Receding Horizon Strategy Research Articles

Multiplayer Homicidal Chauffeur reach-avoid games: A pursuit enclosure function approach

This paper presents a multiplayer Homicidal Chauffeur reach-avoid differential game, which involves Dubins-car pursuers and simple-motion evaders. The goal of the pursuers is to cooperatively protect a planar convex region from the evaders, who strive to reach the region. We propose a cooperative strategy for the pursuers based on subgames for multiple pursuers against one evader and optimal task allocation. We introduce pursuit enclosure functions (PEFs) and propose a new enclosure region pursuit (ERP) winning approach that supports the forward analysis for the strategy synthesis in the subgames. We show that if a pursuit coalition is able to defend the region against an evader under the ERP winning, then no more than two pursuers in the coalition are necessarily needed. We also propose a steer-to-ERP approach to certify the ERP winning and synthesize the ERP winning strategy. To implement the strategy, we introduce a positional PEF and provide the necessary parameters, states, and strategies that ensure the ERP winning for both one pursuer and two pursuers against one evader. Additionally, we formulate a binary integer program using the subgame outcomes to maximize the captured evaders in the ERP winning for the pursuit task allocation. Finally, we propose a multiplayer receding-horizon strategy where the ERP winnings are checked in each horizon, the task is allocated, and the strategies of the pursuers are determined. Numerical examples are provided to illustrate the results.

Collision avoidance for autonomous vehicles using reachability-based trajectory planning in highway driving

As vehicle applications have evolved to a more intelligent and self-driving stage, autonomous vehicles have attracted more attention in recent years. This paper proposes a trajectory planner that considers feasibility, safety and passenger acceptance. This will ensure autonomous vehicles satisfy the constraints of the traffic environment, driving ability, and comfort drivers experience during collision avoidance. This paper deals with planning collision-free trajectories for autonomous vehicles on highways. The problem is formulated using reachability-based planning via zonotope. According to the vehicle dynamics model, the trajectory feasibility is determined by the vehicle motion feasibility set. The next step is to apply safety constraints to the base planner by collision avoidance checking. Given that this planner uses a receding horizon strategy, it selects a safe parameter in each planning iteration. At each stage of planning, the set of reachable vehicles should not intersect with any obstacles. Since braking cannot prevent a collision, this approach consists of lane changing and overtaking maneuvers to avoid collisions. Finally, knowledge from the safety of the intended functionality (SOTIF) standard is utilized to verify the algorithm performance. The efficiency and performance of different driving styles of trajectory planners are verified by vehicle tests under different vehicle velocities and different obstacle disturbances. Satisfactory results are obtained from the set of simulated scenarios.

Byzantine Agents’ Detection in Distributed Nash Equilibrium Seeking Algorithms Using an Adaptive Event-Triggered Scheme

In this article, a resilient, adaptive event-triggered distributed Nash equilibrium seeking algorithm is investigated for a class of multimicrogrid systems. Since the strategy of each microgrid affects others’ costs through total generation cost, such interaction among microgrids is modeled as a noncooperative game. To reduce unnecessary signal transmission among the aggregators, an adaptive algorithm, where threshold parameters are adjusted based on the behavior of the estimated signals in the last two iterations, is proposed. It is observed that when false data is injected into an agent, its estimated signals begin to diverge from the equilibrium point, and as a result, the threshold value becomes increasing. Furthermore, the misbehaving agents are identified and isolated using a reputation-based mechanism and are allowed to rejoin the network when they behave normally again. To deal with arbitrary behavior of users, receding horizon scheme of predictive control is used. Finally, a set of simulation results is presented to evaluate the effectiveness of the suggested algorithm.

Dynamic Data-Driven Application System for Flow Field Prediction with Autonomous Marine Vehicles

