The trajectory planning for a fleet of automated guided vehicles (AGVs) on a roadmap is commonly referred to as the multi-agent path finding (MAPF) problem, the solution to which dictates each AGV's spatial and temporal location until it reaches its goal without collision. When executing MAPF plans in dynamic workspaces, AGVs can be frequently delayed, e.g., due to encounters with humans or third-party vehicles. If the remainder of the AGVs keeps following their individual plans, synchrony of the fleet is lost and some AGVs may pass through roadmap intersections in a different order than originally planned. Although this could reduce the cumulative route completion time of the AGVs, generally, a change in the original ordering can cause conflicts, such as deadlocks. In practice, synchrony is therefore often enforced by using a MAPF execution policy employing, e.g., an action dependency graph (ADG) to maintain ordering. To safely re-order without introducing deadlocks, we present the concept of the switchable action dependency graph (SADG). Using the SADG, we formulate a comparatively low-dimensional mixed-integer linear program that repeatedly re-orders AGVs in a recursively feasible manner, thus maintaining deadlock-free guarantees, while dynamically minimizing the cumulative route completion time of all AGVs. Various simulations validate the efficiency of our approach when compared to the original ADG method as well as robust MAPF solution approaches.

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This paper considers the problem of fault estimation in linear time-invariant systems when actuators are subject to unknown additive faults. A data-driven approach is proposed to design an inverse-system-based filter for reconstructing fault signals when the underlying fault subsystem can be either a minimum phase or non-minimum phase system. Unlike traditional two-step data-driven methods in the literature, the proposed method directly computes the filter parameters from input-output data to avoid the propagation of identification errors through an inverse operation into the fault estimates, which is the case in state-of-the-art filter designs. Furthermore, regarding out-of-sample performance of the filter, a kernel-based regularization is exploited to not only reduce the model complexity but also enable the design scheme to take advantage of available prior knowledge on the underlying system behavior. This knowledge can be incorporated into basis functions, promoting the desired solution to the optimization problem. To validate the effectiveness of the proposed method, a simulation study is conducted, demonstrating a notable reduction in estimation error compared to state-of-the-art methods.

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Control systems are essential to support the use of building structures as short-term thermal energy storage (TES). Due to modeling and forecast imperfections, the controller must be able to deal with uncertainties. This paper proposes a robust model predictive controller (MPC) with a new uncertainty set construction technique to regulate the heat supply in a building envelope. We extend the Support Vector Clustering-based set construction technique to estimate modeling and forecast uncertainty sets. Subsequently, we integrate the sets into a Min-Max MPC framework to ensure robust feasibility by tightening the constraints. The resulting controller successfully deals with modeling and forecast uncertainties. The quality of the presented framework is compared with a nominal MPC and a robust MPC with different uncertainty set estimates. On the basis of a numerical simulation, we demonstrate that the proposed controller successfully maintains the room temperature within the comfort limits. The result also shows that our MPC is less conservative than the controller designed using a box-shaped non-falsified parametric uncertainty set.

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Heat pump and thermal energy storage (HPTES) systems, which are widely utilized in modern buildings for providing domestic hot water, contribute to a large share of household electricity consumption. With the increasing integration of renewable energy sources (RES) into modern power grids, demand-side management (DSM) becomes crucial for balancing power generation and consumption by adjusting end users' power consumption. This paper explores an energy flexible Model Predictive Control (MPC) design for a class of HPTES systems to facilitate demand-side management. The proposed DSM strategy comprises two key components: i) flexibility assessment, and ii) flexibility exploitation. Firstly, for flexibility assessment, a tailored MPC formulation, supplemented by a set of auxiliary linear constraints, is developed to quantitatively assess the flexibility potential inherent in HPTES systems. Subsequently, in flexibility exploitation, the energy flexibility is effectively harnessed in response to feasible demand response (DR) requests, which can be formulated as a standard mixed-integer MPC problem. Numerical experiments, based on a real-world HPTES installation, are conducted to demonstrate the efficacy of the proposed design.

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Robust Optimal Control (ROC) with adjustable uncertainties has proven to be effective in addressing critical challenges within modern energy networks, especially the reserve and provision problem. However, prior research on ROC with adjustable uncertainties has predominantly focused on the scenario of uncertainties modeled as continuous variables. In this paper, we explore ROC with binary adjustable uncertainties, where the uncertainties are modeled by binary decision variables, marking the first investigation of its kind. To tackle this new challenge, firstly we introduce a metric designed to quantitatively measure the extent of binary adjustable uncertainties. Then, to balance computational tractability and adaptability, we restrict control policies to be affine functions with respect to uncertainties, and propose a general design framework for ROC with binary adjustable uncertainties. To address the inherent computational demands of the original ROC problem, especially in large-scale applications, we employ strong duality (SD) and big-M-based reformulations to create a scalable and computationally efficient Mixed-Integer Linear Programming (MILP) formulation. Numerical simulations are conducted to showcase the performance of our proposed approach, demonstrating its applicability and effectiveness in handling binary adjustable uncertainties within the context of modern energy networks.

