness of our framework in an experiment including a group of three omnidirectional robots.

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arXiv2021

Obstacle Avoidance via Hybrid Feedback

In this paper we present a hybrid feedback approach to solve the navigation problem of a point mass in the n-dimensional space containing an arbitrary number of ellipsoidal shape obstacles. The proposed hybrid control algorithm guarantees both global asymptotic stabilization to a reference and avoidance of the obstacles. The intuitive idea of the proposed hybrid feedback is to switch between two modes of control: stabilization and avoidance. The geometric construction of the flow and jump sets of the proposed hybrid controller, exploiting hysteresis regions, guarantees Zeno-free switching between the stabilization and the avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for 2-dimensional and 3-dimensional scenarios.

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arXiv2020

Event-triggered Feedback Control for Signal Temporal Logic Tasks

A framework for the event-triggered control synthesis under signal temporal logic (STL) tasks is proposed. In our previous work, a continuous-time feedback control law was designed, using the prescribed performance control technique, to satisfy STL tasks. We replace this continuous-time feedback control law by an event-triggered controller. The event-triggering mechanism is based on a maximum triggering interval and on a norm bound on the difference between the value of the current state and the value of the state at the last triggering instance. Simulations of a multi-agent system quantitatively show the efficacy of using an event-triggered controller to reduce communication and computation efforts.

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arXiv2020

Decentralized Control Barrier Functions for Coupled Multi-Agent Systems under Signal Temporal Logic Tasks

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.

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arXiv2020

Symbolic Abstractions for Nonlinear Control Systems via Feedback Refinement Relation

This paper studies the construction of symbolic abstractions for nonlinear control systems via feedback refinement relation. Both the delay-free and time-delay cases are addressed. For the delay-free case, to reduce the computational complexity, we propose a new approximation approach for the state and input sets based on a static quantizer, and then a novel symbolic model is constructed such that the original system and the symbolic model satisfy the feedback refinement relation. For the time-delay case, both static and dynamic quantizers are combined to approximate the state and input sets. This leads to a novel dynamic symbolic model for time-delay control systems, and a feedback refinement relation is established between the original system and the symbolic model. Finally, a numerical example is presented to illustrate the obtained results.

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arXiv2020

Dynamic Quantization based Symbolic Abstractions for Nonlinear Control Systems

This paper studies the construction of dynamic symbolic abstractions for nonlinear control systems via dynamic quantization. Since computational complexity is a fundamental problem in the use of discrete abstractions, a dynamic quantizer with a time-varying quantization parameter is first applied to deal with this problem. Due to the dynamic quantizer, a dynamic approximation approach is proposed for the state and input sets. Based on the dynamic approximation, dynamic symbolic abstractions are constructed for nonlinear control systems, and an approximate bisimulation relation is guaranteed for the original system and the constructed dynamic symbolic abstraction. Finally, the obtained results are illustrated through a numerical example from path planning of mobile robots.

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arXiv2020

Logarithmic Quantization based Symbolic Abstractions for Nonlinear Control Systems

This paper studies symbolic abstractions for nonlinear control systems using logarithmic quantization. With a logarithmic quantizer, we approximate the state and input sets, and then construct a novel discrete abstraction for nonlinear control systems. A feedback refinement relation between the constructed discrete abstraction and the original system is established. Using the constructed discrete abstraction, the safety controller synthesis problem is studied. With the discrete abstraction and the abstract specification, the existence of a safety controller is investigated, and the algorithm is proposed to compute the abstract controller. Finally, a numerical example is given to illustrate the obtained results.

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arXiv2020

Symmetry Reduction in Optimal Control of Multiagent Systems on Lie Groups

We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the physical symmetries of agents, where the kinematics of each agent is given by a left-invariant control system. Reduced optimality conditions are obtained using techniques from variational calculus and Lagrangian mechanics. A Hamiltonian formalism is also studied, where the problem is explored through an application of Pontryagin's maximum principle for left-invariant systems, and the optimality conditions are obtained as integral curves of a reduced Hamiltonian vector field. We apply the results to an energy-minimum control problem for multiple unicycles.

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