Efficiently predicting high-resolution and accurate flow fields through networked autonomous marine vehicles (AMVs) is crucial for diverse applications. Nonetheless, a research gap exists in the seamless integration of data-driven flow modeling, real-time data assimilation from flow sensing, and the optimization of AMVs’ sensing strategies, culminating in a closed-loop dynamic data-driven application system (DDDAS). This article presents a novel DDDAS that systematically integrates flow modeling, data assimilation, and adaptive flow sensing using networked AMVs. It features a hybrid data-driven flow model, uniting a neural network for trend prediction and a Gaussian process model for residual fitting. The neural network architecture is designed using knowledge extracted from historic flow data through tidal harmonic analysis, enhancing its capability in flow prediction. The Kriged ensemble transform Kalman filter is introduced to assimilate spatially correlated flow-sensing data from AMVs, enabling effective model learning and accurate spatiotemporal flow prediction, while forming the basis for optimizing AMVs’ flow-sensing paths. A receding horizon strategy is proposed to implement non-myopic optimal path planning, and a distributed strategy of implementing Monte Carlo tree search is proposed to solve the resulting large-scale tree searching-based optimization problem. Computer simulations, employing underwater gliders as sensing networks, demonstrate the effectiveness of the proposed DDDAS in predicting depth-averaged flow in nearshore ocean environments.

Two-step optimization algorithm for energy management and active-reactive power commands for real-time operation of hybrid microgrids

This paper proposes a two-step optimization algorithm for energy management and optimal control of activereactive power commands in microgrids. The first step ensures an optimal energy management and provides the active power setpoints for power plants and energy storage. The second step calculates the voltage setpoints for power plants and reactive power flows whilst minimizing power transmission losses. This work focuses on the second step of the algorithm and the framework to combine both. A previous study introduces the first step based on a receding-horizon scheme. It is analysed and discussed the performance of the algorithm against two decentralized methods widely used in the literature. The results show that the proposed algorithm reduces power transmission losses by more than 20% compared to other methods.

Nonlinear receding-horizon filter approximation with neural networks for fast state of charge estimation of lithium-ion batteries

An important component of electric vehicles is the Battery Management System (BMS), whose main objective is to monitor the state of charge (SoC) of the battery, which can significantly impact the vehicle’s autonomy. The SoC may be estimated using filtering algorithms; in this context, higher accuracy and computational complexity are of great importance. The present paper aims to propose receding-horizon strategies, namely Moving-Horizon State Estimation (MHSE) and Neural Network Moving-Horizon Estimation (NNMHE), for SoC estimation. MHSE is based on a constrained optimization problem, with information of measured samples along a larger observation window, which ensures high accuracy and robustness but requires a better processing capacity. Simulated results are obtained through this method, and it is demonstrated its capacity to jointly estimate the states and the unknown lumped parameters of the battery model using an augmented states formulation. The accuracy of MHSE in the process is high enough that its results may be used for training the NNMHE, so that a machine learning-based solution, with reduced processing time, is found. In this proposed method, a Neural Network is used to emulate the optimization problem solver, by which faster and approximate results are obtained. This approach is evaluated with an experimental dataset, achieving a coefficient of determination of almost 99% and about 20 times faster, which proves that it is effective and can be readily employed in an embedded systems application requiring less computational resources.

From Online Systems Modeling to Fault Detection for a Class of Unknown High-Dimensional Distributed Parameter Systems

Fault detection for distributed parameter systems reported so far is model-based in general and the performance heavily relies on the prior known model information. This restricts the usability of these methods in industrial applications. In this paper, we make the first attempt to establish a brand-new framework that contains both on-line systems modeling and fault detection of unknown high-dimensional DPSs. These two parts interact with each other in the sense that the systems modeling error is transformed into the residual signal for fault detection while the on-line modeling switches to off-line mode depending on the fault detection results. The high-dimensional DPSs are first decomposed into spatial features and temporal sequences. Then a receding-horizon scheme is applied for the temporal dynamics learning and the residual signal is converted by the temporal validation error. Experiments on sensor faults diagnosis for the thermal process of a 2-D battery cell are provided for method validation.

Bi-level ramp merging coordination for dense mixed traffic conditions

Connected and Autonomous Vehicles (CAVs) hold great potential to improve traffic efficiency, emissions and safety in freeway on-ramp bottlenecks through coordination between mainstream and on-ramp vehicles. This study proposes a bi-level coordination strategy for freeway on-ramp merging of mixed traffic consisting of CAVs and human-driven vehicles (HDVs) to optimize the overall traffic efficiency and safety in congested traffic scenarios at the traffic flow level instead of platoon levels. The macro level employs an optimization model based on fundamental diagrams and shock wave theories to make optimal coordination decisions, including optimal minimum merging platoon size to trigger merging coordination and optimal coordination speed, based on macroscopic traffic state in mainline and ramp (i.e., traffic volume and penetration rates of CAVs). Furthermore, the micro level determines the real platoon size in each merging cycle as per random arrival patterns and designs the coordinated trajectories of the mainline facilitating vehicle and ramp platoon. A receding horizon scheme is implemented to accommodate human drivers’ stochastics as well. The developed bi-level strategy is tested in terms of improving efficiency and safety in a simulation-based case study under various traffic volumes and CAV penetration rates. The results show the proposed coordination addresses the uncertainties in mixed traffic as expected and substantially improves ramp merging operation in terms of merging efficiency and traffic robustness, and reducing collision risk and emissions, especially under high traffic volume conditions.

