arXiv subjects

Christos G. Cassandras

Publications and source records attributed to Christos G. Cassandras.

At least 37 records · Page 2Linked to original sources

arXiv2024

Spline Trajectory Tracking and Obstacle Avoidance for Mobile Agents via Convex Optimization

We propose an output feedback control-based motion planning technique for agents to enable them to converge to a specified polynomial trajectory while imposing a set of safety constraints on our controller to avoid collisions within the free configuration space (polygonal environment). To achieve this, we 1) decompose our polygonal environment into different overlapping cells 2) write out our polynomial trajectories as the output of a reference dynamical system with given initial conditions 3) formulate convergence and safety constraints as Linear Matrix Inequalities (LMIs) on our controller using Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs) and 4) solve a semi-definite programming (SDP) problem with convergence and safety constraints imposed to synthesize a controller for each convex cell. Extensive simulations are included to test our motion planning method under different initial conditions and different reference trajectories. The synthesized controller is robust to changes in initial conditions and is always safe relative to the boundaries of the polygonal environment.

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arXiv2024

Performance-Guaranteed Solutions for Multi-Agent Optimal Coverage Problems using Submodularity, Curvature, and Greedy Algorithms

We consider a class of multi-agent optimal coverage problems in which the goal is to determine the optimal placement of a group of agents in a given mission space so that they maximize a coverage objective that represents a blend of individual and collaborative event detection capabilities. This class of problems is extremely challenging due to the non-convex nature of the mission space and of the coverage objective. With this motivation, greedy algorithms are often used as means of getting feasible coverage solutions efficiently. Even though such greedy solutions are suboptimal, the submodularity (diminishing returns) property of the coverage objective can be exploited to provide performance bound guarantees. Moreover, we show that improved performance bound guarantees (beyond the standard (1-1/e) performance bound) can be established using various curvature measures of the coverage problem. In particular, we provide a brief review of all existing popular applicable curvature measures, including a recent curvature measure that we proposed, and discuss their effectiveness and computational complexity, in the context of optimal coverage problems. We also propose novel computationally efficient techniques to estimate some curvature measures. Finally, we provide several numerical results to support our findings and propose several potential future research directions.

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arXiv2024

Optimal Sequencing and Motion Control in a Roundabout with Safety Guarantees

This paper develops a controller for Connected and Automated Vehicles (CAVs) traversing a single-lane roundabout. The controller simultaneously determines the optimal sequence and associated optimal motion control jointly minimizing travel time and energy consumption while providing speed-dependent safety guarantees, as well as satisfying velocity and acceleration constraints. This is achieved by integrating (a) Model Predictive Control (MPC) to enable receding horizon optimization with (b) Control Lyapunov-Barrier Functions (CLBFs) to guarantee convergence to a safe set in finite time, thus providing an extended stability region compared to the use of classic Control Barrier Functions (CBFs). The proposed MPC-CLBF framework addresses both infeasibility and myopic control issues commonly encountered when controlling CAVs over multiple interconnected control zones in a traffic network, which has been a limitation of prior work on CAVs going through roundabouts, while still providing safety guarantees. Simulations under varying traffic demands demonstrate the controller's effectiveness and stability.

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arXiv2024

Robust Optimal Lane-changing Control for Connected Autonomous Vehicles in Mixed Traffic

We derive time and energy-optimal policies for a Connected Autonomous Vehicle (CAV) to execute lane change maneuvers in mixed traffic, i.e., in the presence of both CAVs and Human Driven Vehicles (HDVs). These policies are also shown to be robust with respect to the unpredictable behavior of HDVs by exploiting CAV cooperation which can eliminate or greatly reduce the interaction between CAVs and HDVs. We derive a simple threshold-based criterion on the initial relative distance between two cooperating CAVs based on which an optimal policy is selected such that the lane-changing CAV merges ahead of a cooperating CAV in the target lane; in this case, the lane-changing CAV's trajectory becomes independent of HDV behavior. Otherwise, the interaction between CAVs and neighboring HDVs is formulated as a bilevel optimization problem with an appropriate behavioral model for an HDV, and an iterated best response (IBR) method is used to determine an equilibrium. We demonstrate the convergence of the IBR process under certain conditions. Furthermore, Control Barrier Functions (CBFs) are implemented to ensure the robustness of lane-changing behaviors by guaranteeing safety in both longitudinal and lateral directions despite HDV disturbances. Simulation results validate the effectiveness of our CAV controllers in terms of cost, safety guarantees, and limited disruption to traffic flow. Additionally, we demonstrate the robustness of the lane-changing behaviors in the presence of uncontrollable HDVs.

