Receding Horizon Optimization Research Articles

General Optimal Trajectory Planning: Enabling Autonomous Vehicles with the Principle of Least Action

This study presents a general optimal trajectory planning (GOTP) framework for autonomous vehicles (AVs) that can effectively avoid obstacles and guide AVs to complete driving tasks safely and efficiently. Firstly, we employ the fifth-order Bezier curve to generate and smooth the reference path along the road centerline. Cartesian coordinates are then transformed to achieve the curvature continuity of the generated curve. Considering the road constraints and vehicle dynamics, limited polynomial candidate trajectories are generated and smoothed in a curvilinear coordinate system. Furthermore, in selecting the optimal trajectory, we develop a unified and auto-tune objective function based on the principle of least action by employing AVs to simulate drivers’ behavior and summarizing their manipulation characteristics of “seeking benefits and avoiding losses.” Finally, by integrating the idea of receding-horizon optimization, the proposed framework is achieved by considering dynamic multi-performance objectives and selecting trajectories that satisfy feasibility, optimality, and adaptability. Extensive simulations and experiments are performed, and the results demonstrate the framework’s feasibility and effectiveness, which avoids both dynamic and static obstacles and applies to various scenarios with multi-source interactive traffic participants. Moreover, we prove that the proposed method can guarantee real-time planning and safety requirements compared to drivers’ manipulation.

Receding Horizon Optimization for Cooperation of Connected Vehicles at Signal-Free Intersections under Mixed-Automated Traffic

This paper proposes a distributed coordination scheme for connected vehicles, including automated vehicles (AVs) and manual vehicles (MVs), at signal-free intersections. The cooperation issue of vehicles at an intersection is formulated into a multi-objective optimization problem that aims to eliminate conflicts and improve traffic mobility and fuel economy. For this purpose, the future trajectories of AVs and MVs are predicted by the respective car-following models, and are shared with neighboring vehicles in conflict relationships. The proposed scheme optimizes the sum of the performance of AVs within the cooperative zone in a prediction horizon. A distributed optimization algorithm in the receding horizon is presented to obtain the local optimal solutions, and is tested in simulations with different demand levels and penetration rates of AVs. The results show that the proposed scheme reduces travel time by 29.7–45.5% and 34.5–49.2%, and decreases fuel consumption by 27.6–35.3% and 21.6–29.9% under 70–100% penetration rates of AVs, compared to the no-control operation and fixed-time signal control strategy. In addition, a comparison simulation with the strategy of jointly optimizing the vehicle trajectory and signal timing is conducted to evaluate the relative merits of the proposed scheme.

Eco-Driving Control of Connected and Automated Vehicles Using Neural Network–Based Rollout

Abstract Connected and autonomous vehicles have the potential to minimize energy consumption by optimizing the vehicle velocity and powertrain dynamics with Vehicle-to-Everything info en route. Existing deterministic and stochastic methods created to solve the eco-driving problem generally suffer from high computational and memory requirements, which makes online implementation challenging. This work proposes a hierarchical multi-horizon optimization framework implemented via a neural network. The neural network learns a full-route value function to account for the variability in route information and is then used to approximate the terminal cost in a receding horizon optimization. Simulations over real-world routes demonstrate that the proposed approach achieves comparable performance to a stochastic optimization solution obtained via reinforcement learning, while requiring no sophisticated training paradigm and negligible on-board memory.

Cooperative Merging Strategy in Mixed Traffic Based on Optimal Final-State Phase Diagram With Flexible Highway Merging Points

The cooperation between connected and automated vehicles (CAVs) has emerged as a promising way to improve traffic efficiency and safety for ramp merging on highways. Existing research mostly focused on the collaboration of individual CAVs, while the cooperative merging strategy in mixed traffic considering vehicle platoons has been less explored. To address the above problem, this study aims to build connections between sequence scheduling and motion planning in mixed traffic, where individual CAVs, CAVs platoons, and mixed platoons coexist. First, optimal control strategies are presented for vehicles with flexible merging points based on Pontryagin’s minimum principle (PMP), and the final vehicle states in variable conditions are summarized in a phase diagram. Subsequently, the optimal final-state phase diagram is introduced into the passing sequence tree search process, which is designed for different vehicle groups in mixed traffic. Heuristic pruning rules are added to the depth-first search strategy to facilitate finding the optimal solution. Finally, an event-triggered receding horizon optimization algorithm is developed for continuous implementation. The numerical simulations are conducted in multiple traffic volumes, and the simulation results reveal that our proposed algorithm significantly improves the overall traffic efficiency and reduces vehicle-passing delays compared with the traditional FIFO-based cooperation method.

