Nonlinear Model Predictive Control Method Research Articles

Dynamic Modeling and Improved Nonlinear Model Predictive Control of a Free-Floating Dual-Arm Space Robot

With the increasing demand for space missions, space robots have become the focus of research and attention. As a typical representative, the free-floating dual-arm space robot has the characteristics of multiple degrees of freedom, a floating base, and dynamic coupling between the manipulator and the base, so its modeling and control are very challenging. To address these challenges, a novel dynamic modeling and control method is proposed for a free-floating dual-arm space robot. First, an explicit dynamic model of a free-floating dual-arm space robot is established based on the explicit canonical multi-rigid-body dynamic modeling theory and combined with the concept of a dynamic equivalent manipulator. The establishment process of this model is not only simple and canonical to avoid the definition and calculation of many intermediate variables, but the symbolic result expression of the model also has the characteristics of iteration, which is convenient for computer automatic modeling. Next, aiming at addressing the problem of trajectory tracking and the base attitude stability of a free-floating dual-arm space robot with parameter perturbation and external disturbance, an improved nonlinear model predictive control method introducing the idea of sliding mode variable structure is proposed. Theoretical analysis shows that the proposed controller has better robustness than the traditional nonlinear model predictive controller. Then, an in-orbit service task is designed to verify the effectiveness of the proposed dynamic modeling and control strategy of the free-floating dual-arm space robot. Finally, the dynamic modeling and control methods proposed are discussed and summarized. The proposed methods can not only realize the tracking of the desired trajectory of the arms of the free-floating space robot, but can also realize the stable control of the base of the free-floating space robot. This paper provides new insights into the difficult problems regarding the dynamics and control of free-floating dual-arm space robots.

Motion Planning and Control of Autonomous Aggressive Vehicle Maneuvers

Aggressive vehicle maneuvers such as those performed by professional racing drivers achieve high agility motion at the edge of handling limits. These aggressive maneuvers can be used to design human-inspired active safety features for next-generation “accident-free” vehicles. We present a motion planning and control design for autonomous aggressive vehicle maneuvers. The motion planner takes advantages of the sparse stable trees and the enhanced rapidly exploring random tree (RRT*) algorithms. The use of the sparsity property helps to reduce the computational cost of the RRT* method by removing non-useful nodes in each iteration and therefore to rapidly converge to the optimal solution. The proposed motion control design allows the vehicle to operate outside the stability region to accomplish a safe, agile maneuver. A safety region is computed to augment the stability region and the motion control is built on a modified nonlinear model predictive control method. We implement the proposed planner and controller and demonstrate the autonomous aggressive maneuvers on a 1/7-scale racing vehicle platform. Comparison with human expert driver and other existing methods is also presented to demonstrate the performance and robustness. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Motion planning and control of human driver-inspired aggressive vehicle maneuvers is a challenging task because of high-agility, unstable fast vehicle motions. This paper is motivated by addressing this challenge in autonomous driving technologies. Instead of restricting vehicle motions within a stability region that is taken by existing methods, we augment the conservative stability region to a safety region with guaranteed performance. To improve the computational efficiency of sampling-based motion planners, we take advantage of sparsity and also integration of a nonlinear predictive control method to compute feasible vehicle motion in searching space. The stability of the vehicle motion controller and sub-optimality of the motion planner are analyzed and guaranteed. Using a scaled vehicle testbed, we validate and compare the proposed motion planning and control design with other existing methods and human expert driver. The experimental results demonstrate the superior performance than the other methods and comparable with human expert driving skills.