Model Predictive Control of Time-Varying Aberrations for Sensorless Adaptive Optics

We propose a model predictive control (MPC) method to compensate for the time-varying phase aberrations in a sensorless adaptive optics (AO) system. The approximate model for the point spread function (PSF) of the imaging system with phase diversity is mathematically derived, and its validity is verified. The proposed MPC, which considers the operating limits of the deformable mirror (DM), computes the optimal applied voltage of each actuator over a prediction horizon, and the receding horizon scheme is applied as feedback control. Numerical case studies with the time-varying phase aberrations generated by an atmospheric turbulence simulator are presented to demonstrate the correction performance of the MPC strategy. The proposed method caused a 50% improvement in the reduction in residual aberration, making it competitive with a saturation linear quadratic regulator (LQR). The computational feasibility of the proposed method is validated using fast MPC, which approximates the primal barrier method.

Model-based predictive control of multi-stage air-source heat pumps integrated with phase change material-embedded ceilings

This paper presents a model-based predictive control strategy to optimize the operations of phase change material (PCM) ceiling panels coupled with a multi-stage air-source heat pump. A three-stage prototype heat pump unit has been built and tested in the laboratory, with the low and medium stages designed for space heating/cooling and the high compression stage dedicated to charging of the PCM energy storage. To facilitate optimal control of the integrated heat pump system, a mixed-integer linear programming formulation is derived through linearization of the heat pump model and a mixed-integer reformulation of the PCM dynamic governing equations. A predictive control strategy is synthesized based on the resultant control formulation and implemented in a receding horizon scheme that optimizes the PCM charging and the zone temperature schedules simultaneously to leverage both the passive (associated with building construction materials) and active (PCM) storage capacities of a building. The control strategy has been tested along with three benchmarking control scenarios using a co-simulation platform for a prototypical detached house in Atlanta, GA. Test results showed that application of the proposed control strategy to the PCM-integrated heat pump could provide 27.1% electricity cost savings while a fine tuned rule-based control strategy could achieve cost savings of 20.4%, compared to a baseline case without PCM storage, under a time-of-use rate tariff.

Moving horizon estimation of vehicle state and parameters

For the active safety control of the vehicle, it is extremely important to estimate the vehicle state in real-time and accurately during the driving process. A joint state and parameter estimation method based on QR decomposition and receding horizon estimation (RHE) is proposed. Firstly, by introducing the receding horizon strategy, the authors optimized the state and parameter estimation with a fixed number of variables, which can better deal with the estimation problem of time-varying parameters. Then, based on the principle of forward dynamic programming, the calculation of arrival cost is transformed into a least square equation, which is solved by QR decomposition. At the same time, an update method of arrival cost based on QR decomposition is given. In this way, the whole receding horizon estimation method is based on the optimization, and the feedback mechanism is introduced to improve the estimation accuracy and speed. The simulation results show that the accuracy of receding horizon estimation is obviously better than that of unscented Kalman filter (UKF), and the arrival cost update method based on QR decomposition is more convenient than the traditional arrival cost update method based on error covariance estimation.