Online trajectory optimization for safe autonomous overtaking with active obstacle avoidance

Autonomous driving with active obstacle avoidance in dynamic urban environment has attracted significant attention to improve road safety and traffic efficiency. In this paper, an online optimization-based trajectory planning method for autonomous overtaking is developed to prevent collision and realize safe efficient driving. Unlike traditional methods which solve the overtaking problem with segmented reference path in multi-stages with integer variables, this paper proposes a novel dual-variable trajectory planning framework to get the optimal trajectory for active collision avoidance. First, the nonlinear non-differentiable collision-free constraint between vehicles is reformulated using dual problem optimization. Then, the optimal trajectory for longitudinal and lateral movement is obtained jointly in a receding horizon optimization framework based on the optimized dual variable considering the safety and dynamic performance. The key novelty lies in the reformulation of the nonlinear optimal trajectory planning problem and the formulated whole optimization framework can be solved using efficient open-source solvers for online computation. Simulation studies in different dynamic cases are provided to show the efficiency and robustness for safe driving. The method reaches safe overtaking performance with much less calculation time. Real-world experiment with a static obstacle demonstrates its capability for the safe efficient trajectory planning and online implementation in autonomous driving.

A hybrid receding horizon optimization and active disturbance rejection control of boiler superheated steam temperature

Efficient control of superheated steam temperature is critical for maintaining the safety and efficiency of a power plant boiler. Exceeding the safe temperature range can cause irreversible damage. However, unknown disturbances and uncertainties, as well as large delay dynamics, often make superheated steam temperature safety control challenging. To this end, this paper proposes a hybrid bi-level safety control for superheated steam temperature control in a power plant boiler. The bottom level uses active disturbance rejection control, while upper level uses receding horizon optimization. The proposed method combines the advantages of active disturbance rejection control in solving unknown disturbances and the dynamic optimization of receding horizon optimization to effectively and safely control superheated steam temperature and optimize the control system performance. The main novelty of the scheme lies in making receding horizon optimization independent of the model of the plant, in terms of making full use of the closed-loop desired dynamics under active disturbance rejection control. Practical synthesis design methods are also presented to illustrate the tuning and optimization of this control strategy. On-site testing results show that the proposed method improves both disturbance rejection and tracking performance, with improvements of at least 20 % over comparison methods. In conclusion, the proposed bi-level control strategy is a promising approach for improving the safety and efficiency of power plants.

Synchronization control of blanket remote maintenance robot based on MPC-CCC algorithm

AbstractThis paper studies the synchronization control of the blanket remote maintenance robot (BRMR) of the China fusion engineering test reactor (CFETR). First, the general state space mathematical model of BRMR was established by using a physical-based method. Second, based on the receding horizon optimization of model predictive control (MPC) and cross-coupling error reduction in cross-coupling control (CCC), the innovative MPC-CCC controller was proposed to realize the single-system and multisystem error convergence and high accuracy transportation of blanket through the high accuracy synchronization control of BRMR. Third, to verify the control effectiveness of the MPC-CCC controller, two types of simulations and experiments were implied compared with the original proportional-integral (PI) controller in Mover. Results showed that simulation and experiments were highly consistent. It is found that the use of an MPC-CCC controller can result in up to a 70% reduction in displacement error and up to a 59% reduction in synchronization error compared to the PI controller. And the accuracy of the MPC-CCC controller satisfies the real requirement of the maintenance process of the blanket. This work provides the theoretical basis and practical experience for the highly stable, safe, and efficient maintenance of blankets in the future.

Self-learning sliding mode control based on adaptive dynamic programming for nonholonomic mobile robots

This paper proposes a self-learning sliding mode control (SlSMC) strategy with stability guarantee for the trajectory tracking of nonholonomic mobile robots (NMRs) under matched uncertainties, which improves the control performance of NMRs by optimizing the reaching law and the sliding mode surface of SMC as well as retaining the finite-time convergence and the robustness to uncertainties. In the presence of adverse factors such as skidding, slipping and environmental noise, the kinematic model of NMRs is reconstructed and an integral terminal sliding mode controller is designed for the trajectory tracking of NMRs. Then, based on the sliding mode controller, the proposed control strategy formulates the optimization of the SMC’s reaching law and the sliding mode surface under stability constraints as two asynchronous optimal control problems with control constraints. Meanwhile, an online continuous-time receding-horizon optimization mechanism based on an actor-critic algorithm is proposed to solve the optimal problems asynchronously and improve online learning efficiency. The stability and the convergence of the proposed strategy are validated both in theory and simulations. Furthermore, extensive contrastive simulation results illustrate that the proposed receding horizon learning-based control strategy outperforms three recent methods in control performance. Finally, experiments of the proposed self-learning SMC strategy are carried out based on a real intelligent vehicle, and the experimental results also verify that the proposed method can meet the actual control needs of NMRs.