Cascade NMPC-PID control strategy of active heave compensation system for ship-mounted offshore crane

In this paper, the problem associated with active heave motion compensation during heavy-lift operations performed by ship-mounted offshore cranes beneath rough marine environment is investigated. To effectively decouple the correlated motion of the suspended payload from the support vessel via the secondary regulated active heave compensation (SRAHC) system, a novel hierarchical control strategy is proposed by integrating a cascade control structure with an adaptive robust control scheme that incorporates a vertical motion forecast algorithm based on autoregressive integrated moving average (ARIMA) model, a conventional proportional-integral-derivative (PID) framework, and a nonlinear model predictive control (NMPC) method. The introduction of the cascade structure is motivated by its prompt error response against control lag and efficient system order reduction for computational burden alleviation, which forms a crucial foundation for the NMPC-based real-time regulation of PID gains, ensuring optimal evolution of the SRAHC system while improving its practical feasibility. Furthermore, the enhancements in heave compensation and trajectory tracking performance, noise resistance, constraint satisfaction, and engineering application potential of the proposal are demonstrated through a thorough comparative analysis conducted in a practical co-simulation research system.

Koopman-Based MPC With Learned Dynamics: Hierarchical Neural Network Approach.

This article presents a data-driven control strategy for nonlinear dynamical systems, enabling the construction of a Koopman-based linear system associated with nonlinear dynamics. The primary idea is to apply the deep learning technique to the Koopman framework for globally linearizing nonlinear dynamics and impose a Koopman-based model predictive control (MPC) approach to stabilize the nonlinear dynamical systems. In this work, we first generalize the Koopman framework to nonlinear control systems, enabling comprehensive linear analysis and control methods to be effective for nonlinear systems. We next present a hierarchical neural network (HNN) approach to deal with the crucial challenge of the finite-dimensional Koopman representation approximation. In particular, a scale-invariant constrained network in the HNN includes four modules, in which a predictor module and a linear module can accurately approximate the finite Koopman eigenfunctions and Koopman operator, respectively, thus forming the lifted linear system. Then, we design the Koopman-based MPC scheme for controlling nonlinear systems with constraints by adopting the modified MPC with a saturation-like function on the lifted linear system. Importantly, the Koopman-based MPC enjoys higher computational efficiency compared to the classical linear MPC and nonlinear MPC methods. Finally, a physical experiment on an overhead crane system is provided to demonstrate the effectiveness of the proposed data-driven control framework.

Inertia load reduction for loadoff during floating offshore wind turbine installation: Release decision and ballast control

High offshore installation costs are a significant factor limiting the competitiveness of offshore wind energy. One efficient installation approach for floating offshore wind turbines is to preassemble the tower, nacelle, and rotor onshore and perform a single lifting operation to mate the superstructure with the floating foundation at the installation site. It is heavy lifting, due to the weighty payload. At the end of the mating process, a loadoff operation is conducted to transfer the preassembly to the floating foundation. It results in a sudden change in total force acting on the vessel and causes substantial acceleration and potential damage to the mechanism in the onboard nacelles. The magnitude of acceleration of the onboard nacelles can vary greatly at different release instants. In this research, a simplified two-degrees-of-freedom (DOF) (heave and pitch) model is also proposed to account for the heavy lifting process and variable ballast tanks. The sudden payload transfer is approximated using a hyperbolic tangent function to guarantee continuity and differentiability. The loadoff operation consists of the decision-making and vessel-stabilizing phases. Based on the nonlinear model predictive control method, a payload-transfer time selector and anti-pitch ballast controller have been developed to achieve optimal release time decisions and stabilize the vessel after payload release, respectively. Six-DOF simulation results show that the proposed algorithms are capable to a satisfying level of robustness of deciding the optimal payload release time instant, as well as limiting the peak and mean acceleration magnitudes of the onboard nacelles after payload release. The decision-making and control strategies may promote the sustainable energy transformation by extending the operation window and reduce the installation costs.

