Linear Model Predictive Control Research Articles

On the simplification of the internal nonlinear robot models for the MPC-based visual servoing

AbstractVisual servoing enables tracking and grasping of static and moving objects and locating regions of interest. Its implementation requires the coordination of low-level control tasks with high-level supervision and planning. The use of the PID-based manipulation control addresses only the dynamical response and requires the use of optimization-based techniques at the supervisory level. On the contrary, model predictive control (MPC) simplifies the design as it combines both tasks within a single algorithm. However, successful MPC implementation depends on the quality of the internal model utilized by the algorithm. Robots are intrinsically and significantly nonlinear control objects, so their models are inherently complex. This leads to computational problems. Standard solutions are to shorten the MPC horizons or to parallelize calculations. The approach suggested here returns to the problem roots, i.e. to the model. This study proposes simplified models that allow the use of the MPC. General Hammerstein–Wiener-like model is applied to an arm, which is further simplified into the linear dynamics used as the predictive supervisory control over the torque control. The head uses linear dynamics used by the supervisory MPC working with the base servomotors. It is shown that they are computationally efficient and sufficiently accurate. It is shown that the linear MPC controllers, which use the suggested simplified dynamic robot models, can successfully support visual servoing with accurate control. They are compared with standard PID-based structures and show their superiority. The proposed approach is successfully validated using Matlab and Gazebo robot simulator and is ultimately confirmed by experiments on a real robot.

Steering control for handling and stability and wear resistance of multi-axle vehicles

The steering performance of a vehicle directly affects its handling and stability, and tire wear during steering. For multi-axle vehicles equipped with a mechanical hydraulic steering system (MHS), this paper describes a steering-by-wire hydraulic system (SHS) for a third axle that can reduce the steering wear of third-axle tires while improving the handling and stability. A hydraulic steering system based on a reliable self-locking alignment cylinder was designed in this study, and a nonlinear dynamics model of a multi-axle vehicle was developed. In terms of the control strategy, the upper controller was a decision selector with a lateral acceleration threshold of 0.3 g , at which point the system entered the nonlinear kinematic state as a criterion for decision-making. The suboptimal linear time-varying model predictive control (S-LTV-MPC) method or Ackermann steering theory was used to calculate the target steering angle of the third axle. The lower controller was a fuzzy proportional–integral–derivative controller for tracking the steering angle of the third axle. The simulation and test results showed that the S-LTV-MPC method can meet the requirements of real-time control and accuracy. The designed SHS exhibited good handling and stability, and anti-wear properties during steering.

Modeling of Cooperative Robotic Systems and Predictive Control Applied to Biped Robots and UAV-UGV Docking with Task Prioritization.

This paper studies a cooperative modeling framework to reduce the complexity in deriving the governing dynamical equations of complex systems composed of multiple bodies such as biped robots and unmanned aerial and ground vehicles. The approach also allows for an optimization-based trajectory generation for the complex system. This work also studies a fast-slow model predictive control strategy with task prioritization to perform docking maneuvers on cooperative systems. The method allows agents and a single agent to perform a docking maneuver. In addition, agents give different priorities to a specific subset of shared states. In this way, overall degrees of freedom to achieve the docking task are distributed among various subsets of the task space. The fast-slow model predictive control strategy uses non-linear and linear model predictive control formulations such that docking is handled as a non-linear problem until agents are close enough, where direct transcription is calculated using the Euler discretization method. During this phase, the trajectory generated is tracked with a linear model predictive controller and addresses the close proximity motion to complete docking. The trajectory generation and modeling is demonstrated on a biped robot, and the proposed MPC framework is illustrated in a case study, where a quadcopter docks on a non-holonomic rover using a leader-follower topology.