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arXiv2023

Safe Optimal Interactions Between Automated and Human-Driven Vehicles in Mixed Traffic with Event-triggered Control Barrier Functions

This paper studies safe driving interactions between Human-Driven Vehicles (HDVs) and Connected and Automated Vehicles (CAVs) in mixed traffic where the dynamics and control policies of HDVs are unknown and hard to predict. In order to address this challenge, we employ event-triggered Control Barrier Functions (CBFs) to estimate the HDV model online, construct data-driven and state-feedback safety controllers, and transform constrained optimal control problems for CAVs into a sequence of event-triggered quadratic programs. We show that we can ensure collision-free between HDVs and CAVs and demonstrate the robustness and flexibility of our framework on different types of human drivers in lane-changing scenarios while guaranteeing safety with human-in-the-loop interactions.

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arXiv2023

Scaling up the Optimal Safe Control of Connected and Automated Vehicles to a Traffic Network: A Hierarchical Framework of Modular Control Zones

We consider the problem of scaling up optimal and safe controllers for Connected and Automated Vehicles (CAVs) from a single Control Zone (CZ) around a traffic conflict area to an entire network. The goal is to jointly minimize travel time and energy consumption for all CAVs, while providing speed-dependent safety guarantees within a CZ and satisfying velocity and acceleration constraints. A hierarchical modular CZ framework is developed consisting of a lower level where decentralized controllers are used that combine Optimal control and Control Barrier Functions (OCBF) and a higher level where a feedback flow controller is proposed to coordinate adjacent CZs. The flow controller is parameterized by a terminal velocity constraint that serves as the interface between CZs. Simulation results show that the proposed modular control zone framework outperforms a direct extension of the OCBF framework to multiple CZs without any flow control.

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arXiv2023

Trust-Aware Resilient Control and Coordination of Connected and Automated Vehicles

We address the security of a network of Connected and Automated Vehicles (CAVs) cooperating to navigate through a conflict area. Adversarial attacks such as Sybil attacks can cause safety violations resulting in collisions and traffic jams. In addition, uncooperative (but not necessarily adversarial) CAVs can also induce similar adversarial effects on the traffic network. We propose a decentralized resilient control and coordination scheme that mitigates the effects of adversarial attacks and uncooperative CAVs by utilizing a trust framework. Our trust-aware scheme can guarantee safe collision free coordination and mitigate traffic jams. Simulation results validate the theoretical guarantee of our proposed scheme, and demonstrate that it can effectively mitigate adversarial effects across different traffic scenarios.

cs.MA↗

arXiv2023

Optimal Control of Connected Automated Vehicles with Event-Triggered Control Barrier Functions: a Test Bed for Safe Optimal Merging

We address the problem of controlling Connected and Automated Vehicles (CAVs) in conflict areas of a traffic network subject to hard safety constraints. It has been shown that such problems can be solved through a combination of tractable optimal control problems and Control Barrier Functions (CBFs) that guarantee the satisfaction of all constraints. These solutions can be reduced to a sequence of Quadratic Programs (QPs) which are efficiently solved on line over discrete time steps. However, guaranteeing the feasibility of the CBF-based QP method within each discretized time interval requires the careful selection of time steps which need to be sufficiently small. This creates computational requirements and communication rates between agents which may hinder the controller's application to real CAVs. In this paper, we overcome this limitation by adopting an event-triggered approach for CAVs in a conflict area such that the next QP is triggered by properly defined events with a safety guarantee. We present a laboratory-scale test bed we have developed to emulate merging roadways using mobile robots as CAVs which can be used to demonstrate how the event-triggered scheme is computationally efficient and can handle measurement uncertainties and noise compared to time-driven control while guaranteeing safety.