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The acceptance of automated driving is under the potential threat of motion sickness. It hinders the passengers' willingness to perform secondary activities. In order to mitigate motion sickness in automated vehicles, we propose an optimization-based motion planning algorithm that minimizes the distribution of acceleration energy within the frequency range that is found to be the most nauseogenic. The algorithm is formulated into integral and receding-horizon variants and compared with a commonly used alternative approach aiming to minimize accelerations in general. The proposed approach can reduce frequency-weighted acceleration by up to 11.3% compared with not considering the frequency sensitivity for the price of reduced overall acceleration comfort. Our simulation studies also reveal a loss of performance by the receding-horizon approach over the integral approach when varying the preview time and nominal sampling time. The computation time of the receding-horizon planner is around or below the real-time threshold when using a longer sampling time but without causing significant performance loss. We also present the results of experiments conducted to measure the performance of human drivers on a public road section that the simulated scenario is actually based on. The proposed method can achieve a 19% improvement in general acceleration comfort or a 32% reduction in squared motion sickness dose value over the best-performing participant. The results demonstrate considerable potential for improving motion comfort and mitigating motion sickness using our approach in automated vehicles.

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The way how the uncertainties are represented by sets plays a vital role in the performance of robust optimization (RO). This paper presents a novel approach leveraging machine learning (ML) techniques to construct data-driven uncertainty sets from historical uncertainty data for RO problems. The proposed method integrates Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Gaussian Mixture Model (GMM), and Principle Component Analysis (PCA) systematically to eliminate the influence of uncertainty scenarios with low occurrence probability and generate a nonconvex uncertainty set that is a union of multiple basic subsets (box or ellipsoid) without sacrificing its computational tractability. In addition to presenting a comprehensive algorithm for uncertainty set development, this paper offers detailed guidelines for parameter tuning and performance analysis. By harnessing the well-established ML packages scikit-learn, a Python-based toolkit for implementing the proposed approach is also provided. Furthermore, a computationally efficient solution for a two-stage linear RO problem with the proposed data-driven uncertainty set is derived, alongside establishing a probabilistic guarantee of constraint satisfaction for out-of-sample uncertainties. Extensive numerical experiments, conducted on both synthetic and real-world datasets as well as an optimization-based control problem, are performed to demonstrate the efficacy of the proposed methodology.

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The inherently nonlinear, large-scale, and time-varying nature of district heating systems pose significant challenges from a control perspective. In this paper, we address these challenges by applying an economic MPC. Economic MPC is a dynamic real-time optimization method, enabling both optimal planning and stability of the closed-loop system. Our strategy constitutes several steps. First, we introduce a discrete-time modular framework for the district heating system, establishing its strict dissipativity with respect to a desired, potentially time-varying, equilibrium. We identify a set of meaningful objective functions for the district heating systems, preserving this property. Second, we show how strict dissipativity implies the turnpike property, which, in turn, guarantees approximate optimality, practical stability, and recursive feasibility for the EMPC closed-loop. Finally, we provide numerical simulations to demonstrate the effectiveness of our work.

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This work presents a method for multi-robot coordination based on a novel distributed nonlinear model predictive control (NMPC) formulation for trajectory optimization and its modified version to mitigate the effects of packet losses and delays in the communication among the robots. Our algorithms consider that each robot is equipped with an onboard computation unit to solve a local control problem and communicate with neighboring autonomous robots via a wireless network. The difference between the two proposed methods is in the way the robots exchange information to coordinate. The information exchange can occur in a following: 1) synchronous or 2) asynchronous fashion. By relying on the theory of the nonconvex alternating direction method of multipliers (ADMM), we show that the proposed solutions converge to a (local) solution of the centralized problem. For both algorithms, the communication exchange preserves the safety of the robots; that is, collisions with neighboring autonomous robots are prevented. The proposed approaches can be applied to various multi-robot scenarios and robot models. In this work, we assess our methods, both in simulation and with experiments, for the coordination of a team of autonomous vehicles in the following: 1) an unsupervised intersection crossing and 2) the platooning scenarios.