Trajectory Tracking Control of a Skid-Steer Mobile Robot Based on Nonlinear Model Predictive Control with a Hydraulic Motor Velocity Mapping

In this study, we address the trajectory tracking control problem of a hydraulic-driven skid-steer mobile robot. A hierarchical control strategy is proposed to simultaneously consider the robot’s position control and the velocity control of the hydraulic motors. At the upper level, a nonlinear model predictive control (NMPC) method is employed to control the position and heading of the mobile robot. The NMPC controller takes into account the robot’s physical constraints and generates the desired robot motion velocity. Then, to control the hydraulic drive system, a current–velocity mapping-based control method is introduced. By establishing the mapping relationship between the control current applied to the hydraulic motor and its corresponding output velocity, the dynamics of the hydraulic motors are characterized. Consequently, the lower-level controller can directly obtain the control signal for the hydraulic actuator through lookup mappings. Additionally, PID controllers are adopted to compensate for velocity tracking errors. The proposed hierarchical control strategy decouples the robot’s position control and the hydraulic system control, simplifying the overall controller design, leading to improved control performance. To validate the effectiveness of the proposed control strategy, several experiments were conducted on a hydraulic-driven skid-steer mobile robot, and the results demonstrate the effectiveness of the proposed approach.

Trajectory Tracking Control of Transformer Inspection Robot Using Distributed Model Predictive Control.

To overcome the difficulty in tracking the trajectory of an inspection robot inside a transformer, this paper proposes a distributed model predictive control method. First, the kinematics and dynamics models of a robot in transformer oil are established based on the Lagrange equation. Then, by using the nonlinear model predictive control method and following the distributed control theory, the motion of a robot in transformer oil is decoupled into five independent subsystems. Based on this, a distributed model predictive control (DMPC) method is then developed. Finally, the simulation results indicate that a robot motion control system based on DMPC achieves high tracking accuracy and robustness with reduced computing complexity, and it provides an effective solution for the motion control of robots in narrow environments.

Dynamic obstacle avoidance of unmanned ship based on event-triggered adaptive nonlinear model predictive control

This article studies trajectory tracking and dynamic obstacle avoidance problems of unmanned ships, and an event-triggered adaptive nonlinear model predictive control (EANMPC) method is constructed to solve the above problems. Firstly, a novel adaptive nonlinear model predictive control is used to track the trajectory of the unmanned ship. And then, an obstacle avoidance mechanism is formulated to deal with the condition of dynamic obstacles that appear during the unmanned ship trajectory tracking process. Secondly, an event-triggered mechanism is established to reduce the computational burden of the controller. Finally, several simulation results are provided for demonstrating the effectiveness and advantage of EANMPC.

Intelligent frequency stabilization of low-inertia islanded power grids-based redox battery

Renewable energy sources (RES)-generated electricity is increasing at a fast pace and is becoming more prevalent in microgrids (MGs). System inertia is much decreased due to the fact that MGs are mostly powered by RES rather than synchronous generators. As a result, system stability suffers, which is especially problematic with MGs. A suitable solution for this problem is an energy storage system and an appropriate inertial control technique. Redox flow batteries (RFBs) have an unusually long charge-discharge life cycle and a fast reaction time, which allows them to reduce oscillations in the power system when there is a sudden disturbance in the power system. This paper suggests a unique concept for VIC based on RFB in an isolated MG, which emulates the primary frequency control, virtual inertia, and damping all at once. In addition to the VIC concept, we suggest a novel nonlinear model predictive control (NMPC) method for MG secondary control. The NMPC utilizes non-integer order calculus and interval type-3 (IT3) fuzzy logic systems (FLSs). Finally, OPAL-RT-based real-time hardware-in-the-loop (HIL) simulation results are used to examine the validity and applicability of the suggested techniques in low inertia islanded MG.