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arXiv2023

Maximizing Safety and Efficiency for Cooperative Lane-Changing: A Minimally Disruptive Approach

This paper addresses cooperative lane-changing maneuvers in mixed traffic, aiming to minimize traffic flow disruptions while accounting for uncooperative vehicles. The proposed approach adopts controllers combining Optimal control with Control Barrier Functions (OCBF controllers) which guarantee spatio-temporal constraints through the use of fixed-time convergence. Additionally, we introduce robustness to disturbances by deriving a method for handling worst-case disturbances using the dual of a linear programming problem. We present a near-optimal solution that ensures safety, optimality, and robustness to changing behavior of uncooperative vehicles. Simulations demonstrate the effectiveness of the proposed approach in enhancing efficiency and safety.

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arXiv2023

Merging control in mixed traffic with safety guarantees: a safe sequencing policy with optimal motion control

We address the problem of merging traffic from two roadways consisting of both Connected Autonomous Vehicles (CAVs) and Human Driven Vehicles (HDVs). Guaranteeing safe merging in such mixed traffic settings is challenging due to the unpredictability of possibly uncooperative HDVs. We develop a hierarchical controller where at each discrete time step first a coordinator determines the best possible Safe Sequence (SS) which can be realized without any knowledge of human driving behavior. Then, a lower-level decentralized motion controller for each CAV jointly minimizes travel time and energy over a prediction horizon, subject to hard safety constraints dependent on the given safe sequence. This is accomplished using a Model Predictive Controller (MPC) subject to constraints based on Control Barrier Functions (CBFs) which render it computationally efficient. Extensive simulation results are included showing that this hierarchical controller outperforms the commonly adopted Shortest Distance First (SDF) passing sequence over the full range of CAV penetration rates, while also providing safe merging guarantees.

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arXiv2023

Scalable Adaptive Traffic Light Control Over a Traffic Network Including Transit Delays

We study the Traffic Light Control (TLC) problem for a traffic network with multiple intersections in an artery, including the effect of transit delays for vehicles moving from one intersection to the next. The goal is to minimize the overall mean waiting time and improve the ``green wave'' properties in such systems. Using a stochastic hybrid system model with parametric traffic light controllers, we use Infinitesimal Perturbation Analysis (IPA) to derive a data-driven cost gradient estimator with respect to these parameters. We then iteratively adjust them through an online gradient-based algorithm. We show that the event-driven nature of the IPA estimators driving the controllers leads to scalable computationally efficient controllers as the dimensionality of the traffic network increases.

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arXiv2023

Safe Control Synthesis Using Environmentally Robust Control Barrier Functions

In this paper, we study a safe control design for dynamical systems in the presence of uncertainty in a dynamical environment. The worst-case error approach is considered to formulate robust Control Barrier Functions (CBFs) in an optimization-based control synthesis framework. It is first shown that environmentally robust CBF formulations result in second-order cone programs (SOCPs). Then, a novel scheme is presented to formulate robust CBFs which takes the nominally safe control as its desired control input in optimization-based control design and then tries to minimally modify it whenever the robust CBF constraint is violated. This proposed scheme leads to quadratic programs (QPs) which can be easily solved. Finally, the effectiveness of the proposed approach is demonstrated on an adaptive cruise control example.

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arXiv2023

A Bilevel Optimization Scheme for Persistent Monitoring

In this paper we study an infinite-horizon persistent monitoring problem in a two-dimensional mission space containing a finite number of statically placed targets, at each of which we assume a constant rate of uncertainty accumulation. Equipped with a sensor of finite range, the agent is capable of reducing the uncertainty of nearby targets. We derive a steady-state minimum time periodic trajectory over which each of the target uncertainties is driven down to zero during each visit. A hierarchical decomposition leads to purely local optimal control problems, coupled via boundary conditions. We optimize both the local trajectory segments as well as the boundary conditions in an on-line bilevel optimization scheme.