Tire-Road Peak Adhesion Coefficient Estimation Based on Multisource Information Assessment

The tire-road peak adhesion coefficient (TRPAC) is defined as the ratio of the peak adhesion to the vertical load of the tire, which can characterize the ability of a tire to adhere to the road. Reliable TRPAC estimation can not only benefit the vehicle active safety system, but also serve the intelligent transportation system to improve the safety of traffic participants. Considering the problems of low estimation accuracy and poor real-time performance caused by low-quality sensor information in existing TRPAC estimation methods, a TRPAC fusion estimation framework based on the assessment of multisource information quality is proposed in this paper. Based on the observability theory of nonlinear systems, a quantitative indicator of dynamic information quality denoted as the excitation level is established. The region of effective excitation is defined as the criterion for starting and stopping the proposed dynamics-based fusion estimator for the longitudinal-lateral coupling condition. Considering occupant comfort and vehicle stability, an active enhancement method based on hierarchical model predictive control is designed to actively improve the excitation level. Based on the receding horizon optimization theory, a dynamics-image-based fusion estimator is proposed to make full use of visual and dynamic information. An adaptive fusion estimation strategy is then proposed to apply the proper estimation working mode according to the multisource information quality. The results of the simulation and vehicle test show that the proposed framework can still perform competitively when the quality of multisource information is poor and achieve reliable TRPAC estimation.

Real-Time Application of Robust Offset-Free MPC in Maglev Planar Machine

This paper improves the transient response of a magnetically levitated (maglev) planar machine through the model predictive control (MPC) benefiting from explicitly incorporating the tightened constraints of the input vector. The maglev system is characterized as a second-order linear model via the inverse model method to facilitate the fast online receding horizon optimization. The estimated lumped disturbance compensates for the deviations of the prediction caused by the unmodeled errors, so the obtained control signals eventually eliminate the steady-state errors. The robust stability of the motion control system is guaranteed by a reasonable horizon length without requiring the state constraints, which reduces the computational burden for the real-time implementation. Experimental results demonstrate that the proposed controller outperforms the anti-windup PID controller, switching linear quadratic regulator, baseline MPC, and nonlinear MPC in terms of the trajectory tracking.

Generalized Predictive Current Control for Dual-Three-Phase PMSM to Achieve Torque Enhancement Through Harmonic Injection

The output torque capability of a dual-three-phase permanent magnet synchronous machine (DTP-PMSM) can be increased by intentionally injecting proper harmonic currents, which can be beneficial in some applications that require high torque density. To achieve this, current references containing multiple harmonic components with time-varying frequencies must be accurately tracked by the current controllers, which can hardly be achieved by conventional control methods. Fortunately, to track these complex but predetermined current references, generalized predictive control (GPC) shows unique advantages for its characteristic of multi-step prediction and receding horizon optimization. In this paper, a current control strategy based on GPC is proposed for the DTP-PMSM, which enhances the output torque capability by tracking the harmonic current references with high accuracy in both phase and magnitude. Parameter tuning and model mismatch issues of the proposed GPC are discussed. The effectiveness and merits of the proposed control strategy are validated by comparison study based on simulation and experiments.

Receding Horizon Optimization of Ethylene Cracking Operation and Scheduling under Supply Chain Fluctuations

The global supply chain is experiencing ongoing turmoil after COVID-19, which inevitably affects the supply and demand of the chemical industry. Ethylene plants are regarded as one of the most profitable chemical industry chains, and thus, there is a need to track fluctuations in the supply chain and responsively adjust their operations and scheduling decisions to achieve optimal economic benefits. However, previous studies about ethylene cracking optimization are mostly limited to fixed supply chain parameters and cannot meet the need for real-time updates according to supply chain fluctuations. To address this problem, we propose an ethylene cracking optimization framework which combines parameter prediction and receding horizon optimization (predictive RHO) for real-time optimal operation and scheduling under supply chain fluctuations. This optimization framework uses historical supply chain data (supply quantities, feedstock prices, and product prices) to predict future parameters and uses the predicted parameters to optimize the operation and scheduling of ethylene cracking furnace systems in a receding horizon way. Two industrial case studies were used to validate the efficacy of the proposed optimization framework. In case 1, the predictive-RHO framework achieved comparable economic profits of 147,370 and 146,483 $/day without violating daily inventory constraints (vs 151,204 $/day from the original model violating inventory constraints) and a faster calculation speed of 40 s (vs 32 min) under two fluctuating feed supply modes. In case 2, predictive RHO improves economic profits by 1.8% through integrating operations with scheduling and 1.1% by tracking the feed and product price fluctuations. These two cases show the strong capability of predictive RHO in tracking supply chain fluctuations and improving the inventory management level as well as the economic profits of ethylene cracking plants.