Economic Performance of Model Predictive Control at Back-off Operating Point

In this paper, we address the economic performance of Model Predictive Control (MPC) while operating at a backed-off operating point. Operating the plant at a constrained optimal point will often cause constraint violations due to uncertainties such as disturbances and measurement errors, etc. To ensure dynamic feasibility, the concept of economic back-off is used. In this work, we select the set point as the economic back-off point such that the dynamic operating region should have the least variability in the active constrained variables while ensuring the feasibility of other variables. In other words, the dynamic operating region is oriented by the proper design of a controller such that variability in active constrained variables is as low as possible. This controller design can be transformed into equivalent objective function weights of the MPC controller. In this study, we demonstrate that the determined back-off point is optimal for both linear controller and MPC controller when there are no unconstrained degrees of freedom. For the case with unconstrained degrees of freedom, the back-off point determined using the presented approach is optimal only for a linear controller but suboptimal for an MPC controller. Demonstrative case studies are presented to illustrate the economic performance of the MPC controller at the determined economic back-off point.

Research on layered control of path tracking for unmanned industrial vehicles based on fully hydraulic steering leakage compensation

Industrial vehicles work in complex terrain, the variable centre of mass position, leakage nonlinearity of full hydraulic steering and other issues lead to poor path tracking stability and accuracy. In this paper, an intelligent hierarchical controller for industrial vehicles’ path tracking is designed with full hydraulic steering leakage compensation, including an upper decision layer and a lower execution layer. The upper decision layer observes the pavement-tyre adhesion coefficients through an extended Kalman filter algorithm, and uses the real-time observations of the adhesion coefficients to establish a variable constraint control for the linear time-varying MPC, and thus performs the path tracking control. The lower actuator layer receives the upper layer’s target steering wheel angle output and performs steering operations. Based on the establishment of a mathematical model of full hydraulic steering considering the leakage characteristics, it analyses the leakage disturbance factors and constructs a fuzzy feed-forward steering leakage compensation controller to compensate for the leakage disturbances in real time for path tracking steering. Simulation and experimental results show that the lateral acceleration, sideslip angle, tyre side slip angle and tracking error of intelligent industrial vehicles under different loads and working conditions are improved by more than 32.4%, 35.8%, 40.2% and 45.8% respectively, and the designed hierarchical controller for the path tracking of intelligent industrial vehicles, which considers the compensation of all-hydraulic steering leakage, can effectively improve the path tracking stability and tracking accuracy of intelligent industrial vehicles under different loads and working conditions.

A Unified Motion Generation Approach for Quadruped L-S Walk and Trot Gaits Based on Linear Model Predictive Control

A Unified Motion Generation Approach for Quadruped L-S Walk and Trot Gaits Based on Linear Model Predictive Control

An accurate trajectory tracking method for low-speed unmanned vehicles based on model predictive control

Trajectory tracking on a low-speed vehicle using the model predictive control (MPC) algorithm usually assumes a simple road terrain. This assumption does not correspond to the actual road situation, leading to low tracking accuracy. Therefore, a trajectory tracking method considering road curvature based on MPC is proposed in this paper. In this method, the controller can automatically switch between MPC types. Linear model predictive control (LMPC) is selected for small road curvatures, while nonlinear model predictive control (NMPC) is employed for large road curvatures. In addition, the NMPC algorithm in this work considers the effect of road curvature on tracking accuracy, making it suitable for tracking time-varying curvature roads. To verify the feasibility of the algorithm, simulation comparisons with the basic MPC model were carried out at different testing roads and vehicle longitudinal speeds. The results indicate that the method significantly improves trajectory tracking accuracy, all while ensuring real-time calculations. The intelligent switching capability of control models based on road curvature allows its application to track trajectories on arbitrarily complex roads.

A cascaded linear active disturbance rejection control-based multi-stage model predictive control for permanent magnet synchronous motor

A cascaded linear active disturbance rejection control-based multi-stage model predictive control for permanent magnet synchronous motor

A novel model predictive controller for the drifting vehicle to track a circular trajectory

ABSTRACT In rally racing, a high sideslip cornering technique known as drifting is employed to minimise the lap time. However, for autonomous vehicles, tracking the trajectory while drifting is a challenging control problem due to the conflict between the two objectives. This paper proposes a novel model predictive controller (MPC) with two operation modes to address this conflict. In Mode 1, fuzzy expert strategies combined with the lateral error are designed to calculate the drift equilibrium point. Subsequently, the linear MPC controller is utilised to achieve quick adjustments of the lateral error. In Mode 2, terminal state constraints and error constraints are added to the MPC optimisation problem. The stability of the MPC controller is guaranteed to keep the vehicle within the expected error range. Finally, a comparison between the existing expert controller and the proposed controller is carried out on both the CarSim platform and a 1:10 scale race car. The results demonstrate that the proposed controller outperforms the existing expert controller in terms of tracking performance and drift stability.