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arXiv2023

Cooperative Lane Changing in Mixed Traffic can be Robust to Human Driver Behavior

We derive time and energy-optimal control policies for a Connected Autonomous Vehicle (CAV) to complete lane change maneuvers in mixed traffic. The interaction between CAVs and Human-Driven Vehicles (HDVs) requires designing the best possible response of a CAV to actions by its neighboring HDVs. This interaction is formulated using a bilevel optimization setting with an appropriate behavioral model for an HDV's. Then, an iterated best response (IBR) method is used to determine a Nash equilibrium. However, we also show that when a common and simple-to-detect condition applies, the optimal lane-changing policy is in fact independent of HDV behavior with a CAV changing lanes by cooperating with another CAV in the target lane and always merging ahead of it. Thus, the dependence on the interaction between CAVs and HDVs may be eliminated in such cases. Simulation results are included to show the effectiveness of our controllers in terms of cost, safety guarantees, and disruption to the traffic flow when uncontrollable HDVs are present.

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arXiv2023

Adaptive Traffic Light Control for Competing Vehicle and Pedestrian Flows

We study the Traffic Light Control (TLC) problem for a single intersection, considering both straight driving vehicle flows and corresponding crossing pedestrian flows with the goal of achieving a fair jointly optimal sharing policy in terms of average waiting times. Using a stochastic hybrid system model, we design a quasi-dynamic policy controlling the traffic light cycles with several threshold parameters applied to the light cycles and the partially observed contents of vehicle and pedestrian queues. Infinitesimal Perturbation Analysis (IPA) is then used to derive a data-driven gradient estimator of a cost metric with respect to the policy parameters and to iteratively adjust these parameters through an online gradient-based algorithm in order to improve overall performance on this intersection and adapt the policy to changing traffic conditions. The controller is applied to a simulated intersection in the town of Veberöd, Sweden, to illustrate the performance of this approach using real traffic data from this intersection.

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arXiv2023

Learning Feasibility Constraints for Control Barrier Functions

It has been shown that optimizing quadratic costs while stabilizing affine control systems to desired (sets of) states 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 this paper, we employ machine learning techniques to ensure the feasibility of these QPs, which is a challenging problem, especially for high relative degree constraints where High Order CBFs (HOCBFs) are required. To this end, we propose a sampling-based learning approach to learn a new feasibility constraint for CBFs; this constraint is then enforced by another HOCBF added to the QPs. The accuracy of the learned feasibility constraint is recursively improved by a recurrent training algorithm. We demonstrate the advantages of the proposed learning approach to constrained optimal control problems with specific focus on a robot control problem and on autonomous driving in an unknown environment.

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arXiv2023

Minimally Disruptive Cooperative Lane-change Maneuvers

A lane-change maneuver on a congested highway could be severely disruptive or even infeasible without the cooperation of neighboring cars. However, cooperation with other vehicles does not guarantee that the performed maneuver will not have a negative impact on traffic flow unless it is explicitly considered in the cooperative controller design. In this letter, we present a socially compliant framework for cooperative lane-change maneuvers for an arbitrary number of CAVs on highways that aims to interrupt traffic flow as minimally as possible. Moreover, we explicitly impose feasibility constraints in the optimization formulation by using reachability set theory, leading to a unified design that removes the need for an iterative procedure used in prior work. We quantitatively evaluate the effectiveness of our framework and compare it against previously offered approaches in terms of maneuver time and incurred throughput disruption.

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arXiv2022

Cooperative Energy and Time-Optimal Lane Change Maneuvers with Minimal Highway Traffic Disruption

We derive optimal control policies for a Connected Automated Vehicle (CAV) and cooperating neighboring CAVs to carry out a lane change maneuver consisting of a longitudinal phase where the CAV properly positions itself relative to the cooperating neighbors and a lateral phase where it safely changes lanes. In contrast to prior work on this problem, where the CAV "selfishly" only seeks to minimize its maneuver time, we seek to ensure that the fast-lane traffic flow is minimally disrupted (through a properly defined metric). Additionally, when performing lane-changing maneuvers, we optimally select the cooperating vehicles from a set of feasible neighboring vehicles and experimentally show that the highway throughput is improved compared to the baseline case of human-driven vehicles changing lanes with no cooperation. When feasible solutions do not exist for a given maximal allowable disruption, we include a time relaxation method trading off a longer maneuver time with reduced disruption. Our analysis is also extended to multiple sequential maneuvers. Simulation results show the effectiveness of our controllers in terms of safety guarantees and up to 16% and 90% average throughput and maneuver time improvement respectively when compared to maneuvers with no cooperation.

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