N-GKLS: An NMPC problem generator and a test platform for NMPC solvers

Nonlinear Model Predictive Control (NMPC) solves a series of optimization problems online during the entire operational time of the controlled plant, and the performance of NMPC depends on the superiority of the solver embedded in NMPC. Traditionally, gradient-based deterministic methods are used as NMPC solvers, but metaheuristics are now becoming more and more popular for its ability to find the global optimal solution. In order to verify the superiorities of different algorithms to be NMPC solvers, a novel NMPC problem generator named NMPC-based GKLS generator (N-GKLS) is proposed. With the help of Optimal-Replace Method (ORM), a reliable comparison of the closed-loop performances result from receding horizon strategy in NMPC is guaranteed. In addition, comparison techniques named accumulated operational characteristic and accumulated operational zone are proposed to directly compare different optimization algorithms for solving various NMPC problems generated by N-GKLS. An auxiliary comparison table is also proposed to report numerical comparative results. In this way, N-GKLS is not only an NMPC problem generator, but also a test platform for verifying the superiorities of different algorithms as NMPC solvers. Finally, simulation results based on 8 metaheuristics and 3 deterministic methods are used to illustrate the effectiveness of the proposed N-GKLS. A corresponding MATLAB APP demo is designed and is available online: https://github.com/JiahongXu123/N-GKLS.

An efficient MPC algorithm for switched systems with minimum dwell time constraints

This paper presents an efficient suboptimal model predictive control (MPC) algorithm for nonlinear switched systems subject to minimum dwell time constraints (MTC). While MTC are required for most physical systems due to stability, power and mechanical restrictions, MPC optimization problems with MTC are challenging to solve. To efficiently solve such problems, the on-line MPC optimization problem is decomposed into a sequence of simpler problems, which include two nonlinear programs (NLP) and a rounding step, as typically done in mixed-integer optimal control (MIOC). Unlike the classical approach that embeds MTC in a mixed-integer linear program (MILP) with combinatorial constraints in the rounding step, our proposal is to embed the MTC in one of the NLPs using move blocking. Such a formulation can speedup on-line computations by employing recent move blocking algorithms for NLP problems and by using a simple sum-up-rounding (SUR) method for the rounding step. An explicit upper bound of the integer approximation error for the rounding step is given. In addition, a combined shrinking and receding horizon strategy is developed to satisfy closed-loop MTC. Recursive feasibility is proven using a l-step control invariant (l-CI) set, where l is the minimum dwell time step length. An algorithm to compute l-CI sets for switched linear systems off-line is also presented. Numerical studies show significant speed-up and comparable control performance of the proposed MPC algorithm against the classical approach, though at the cost of significant solution quality degradation especially when the MTC are large.

Receding Moving Object Segmentation in 3D LiDAR Data Using Sparse 4D Convolutions

A key challenge for autonomous vehicles is to navigate in unseen dynamic environments. Separating moving objects from static ones is essential for navigation, pose estimation, and understanding how other traffic participants are likely to move in the near future. In this work, we tackle the problem of distinguishing 3D LiDAR points that belong to currently moving objects, like walking pedestrians or driving cars, from points that are obtained from non-moving objects, like walls but also parked cars. Our approach takes a sequence of observed LiDAR scans and turns them into a voxelized sparse 4D point cloud. We apply computationally efficient sparse 4D convolutions to jointly extract spatial and temporal features and predict moving object confidence scores for all points in the sequence. We develop a receding horizon strategy that allows us to predict moving objects online and to refine predictions on the go based on new observations. We use a binary Bayes filter to recursively integrate new predictions of a scan resulting in more robust estimation. We evaluate our approach on the SemanticKITTI moving object segmentation challenge and show more accurate predictions than existing methods. Since our approach only operates on the geometric information of point clouds over time, it generalizes well to new, unseen environments, which we evaluate on the Apollo dataset.

Perception-Aware Planning for Active SLAM in Dynamic Environments

This paper presents a perception-aware path planner for active SLAM in dynamic environments using micro-aerial vehicles (MAV). The “Next-Best-View” planner (NBVP planner) is combined with an active loop closing, which is called the Active Loop Closing Planner (ALCP planner). The planner is proposed to avoid both static and dynamic obstacles in unknown environments while reducing the uncertainty of the SLAM system and further improving the accuracy of localization. First, the receding horizon strategy is adopted to find the next waypoint. The cost function that combines the exploration gain and the loop closing gain is designed. The former can reduce the mapping uncertainty, while the latter takes the loop closing possibility into consideration. Second, a key waypoint selection strategy is designed. The selected key waypoints, instead of all waypoints, are treated as potential loop-closing points to make the algorithm more efficient. Moreover, a fuzzy RRT-based dynamic obstacle avoidance algorithm is adopted to realize obstacle avoidance in dynamic environments. Simulations in different challenging scenarios are conducted to verify the effectiveness of the proposed algorithm.