A novel collision avoidance strategy for highway overtaking considering the driver’s steering intent

Intelligent driving has been prevailing worldwide and is also challenging, which can be complicated by the factors of human drivers. In this paper, a novel collision avoidance strategy is proposed to enhance driving safety in highway overtaking by comprehensively considering the driver’s steering intent. First, in order to capture the driver’s operational characteristics from the driving data, we formulate the prediction of the driver’s steering intent and the ego vehicle’s states as a multivariate time series (MTS) forecasting problem, which is then handled by deep learning with a time pattern attention mechanism (DL-Attn). Second, a predictive risk field (PRF) model is proposed to quantify the real-time overtaking risk based on the above prediction results. Then, the overtaking is evaluated via a personalized risk threshold which can be set for a specific driver via experiments. Next, a linear time-varying model predictive control (LTV-MPC) -based assistance controller is designed so as to interfere in the risky overtaking and take over the ego vehicle from the driver to avoid possible collisions. And the feasibility and stability of the closed system are ensured theoretically. Finally, experiments are carried out in three typical cases. The results demonstrate that the proposed strategy can not only effectively improve driving safety for highway overtaking, but also identify safe overtaking to avoid unnecessary interference.

Comparison of Linear and Nonlinear Model Predictive Control in Path Following of Underactuated Unmanned Surface Vehicles

Model predictive control (MPC), an extensively developed rolling optimization control method, is widely utilized in the industrial field. While some researchers have incorporated predictive control into underactuated unmanned surface vehicles (USVs), most of these approaches rely primarily on theoretical simulation research, emphasizing simulation outcomes. A noticeable gap exists regarding whether predictive control adequately aligns with the practical application conditions of underactuated USVs, particularly in addressing real-time challenges. This paper aims to fill this void by focusing on the application of MPC in the path following of USVs. Using the hydrodynamic model of USVs, we examine the details of both linear MPC (LMPC) and nonlinear MPC (NMPC). Several different paths are designed to compare and analyze the simulation results and time consumption. To address the real-time challenges of MPC, the calculation time under different solvers, CPUs, and programming languages is detailed through simulation. The results demonstrate that NMPC exhibits superior control accuracy and real-time control potential. Finally, we introduce an enhanced A* algorithm and use it to plan a global path. NMPC is then employed to follow that path, showing its effectiveness in tracking a common path. In contrast to some literature studies using the LMPC method to control underactuated USVs, this paper presents a different viewpoint based on a large number of simulation results, suggesting that LMPC is not fit for controlling underactuated USVs.

A Tube Linear Model Predictive Control Approach for Autonomous Vehicles Subjected to Disturbances

The path tracking performance of autonomous vehicles is degraded by common disturbances, especially those that affect the safety of autonomous vehicles (AVs) in obstacle avoidance conditions. To improve autonomous vehicle tracking performances and their computational efficiency when subjected to common disturbances, this paper proposes a tube linear model predictive controller (MPC) framework for autonomous vehicles. A bicycle vehicle dynamics model is developed and employed in the tube MPC control design in the proposed framework. A robust invariant set is calculated with an efficient linear programming (LP) method, and it is used to guarantee that the constraints are satisfied under common disturbance conditions. The results show that the computational cost of robust positively invariant sets that are constructed by the LP method is much less than that obtained by the traditional method. In addition, all the trajectories of the tube linear MPC successfully avoided obstacles when under disturbance conditions, but only about 80% of the trajectories obtained with the traditional MPC successfully avoided obstacles under disturbance conditions. The proposed framework is effective.