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The efficacy of robust optimal control with adjustable uncertainty sets is verified in several domains under the perfect state information setting. This paper investigates constrained robust optimal control for linear systems with linear cost functions subject to uncertain disturbances and state measurement errors that are both residing in adjustable uncertainty sets. We first show that the class of affine feedback policies of state measurements are equivalent to the class of affine feedback policies of estimated disturbances in terms of their conservativeness. Then, we formulate and solve a robust optimal control problem with adjustable uncertainty sets by considering the disturbance feedback policies. In contrast to the conventional robust optimal control, where uncertainty sets are fixed and known a priori, the uncertainty sets themselves are regarded as decision variables in our design. In particular, given the metrics for evaluating the optimal size/shape of the polyhedral uncertainty sets, a bilinear optimization problem is formulated to decide the optimal size/shape of uncertainty sets and a corresponding optimal control policy to robustly guarantee that the system will respect its constraints for all admissible uncertainties. In addition, we introduce a convex approximation for the proposed scheme to provide a computationally efficient inner approximation of the original problem. The proposed scheme is illustrated by numerical simulation of a building temperature control problem to demonstrate its effectiveness.

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Towards integrating renewable electricity generation sources into the grid, an important facilitator is the energy flexibility provided by buildings' thermal inertia. Most of the existing research follows a single-step price- or incentive-based scheme for unlocking the flexibility potential of buildings. In contrast, this paper proposes a novel two-step design approach for better harnessing buildings' energy flexibility. In a first step, a robust optimization model is formulated for assessing the energy flexibility of buildings in the presence of uncertain predictions of external conditions, such as ambient temperature, solar irradiation, etc. In a second step, energy flexibility is activated in response to a feasible demand response (DR) request from grid operators without violating indoor temperature constraints, even in the presence of uncertain external conditions. The proposed approach is tested on a high-fidelity Modelica simulator to evaluate its effectiveness. Simulation results show that, compared with price-based demand-side management, the proposed approach achieves greater energy reduction during peak hours.

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In this work, we propose two cooperative passivity-based control methods for networks of mechanical systems. By cooperatively synchronizing the end-effector coordinates of the individual agents, we achieve cooperation between systems of different types. The underlying passivity property of our control approaches ensures that cooperation is stable and robust. Neither of the two approaches rely on the modeling information of neighbors, locally, which simplifies the interconnection of applicable systems and makes the approaches modular in their use. Our first approach is a generalized cooperative Interconnection-and-Damping Assignment passivity-based control (IDA-PBC) scheme for networks of fully actuated and underactuated systems. Our approach leverages the definition of end-effector coordinates in existing single-agent IDA-PBC solutions for underactuated systems to satisfy the matching conditions, independently of the cooperative control input. Accordingly, our approach integrates a large set of existing single-agent solutions and facilitates cooperative control between these and fully actuated systems. Our second approach proposes agent outputs composed of their end-effector coordinates and velocities to guarantee cooperative stability for networks of fully actuated systems in the presence of communication delays. We validate both approaches in simulation and experiments. @en

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

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Motion comfort is the basis of many societal benefits promised by automated driving and motion planning is primarily responsible for this. By planning the spatial trajectory and the velocity profile, motion planners can significantly enhance motion comfort, ideally without sacrificing time efficiency. Active suspensions can push the boundary further by enabling additional degrees of freedom in the controllable vehicle motions. In this paper, we propose to integrate the planning of roll motion into an optimization-based motion planning algorithm called 3DOP(3 Degrees-of-Freedom Optimal Planning), where the conflicting objectives of comfort and time efficiency are optimized. The feasibility of the planned motion is verified in a realistic simulation environment, where feedforward-proportional control suffices to track the speed, path, and roll references. The proposed scheme achieves a significant reduction of motion discomfort, namely by up to 28.1% over the variant without controllable roll motion, or up to 34.2% over an acceleration-bounded driver model. The results suggest considerable potential for improving motion comfort by equipping automated vehicles with active suspensions.@en

The benefits of automated driving can only be fully realized if the occupants are protected from motion sickness. Active suspensions hold the potential to raise the comfort level in automated passenger vehicles by enabling new functionalities in chassis control. One example is to actively lean the vehicle body toward the center of the corner to counteract the inertial lateral acceleration. Commonly known as curve tilting, the concept is deemed effective in reducing postural disturbance on the occupants and the visual-vestibular conflict when the occupants do not have an external view. We present in this article a nonlinear model predictive control (NMPC) method for the curve tilting functionality. The controller incorporates the nonlinear suspension forces in the prediction model to help achieve high tracking accuracy near the physical limit of the suspension system. The optimization process is accelerated with an explicit initialization method that is based on piecewise-affine (PWA) modeling and offline solution to an alternative optimal control problem (OCP). The controller is able to operate at 20 Hz in a hardware-in-the-loop (HIL) setup. Given sufficient computational resources, we observe a significant reduction in the lateral acceleration sensed by the passenger over a vehicle with passive suspensions, namely, by 46.5%, 25.4%, and 25.4% in the highway, rural, and urban driving scenarios, respectively. The NMPC also outperforms the baseline proportional-integral-derivative (PID) controller by achieving lower tracking error, namely, by 12.9%, 16.4%, and 38.0% in the aforementioned scenarios.