Energy management strategy for hybrid power ships based on nonlinear model predictive control

How to achieve energy saving and emissions reduction is a critical issue of great concern to all countries. The development of marine hybrid power technology provides a new research direction for rational energy distribution and utilization. In this paper, an energy management strategy for real-time regulation of internal combustion engines and motor torque is designed to solve the optimal energy management problem of parallel hybrid power ships. A nonlinear model predictive control method is used as the core, aided by a machine learning technique and an unscented Kalman filter. Machine learning techniques are used to extract representative test cycles and apply them to the testing and evaluation of design strategies. The effect of random waves on propeller load torque is observed using an unscented Kalman filter, which is used as a disturbance variable to participate in establishing the prediction model. Furthermore, a trade-off coefficient is designed to further demonstrate the balance between fuel consumption and carbon emission optimization. To verify the performance of the designed energy management strategy, NMPC is compared with the conventional intelligent optimization algorithm and dynamic programming algorithm, and the fuel consumption and carbon emission trade-off parameterization of the strategy is investigated. The results show that the strategy can resist random wave disturbances and follow the reference data of the ship’s internal combustion engine speed extracted by machine learning. The energy distribution is also performed according to the variation of the trade-off coefficients to achieve the optimal trade-off energy management under the required constraints.

Nonlinear model predictive control of crystal size in batch cooling crystallization processes

The paper proposes a model-based nonlinear model predictive control (NMPC) method for online control of crystal mean size and standard deviation in cooling crystallization process. Image analysis method using deep learning neural network and mathematical statistical method are performed to obtain the mean size and standard deviation of crystal population. The nonlinear prediction model for the NMPC is derived from the input and output data. The effectiveness of the proposed NMPC method is evaluated by the alum cooling crystallization experiments. Experimental results demonstrate the benefits of the proposed combination of image analysis and feedback control of the crystal mean size and standard deviation. The control performance of NMPC is superior to model-free path following control (PFC) method due to the prediction and optimization capabilities of NMPC.

Nonlinear Model Predictive Impedance Control of a Fully Actuated Hexarotor for Physical Interaction.

In this paper, the problem of a fully actuated hexarotor performing a physical interaction with the environment through a rigidly attached tool is considered. A nonlinear model predictive impedance control (NMPIC) method is proposed to achieve the goal in which the controller is able to simultaneously handle the constraints and maintain the compliant behavior. The design of NMPIC is the combination of a nonlinear model predictive control and impedance control based on the dynamics of the system. A disturbance observer is exploited to estimate the external wrench and then provide compensation for the model which was employed in the controller. Moreover, a weight adaptive strategy is proposed to perform the online tuning of the weighting matrix of the cost function within the optimal problem of NMPIC to improve the performance and stability. The effectiveness and advantages of the proposed method are validated by several simulations in different scenarios compared with the general impedance controller. The results also indicate that the proposed method opens a novel way for interaction force regulation.

High-order fully actuated system approaches: Model predictive control with applications to under-actuated systems

The main results of this paper are concentrated on the nonlinear model predictive control (MPC) tracking optimization based on high-order fully actuated (HOFA) system approaches. The proposed HOFA MPC strategy makes full use of full-actuation property to eliminate the nonlinear dynamics of the system, and then the nonlinear optimization problem is equivalently transformed into a series of easy-solve linear convex optimization problems. Different from general nonlinear MPC methods and the current optimal control of the HOFA system approach, an analytical controller with smooth and less energy is obtained by the moving horizon optimization. And it is proven that the proposed controller can stabilize the corresponding tracking error closed-loop system. Finally, not limited to FA systems, as examples, a nonlinear numerical under-actuated model in the mathematical sense and a benchmark nonlinear under-actuated mechanical system are transformed into corresponding equivalent HOFA systems, the simulation results are given to verify the effectiveness of the proposed strategy.