Model-based linear control of nonlinear pneumatic soft bending actuators

Advanced model-based control techniques hold great promise for the precise control of pneumatic soft bending actuators (PSBAs) with strong nonlinearities. However, most previous controllers were designed in a cumbersome nonlinear form. Considering the simplicity of linear system theory, this paper presents a novel perspective on using model-based linear control to handle nonlinear PSBAs, and for the first time, summarizes two methodologies, global linearization and pseudo-linear construction. Derived from them, Koopman-based and hysteresis-based linear control approaches are proposed, respectively. For the former, a novel fusion prediction equation is developed to build a high-fidelity Koopman model, realizing global linearization, and then the linear model predictive control (MPC) is deployed. For the latter, the inverse of the generalized Prandtl–Ishlinskii (GPI) model cascades with the PSBA to construct a pseudo-linear system, eliminating the asymmetric hysteresis, which activates the linear proportional-integral-derivative (PID) control. It is worth noting that the above two are based on data-driven models adapted to various PSBAs with material and structural customization. Finally, the two model-based linear control approaches are verified and compared through a series of experiments. The results show that the proposed linear controls, with more concise designs, achieve comparable or even superior performance than nonlinear controls.

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.

Superiority of model predictive control with robust and stable approach for sliding wheeled mobile systems in the presence of obstacles

AbstractIn this paper, we present two distinct linear Model Predictive Control (MPC) methods for controlling mobile robots in the presence of obstacles while considering the wheel slip. Predictability of the controller enables the robot to automatically choose an alternative path to avoid obstacles. However, environmental conditions and disturbances, including slip, may impact the system model. Therefore, to accurately represent the system, slip angle and slip ratio are factored into the modeling process. Then the kinematic model is linearized using the successive method to reduce computational cost. Next, both Stable MPC (SMPC) and Robust MPC have been designed and implemented on the linearized time‐variant model to control the robot. The superiority of the robust predictive control method over the stable method has been discussed in terms of safety and optimal performance considering wheel slip. Finally, based on experimental tests, it has been found that the robust predictive controller is more effective than stable control when the surface is slippery and there is an obstacle in front of the robot. However, in a case where the wheel slip is neglectable, SMPC can be a better choice in presence of obstacles due to the lower computational cost.

Coordinated control of path tracking and yaw stability for distributed drive electric vehicle based on AMPC and DYC

Maintaining both path-tracking accuracy and yaw stability of distributed drive electric vehicles (DDEVs) under various driving conditions presents a significant challenge in the field of vehicle control. To address this limitation, a coordinated control strategy that integrates adaptive model predictive control (AMPC) path-tracking control and direct yaw moment control (DYC) is proposed for DDEVs. The proposed strategy, inspired by a hierarchical framework, is coordinated by the upper layer of path-tracking control and the lower layer of direct yaw moment control. Based on the linear time-varying model predictive control (LTV MPC) algorithm, the effects of prediction horizon and weight coefficients on the path-tracking accuracy and yaw stability of the vehicle are compared and analyzed first. According to the aforementioned analysis, an AMPC path-tracking controller with variable prediction horizon and weight coefficients is designed considering the change of vehicle speed in the upper layer. The lower layer involves DYC based on the linear quadratic regulator (LQR) technique. Specifically, the intervention rule of DYC is determined by the threshold of the yaw rate error and the phase diagram of the sideslip angle. Extensive simulation experiments are conducted to evaluate the proposed coordinated control strategy under different driving conditions. The results show that, under variable speed and low adhesion conditions, the vehicle yaw stability and path-tracking accuracy have been improved by 21.58% and 14.43%, respectively, compared to AMPC. Similarly, under high speed and low adhesion conditions, the vehicle yaw stability and path-tracking accuracy have been improved by 44.30% and 14.25%, respectively, compared to the coordination of LTV MPC and DYC. The results indicate that the proposed adaptive path-tracking controller is effective across different speeds. Furthermore, the proposed coordinated control strategy successfully enhances the vehicle stability while maintaining good path-tracking accuracy even under extreme conditions.

Path Tracking Control with Constraint on Tire Slip Angles under Low-Friction Road Conditions

This paper presents a method to design a path tracking controller with a constraint on tire slip angles under low-friction road conditions. On a low-friction road surface, a lateral tire force is easily saturated and decreases as a tire slip angle increases by a large steering angle. Under this situation, a path tracking controller cannot achieve its maximum performance. To cope with this problem, it is necessary to limit tire slip angles to a value where the maximum lateral tire force is achieved. The most commonly used controllers for path tracking, linear quadratic regulator (LQR) and model predictive control (MPC), are adopted as a controller design methodology. The control inputs of LQR and MPC are front and rear steering angles and control yaw moment, which have been widely used for path tracking. The constraint derived from tire slip angles is imposed on the steering angles of LQR and MPC. To fully verify the performance of the path tracking controller with the constraint on tire slip angles, a simulation is conducted on vehicle simulation software. From the simulation results, it is shown that the path tracking controller with the constraint on tire slip angles presented in this paper is quite effective for path tracking on low-friction road surface.