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The public acceptance of automated driving is influenced by multiple factors. Apart from safety being of top priority, comfort and time efficiency also have an impact on the popularity of automated vehicles. These two factors contradict each other as optimizing for one results in the degradation of the other. We investigate in this paper how such a multiobjective problem is approached by human drivers and by numerical optimization in the roundabout scenario, which is compact in size but complex to handle. The human drivers' behavior is first observed using naturalistic driving data. The average trajectories and distribution of peak accelerations were extracted after model-based fitting and removal of erroneous samples. The processed data is shared online as an open-access dataset. Then, an optimization problem is formulated and solved to find the numerically optimal motion profile in terms of comfort and time efficiency. The weighted sum of travel time and discomfort is minimized. By adjusting the weight distribution, we present different motion profiles favoring optimal comfort, human-like acceleration magnitudes, and agility, respectively.@en

This paper presents a distributed computational framework for stochastic convex optimization problems using the so-called scenario approach. Such a problem arises, for example, in a large-scale network of interconnected linear systems with local and common uncertainties. Due to the large number of required scenarios to approximate the stochasticity of these problems, the stochastic optimization involves formulating a large-scale scenario program, which is in general computationally demanding. We present two novel ideas in this paper to address this issue. We first develop a technique to decompose the large-scale scenario program into distributed scenario programs that exchange a certain number of scenarios with each other to compute local decisions using the alternating direction method of multipliers (ADMM). We show the exactness of the de-composition with a-priori probabilistic guarantees for the desired level of constraint fulfillment for both local and common uncertainty sources. As our second contribution, we develop a so-called soft communication scheme based on a set parametrization technique together with the notion of probabilistically reliable sets to reduce the required communication between the subproblems. We show how to incorporate the probabilistic reliability notion into existing results and provide new guarantees for the desired level of constraint violations. Two different simulation studies of two types of interconnected network, namely dynamically coupled and coupling constraints, are presented to illustrate advantages of the proposed distributed framework.

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In this work we consider the problem of cooperative end-effector control between heterogeneous fully actuated agents when varying-time delays and/or packet loss are present. We couple agents via outputs encoded with task-space coordinates and velocities that are transformed into wave-variables to overcome the destabilising effects of the communication network. The scheme poses dynamic requirements on the agents which are locally satisfied with feedback control that integrates subtasks, such as joint-limit avoidance or local tracking, when there are redundant degrees-of-freedom. The proposed approach extends existing methods to task-space control. The approach is robust to network effects, applies to nonlinear systems and is scalable by design. The tuning task is simplified considerably by separation of the cooperative and non-cooperative control terms. We demonstrate the efficacy of the proposed approach experimentally.

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In the past, many greenhouse control algorithms have been developed. However, the majority of these algorithms rely on an explicit parametric model description of the greenhouse. These models are often based on physical laws such as conservation of mass and energy and contain many parameters which should be identified. Due to the complex and nonlinear dynamics of greenhouses, these models might not be applicable to control greenhouses other than the ones for which these models have been designed and identified. Hence, in current horticultural practice these control algorithms are scarcely used. Therefore, the need rises for a control algorithm which does not rely on a parametric system representation but rather on input/output data of the greenhouse system, hereby establishing a way to control the system with unknown or unmodeled dynamics. A recently proposed algorithm, Data-Enabled Predictive Control (DeePC), is able to replace system identification, state estimation and future trajectory prediction by one single optimization framework. The algorithm exploits a non-parametric model constructed solely from input/output data of the system. In this work, we apply this algorithm in order to control the greenhouse climate. It is shown that in numerical simulation the DeePC algorithm is able to control the greenhouse climate while only relying on past input/output data. The algorithm is bench-marked against the Nonlinear Model Predictive (NMPC) algorithm in order to show the differences between a predictive control algorithm that has direct access to the nonlinear greenhouse simulation model and a purely data-driven predictive control algorithm. Both algorithms are compared based on reference tracking accuracy and computational time. Furthermore, it is shown in numerical simulation that the DeePC algorithm is able to cope with changing dynamics within the greenhouse system throughout the crop cycle.@en