Matching-based capture strategies for 3D heterogeneous multiplayer reach-avoid differential games

This paper studies a 3D multiplayer reach-avoid differential game with a goal region and a play region. Multiple pursuers defend the goal region by consecutively capturing multiple evaders in the play region. The players have heterogeneous moving speeds and the pursuers have heterogeneous capture radii. Since this game is hard to analyze directly, we decompose the whole game as many subgames which involve multiple pursuers and only one evader. Then, these subgames are used as a building block for the pursuer–evader matching. First, for multiple pursuers and one evader, we introduce an evasion space (ES) method characterized by a potential function to construct a guaranteed pursuer winning strategy. Then, based on this strategy, we develop conditions to determine whether a pursuit team can guard the goal region against one evader. It is shown that in 3D, if a pursuit team is able to defend the goal region against an evader, then at most three pursuers in the team are necessarily needed. We also compute the value function of the Hamilton–Jacobi–Isaacs (HJI) equation for a special subgame of degree. To capture the maximum number of evaders in the open-loop sense, we formulate a maximum bipartite matching problem with conflict graph (MBMC). We show that the MBMC is NP-hard and design a polynomial-time constant-factor approximation algorithm to solve it. Finally, we propose a receding horizon strategy for the pursuit team where in each horizon an MBMC is solved and the strategies of the pursuers are given. We also extend our results to the case of a bounded convex play region where the evaders escape through an exit. Two numerical examples are provided to demonstrate the results.

Improvement of Airport Surface Operation at Tokyo International Airport Using Optimization Approach

Congestion and delays occur on airport surfaces as a result of a rapid increase in the demand for air transport. The aim of this study is to determine the differences between optimized and observed operations to improve airport surface operation at Tokyo International Airport by using mixed-integer linear programming to minimize the total ground movement distance and time based on real-time flight information. Receding horizon schemes are considered to adapt to dynamic environments. The model obtains results that reduce the taxi distance by 18.54% and taxi time by 29.77% compared with the observed data. A comparison of taxiway usage patterns between the optimization results and observed data provides insight into the optimization process, for example, changes in runway cross strategies and taxiway direction rules. Factors such as the objective function weights and airline–terminal relationship were found to significantly affect the optimization result. This study suggests improvements that can be made at airports to achieve a more efficient surface operation.

The scheduling of alkaline water electrolysis for hydrogen production using hybrid energy sources

This paper presents a scheduling approach to maximize the profitability of alkaline water electrolysis (AWE) coupled with hybrid energy sources. AWE combined with solar power can produce extremely pure and green hydrogen. However, the capital investment of solar-powered AWE plant is still high, and thus its operating profitability should be carefully optimized. To this end, optimization-based operations are developed to schedule AWE productions with solar power and grid electricity supply. The AWE is modeled by computational fluid dynamics (CFD) software to obtain its polarization curve and efficiency. The solar power prediction, time-of-use (TOU) price, startup cost, and demand constraints are integrated with the AWE operational characteristics to form single-step and multi-step optimization formulas. The scheduling plan is determined by rapidly solving those formulas to global optimality. The case studies show that (i) AWE power consumption should follow the solar energy generation profile from 8 AM to 4 PM if TOU price is high; (ii) multi-step optimization with the receding horizon strategy can improve the AWE profitability; (iii) producing hydrogen is more profitable than selling PV electricity back to grid; (iv) PV capacity impacts the levelized cost of hydrogen, and thus should be carefully selected.

An MILP approach for persistent coverage tasks with multiple robots and performance guarantees

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.

Game-Based Lateral and Longitudinal Coupling Control for Autonomous Vehicle Trajectory Tracking

In this paper, we propose a game-based coupling controller to solve the problem of autonomous vehicles in the trajectory tracking process. The controller ensures path tracking accuracy and shows good tracking performance for the desired speed profile that changes based on navigation while driving. Furthermore, it improves ride comfort and addresses the lateral stability problems that occur when applying classical model predictive control (MPC) controllers. We implemented this controller to plan the trajectory by considering the fundamental interaction between longitudinal and lateral vehicle dynamics, as well as to track the trajectory by using a receding horizon strategy. A comparative study was conducted to compare the proposed controller with the classical MPC controller. Based on CarMaker-Matlab/Simulink co-simulations, this controller outperformed the classical MPC in terms of trajectory tracking performance. Moreover, it exhibits excellent ride comfort and lateral stability that passengers will experience.