Eco-Driving Cruise Control for 4WIMD-EVs Based on Receding Horizon Reinforcement Learning

Aiming to improve the distance per charge of four in-wheel independent motor-drive electric vehicles in intelligent transportation systems, a hierarchical energy management strategy that weighs their computational efficiency and optimization performance is proposed. According to the information of an intelligent transportation system, a method combining reinforcement learning with receding horizon optimization is proposed at the upper level, which solves the cruising velocity for eco-driving in a long predictive horizon based on the online construction of a velocity planning problem. At the lower level, a multi-objective optimal torque allocation method that considers energy saving and safety is proposed, where an analytical solution based on the state feedback control was obtained with the vehicle following the optimal speed of the upper level and tracking the centerline of the target path. The energy management strategy proposed in this study effectively reduces the complexity of the intelligent energy-saving control system of the vehicle and achieves a fast solution to the whole vehicle energy optimization problem, integrating macro-traffic information while considering both power and safety. Finally, an intelligent, connected hardware-in-the-loop (HIL) simulation platform is built to verify the method formulated in this study. The simulation results demonstrate that the proposed method reduces energy consumption by 12.98% compared with the conventional constant-speed cruising strategy. In addition, the computational time is significantly reduced.

Quantum parallel model predictive control for grid-connected solid oxide fuel cells

The fuel utilization of the grid-connected solid oxide fuel cells (GSOFCs) controlled by model predictive control (MPC) and proportional–integral–derivative (PID) controller is 80.0%, which should be improved. MPC obtains the local optimal control strategy online when the power demand change. The predicted accuracy of MPC should be efficiently improved when the system is in a dynamic environment. This work proposes quantum parallel model predictive control (QPMPC) to solve the optimal local problem of MPC. The QPMPC contains one real-life quantum MPC and three virtual parallel quantum MPC controllers. The quantum revolving gate of the QPMPC can achieve more information about the optimal solution, greatly improving the solution efficiency and effectiveness. The MPC of the QPMPC obtains a current optimal strategy determined by online receding-horizon optimization for minimizing control errors. The QPMPC obtains higher prediction accuracy and better ability of power tracking. The QPMPC for GSOFC can save fuel consumption and improve the economy of renewable power generation. The QPMPC for GSOFC achieves higher fuel utilization of hydrogen (82.0%) than MPC (80.0%), PID (80.0%), reinforcement learning (80.0%), fuzzy control (80.0%) and sliding mode control (79.7%).

Nonlinearities compensation of a parallel piezostage using discrete-time sliding mode predictive control with decoupling and damping properties

Parallel piezostages have been prevalently applied in the micro-/nano-positioning field, but, unluckily, suffer from the undesired effects, like creep, hysteresis, vibration, cross coupling, and input saturation. To eliminate these nonlinearities, a new discrete-time sliding mode predictive control (DSMPC) with decoupling and damping properties (DSMPC-DDP) is proposed for a parallel six-axis piezostage devoted to cell micromanipulation. Firstly, a state-space-based decoupler is applied to make the MIMO system decoupled into six SISO subsystems, and then a damping compensator via the notch filter principle is selected to suppress the high-frequency vibration dynamics of six subsystems. After that, a feedback DSMPC law is designed for each decoupled and damped subsystem. Unlike the traditional linear model predictive control (MPC), the feedback DSMPC is developed based on a nonlinear discrete-time terminal sliding mode prediction model, leading to stronger robustness and faster convergence speed. Through the utilization of the receding horizon optimization, the sliding mode states are optimized to explicitly deal with the input constraints. The stability of the closed-loop subsystems is analyzed based on the terminal constraint theory. Finally, the effectiveness and superiority of the proposed controller is validated by a series of experimental tests. Results show that the proposed DSMPC-DDP scheme can achieve higher tracking accuracy and control bandwidth than the existing proportional–integral (PI) and MPC methods in the context of abovementioned nonlinearities.