Hierarchical and Distributed Eco-Driving Approach for Mixed Vehicle Clusters at Unsignalized Intersections

To improve the driving efficiency and energy-saving characteristics for large-scale mixed traffic flows under different market penetration rates (MPRs) of intelligent and connected vehicles (ICVs) at unsignalized intersections, considering the cooperative eco-driving performance between ICVs and human-driven vehicles (HDVs) with time-varying speed characteristics, the hierarchical and distributed cooperative eco-driving architecture is first established in this paper, consisting of a cloud decision layer and a vehicle control layer. For the cloud decision layer, the multivehicle model-free adaptive predictive cooperative driving (MFAPCD) method is designed by using only the driving data of the HDVs and ICVs formation based on compact form dynamic linearization (CFDL) technique, thereby improving traffic efficiency. Furthermore, the CFDL integral terminal sliding mode predictive control (CFDL-ITSMPC) scheme is utilized to predict the time-varying driving speed of HDVs, and then, the CFDL predictive control (CFDL-PC) scheme is utilized to predict the expected control variables of ICVs formation. For the vehicle control layer, based on the anticipated driving speed obtained from the cloud decision layer, the nonlinear distributed model predictive control (NDMPC) method is utilized for distributed optimal control of each vehicle formation, to achieve optimization in terms of energy saving. Simulation results show that, compared with the signal time assignment strategy, the method can increase the average velocity by about 15.22% and decrease the average fuel consumption by about 36.43% under different MPRs and traffic volumes.

Pneumatic pressure control based on improved NMPC and its application to aeroengine surge simulation

In the semi-physical simulation of aeroengines, using the pneumatic pressure servo control technology to provide realistic pneumatic excitation to the sensors and electronic controller can improve the confidence of the simulation and reduce the test cost and risk. However, the existing methods could not satisfy the precise simulation of large-amplitude and high-frequency pulsating pressure during aeroengine surge. In this paper, a pneumatic pressure control system with asymmetric groups of the High-Speed on–off Valve (HSV) is designed, and an Improved Nonlinear Model Predictive Control (INMPC) method is proposed. First, the volumetric flow characteristics of HSV are tested and analyzed with Pulse Width Modulation (PWM) signal input. Then, a simplified HSV model with the volume flow characteristic correction is developed. Based on these, an integrated model for the whole system is further established and used as the prediction model in INMPC. To improve the computational speed of the rolling optimization process, the mapping scheme from control signal to PWM duty cycle of HSVs and the objective function with exterior penalty function are designed. Finally, the random step, sinusoidal and real engine surge data are set as the reference pressure in multiple comparative experiments to verify the effectiveness of the pressure tracking system.

A Learning-Based Nonlinear Model Predictive Control Approach for Autonomous Driving

This paper introduces a learning-based Nonlinear Model Predictive Control (NMPC) method that combines NMPC with a Reinforcement Learning (RL) algorithm to achieve automatic parameter tuning of the NMPC optimizer, resulting in better control performance. In this study, two learning-based models were designed based on the tabular Q-learning algorithm but with different definitions of state and action spaces. To test the effectiveness of the proposed model, we conducted two kinds of experiments in which the models were applied to optimize the lane-keeping performance of an autonomous driving system. The case study results from simulations showed that the agent could match a proper parameter matrix for the NMPC within one minute. In real-world experiments, we extended the proposed control scheme to practical driving tasks using a 1:8 scale Audi model car in a specific experimental field. The model exhibited acceptable robustness in the face of relatively large deviations from the sensors and other real-time interference. These results demonstrate that the proposed learning-based NMPC method is a promising direction for solving real-time control problems.

Cooperative Multi-Objective Control of Heterogeneous Vehicle Platoons on Highway with Varying Slopes