Linear time-varying fractional-order model predictive attitude control for satellite using two reaction wheels

Achieving precise attitude control in satellites equipped with two reaction wheels remains a significant challenge. During the last decade, model predictive control has emerged as a promising technique for satellite attitude control. However, this paper takes a step by introducing the novel concept of linear time-varying fractional-order model predictive control specifically tailored for satellites with dual reaction wheels, enabling them to achieve desired orientations more effectively. This study begins by elucidating the nonlinear dynamics and kinematic equations governing the satellite's behavior. To facilitate control design, the satellite linear time-varying model is derived by linearizing the nonlinear equations around the operating point. Leveraging this linearized representation, a linear time-varying fractional-order model predictive control method is designed, leveraging the benefits of fractional-order cost functions. Finally, the simulation results show the remarkable performance of the linear time-varying fractional-order model predictive control approach, particularly when confronted with input constraints. Notably, the proposed method outperforms the traditional linear time-varying model predictive control method by achieving an 80% improvement in tracking speed, while simultaneously reducing the applied torque by 67%. Additionally, the proposed approach decreases the mean absolute error of the satellite attitude angles by over 80% compared to the conventional linear time-varying model predictive control method. This research not only addresses the pressing challenge of attitude control in satellites with dual reaction wheels but also presents a novel and highly effective approach that surpasses existing methods in terms of performance and efficiency. As such, it holds immense potential for the field of satellite attitude control, making it an indispensable read for engineers and researchers working in the domain of aerospace engineering and control systems.

Critical Review of Optimal Control Methods for Li‐Ion Batteries in Electric Vehicles

AbstractBattery management systems are important for the safe and efficient operation of electric vehicles. Although high hardware performance and effective configurations of batteries have been realized, a management algorithm is required for ensuring optimal system performance. This review focuses on optimal controllers for charging, thermal control, and cell balancing of electric vehicles. A potential approach for practical applications is the direct optimal control method, particularly model predictive control (MPC). The objective function, prediction model types, and manipulated variables are summarized, along with the computational performance. Typical nonlinear MPC, linear MPC, explicit MPC, and hierarchical MPC are the main formulations for the optimal control of EVs. The AI‐based approach learns the optimal control law as a function from the optimal control result data. Although few studies have applied the reinforcement approach to battery systems, additional safety considerations for constraints must be considered for real applications. Cell variations, aging factors, and uncertainty considerations have been analyzed for improving the controller design. Addressing the computational issue with a reliable optimizer is critical to the implementation of an optimal controller for EVs.

Efficient model predictive control of boiler coal combustion based on NARX neutral network

During coal-fired power generation, uniform combustion temperature in the boiler is desired which will benefit both economical efficiency and pollution reduction. To this end, a model predictive control (MPC) algorithm based on the Nonlinear Auto-Regressive Exogenous Inputs (NARX) neural network and KS-function is proposed, and the uniform combustion in the boiler is realized by controlling the opening travel of secondary windgates. In the modeling process, a multi-input and multi-output(MIMO) NARX neural network is developed using the historical data of the real system The NARX neural network is then used to predict the state variables, and the optimal control input is achieved by applying sequential quadratic programming (SQP), comparing with linear MPC the mean temperature difference is reduced by 64.2%. In addition, this paper proposes a new method to reduce the computational time of the online optimization process based on KS-function, which greatly accelerates the searching speed of SQP by 67.3%. The proposed MPC algorithm is applied to a 660 MW power generating unit. The results show that by applying the proposed algorithm, the temperature difference in the boiler is kept within 100 °C, the average coal consumption of the power plant is reduced by 5.71 g/kWh, and the NOx emission is reduced to 23.84 mg/m3. It can be concluded that the proposed algorithm greatly improves the economical efficiency of the power plant and reduces the emission of pollutants.