Nonlinear model predictive control-based active power dispatch strategy for wind power plant considering dynamic wake effect

Inappropriate active power dispatch strategies can diminish the active power support capability (APSC) of the wind power plant (WPP) due to the wake effect. In existing strategies, the WPP’s APSC and the time delay of wake effect are not thoroughly investigated. This paper proposes an active power dispatch strategy to increase the WPP’s APSC while tracking the power reference. First, WPP’s temporary and sustained APSCs are analyzed considering dynamic wake effect. Correspondingly, the total stored kinetic energy and increasable power of WPP are introduced as evaluation indicators of the capabilities. Furthermore, a bi-level control framework is proposed to accomplish the dispatch task in different timescales. Aiming at improving WPP’s temporary and sustained APSCs comprehensively, the operating status references of each WT, including the power reference and pitch angle, are optimized in the WPP layer. Taking the time delay and nonlinearity of wake effect into account, the receding horizon optimization is solved in a finite time domain using nonlinear model predictive control (NMPC). During the sampling interval of the NMPC, a coordinated control in the WT layer is developed to modify the active power reference dispatched by the WPP layer in case the wind speed fluctuates. Finally, extensive case studies show that the WPP’s temporary and sustained APSCs are improved with the proposed strategy in different wind conditions and power references.

Integrated behaviour decision-making and trajectory tracking for dynamic collision avoidance of an ASV using receding horizon optimisation

This paper develops a receding horizon optimisation scheme for integrated behaviour decision-making and trajectory tracking to ensure the dynamic collision avoidance of an autonomous surface vessel (ASV). We apply Q-learning to make behaviour decisions because manoeuvring habit requirements and COLREGS must be satisfied in dynamic collision avoidance scenarios. The heading course and vessel speed are considered to transmit the outcome of behaviour decision-making to a trajectory tracking model predictive control (MPC) controller. Next, a trajectory tracking nonlinear controller for the ASV is developed within the MPC framework, in which a set of nonlinear constraints is designed for collision avoidance. Specifically, depending on the heading course and vessel speed, the collision avoidance constraints can be switched to allow the controller to execute the behaviour decision. Simulation results verify the effectiveness of the proposed receding horizon optimisation scheme.

HISS: A Pedestrian Trajectory Planning Framework Using Receding Horizon Optimization

The paper proposes a generative pedestrian trajectory modeling framework named HISS - Human Interactions in Shared Space. The trajectory modeling framework is based on a receding horizon optimization approach utilizing pedestrian behavior and interactions that seeks to capture pedestrian trajectory planning and execution. The benefit of the proposed dynamic optimization trajectory generation approach is that it requires minimal calibration data under a variety of traffic scenarios. In this paper, we formalize several pedestrian-pedestrian interaction scenarios and implement trajectories’ conflict avoidance through mixed integer linear programming (MILP). We validate the proposed framework on two benchmark datasets - DUT and TrajNet++. The paper shows that when the framework’s parameters are tuned to certain initial conditions and pedestrian behavior and interaction rules, the framework generates pedestrian trajectories similar to those observable in real-world scenarios, justifying the framework’s capability to provide explanations and solutions to various traffic situations. This feature makes the proposed framework useful for modelers and urban city planners in making policy decisions.

Trajectory-dependent Control Lyapunov Functions for Discrete-time Switched Systems⋆

A method for control of discrete-time switched systems based on parameterized Lyapunov functions is presented. A polynomial representation of the switched system is formulated, and the method of moments is applied to obtain a relaxed model. The control problem is recast as an online receding horizon optimization problem where the Lyapunov function parameters and moment sequences are the decision variables. A novel procedure to synthesize the switching control signal from the recovered measure is described. The method is illustrated in simulation for the case of a pulse-width modulated multicellular converter, showing good reference tracking results.

A Concurrent Switching Model for Traffic Congestion Control

We introduce a new conservation-based approach for traffic coordination modeling and control in a network of interconnected roads (NOIR) with switching movement phase rotations at every NOIR junction. For modeling of traffic evolution, we first assume that the movement phase rotation is cyclic at every NOIR junction, but the duration of each movement phase can be arbitrarily commanded by traffic signals. Then, we propose a novel concurrent switching dynamics (CSD) with deterministic transitions among a finite number of states, representing the NOIR movement phases. We define the CSD control as a cyclic receding horizon optimization problem with periodic quadratic cost and constraints. More specifically, the cost is defined so that the traffic density is minimized and the boundary inflow is uniformly distributed over the boundary inlet roads, whereas the cost parameters are periodically changed with time. The constraints are linear and imposed by a trapezoidal fundamental diagram at every NOIR road so that traffic feasibility is assured and traffic over-saturation is avoided.