Stability, vehicle safety, energy saving, and passenger comfort are the major objectives of vehicle platooning control. These objectives are coupled, interrelated, and even conflicting, so integrated optimization of multiple objectives is quite challenging. Particularly for heterogeneous platoons, the difficulties are intensified for the differences in vehicle dynamics. In this paper, the concept of symmetry is utilized in the platooning control, that is, the design method of each vehicle’s controller is the same. For each controller, it is to solve the optimal solution of multi-objective collaborative optimization. The concept of asymmetry is meanwhile embodied in the parameter setting of each controller, for the vehicle heterogeneity. The contents of this study are as follows. First, a mathematical model is established, in which the differences in vehicle dynamic characteristics of heterogeneous platoon, road slope, and aerodynamics are all taken into account. Then, based on distributed nonlinear model predictive control (DNMPC) method, multi-objective control strategies are proposed for the leader and followers, cooperatively. Furthermore, a weight coefficient optimization method is presented, to further improve the platoon’s multi-objective synthesis performance. Finally, comparative experiments are carried out. Results demonstrate that, compared with the classic cruise control method of vehicle platoons, the proposed approach can reduce energy consumption by more than 5% and improve tracking performance on the premise of passenger comfort. Real-road experiments verify that the proposed control system can function effectively and satisfy the computational requirements in real applications.

Robust predictive thermal management strategy for lithium-ion battery based on thermoelectric cooler

An effective battery thermal management (BTM) strategy is very important for electric vehicles (EVs). In this paper, a robust predictive BTM strategy based on thermoelectric cooler (TEC) is proposed to adjust the battery temperature within an appropriate range and reduce energy consumption. Firstly, a modeling method of TEC based on thermal resistance is presented, which considers the influence of heat sink and fan on modeling effect. Next, a distributed battery thermal model is developed by using the difference method, which takes the tab thermal model as the first kind of boundary condition of the cell core. Then, a thermal management model is developed by combining the TEC model and distributed battery thermal model, and a neural network (NN) observer is proposed to compensate the model uncertainty. Finally, a nonlinear model predictive control (NMPC) method is proposed to optimize the cooling process. Genetic algorithm (GA) optimization is used to solve the nonlinear programming problem in NMPC method. Additional stability analysis shows the convergence of the proposed observer. Experiments and verifications suggest that the proposed method can accurately control the battery working near the target temperatures under four different cycles, and the errors are less than 0.5 °C.

Motion Saliency-Based Collision Avoidance for Mobile Robots in Dynamic Environments

Obstacle avoidance is a sizable challenge for robots working in a multiple dynamic obstacle environment. Conventional obstacle avoidance methods often require complex calculations to process all dynamic obstacles detected in the scene. Avoiding dangerous moving objects in time is often difficult when obstacles are many. In this article, we propose a robot obstacle avoidance method based on motion saliency for dynamic environments. First, we use segmented dynamic objects to calculate the saliency of dynamic objects and segment dangerous dynamic objects. Then, we use the B-spline curve to predict the movement of dangerous dynamic objects and combine it with the nonlinear model predictive control method to avoid dangerous obstacles in the dynamic environment of the robot. Considering the motion behavior of different dynamic objects, our obstacle avoidance strategy is to generate obstacle-free paths by adjusting the speed of the robot or connecting the centers of the rolling variable-size circles. Finally, we conduct a series of experiments to verify the effectiveness of our method.

Integrated Propulsion and Cabin-Cooling Management for Electric Vehicles

This paper presents two nonlinear model predictive control (MPC) methods for the integrated propulsion and cabin-cooling management of electric vehicles. An air-conditioning (AC) model, which has previously been validated on a real system, is used to accomplish system-level optimization. To investigate the optimal solution for the integrated optimal control problem (OCP), we first build an MPC, referred to as a joint MPC, in which the goal is to minimize battery energy consumption while maintaining cabin-cooling comfort. Second, we divide the integrated OCP into two small-scale problems and devise a co-optimization MPC (co-MPC), where speed planning on hilly roads and cabin-cooling management with propulsion power information are addressed successively. Our proposed MPC methods are then validated through two case studies. The results show that both the joint MPC and co-MPC can produce significant energy benefits while maintaining driving and thermal comfort. Compared to regular constant-speed cruise control that is equipped with a proportion integral (PI)-based AC controller, the benefits to the battery energy earned by the joint MPC and co-MPC range from 2.09% to 2.72%. Furthermore, compared with the joint MPC, the co-MPC method can achieve comparable performance in energy consumption and temperature regulation but with reduced computation time.