A Real-time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles

This paper proposes a real-time nonlinear model predictive control (NMPC) strategy for direct yaw moment control (DYC) of distributed drive electric vehicles (DDEVs). The NMPC strategy is based on a control-oriented model built by integrating a single track vehicle model with the Magic Formula (MF) tire model. To mitigate the NMPC computational cost, the continuation/generalized minimal residual (C/GMRES) algorithm is employed and modified for real-time optimization. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the external penalty method is introduced to transform inequality constraints into an equivalently unconstrained optimization problem. Based on the Pontryagin’s minimum principle (PMP), the existence and uniqueness for solution of the proposed C/GMRES algorithm are proven. Additionally, to achieve fast initialization in C/GMRES algorithm, the varying predictive duration is adopted so that the analytic expressions of optimally initial solutions in C/GMRES algorithm can be derived and gained. A Karush-Kuhn-Tucker (KKT) condition based control allocation method distributes the desired traction and yaw moment among four independent motors. Numerical simulations are carried out by combining CarSim and Matlab/Simulink to evaluate the effectiveness of the proposed strategy. Results demonstrate that the real-time NMPC strategy can achieve superior vehicle stability performance, guarantee the given safety constraints, and significantly reduce the computational efforts

A Computationally Efficient Path Following Control Strategy of Autonomous Electric Vehicles with Yaw Motion Stabilization

his paper proposes a computationally efficient path following control strategy of autonomous electric vehicles (AEVs) with yaw motion stabilization. First, the nonlinear control-oriented model including path following model, single track vehicle model, and Magic Formula tire model, are constructed. To handle the stability constraints with ease, the nonlinear model predictive control (NMPC) technique is applied for path following issue. Here NMPC control problem is reasonably established with the constraints of vehicle sideslip angle, yaw rate, steering angle, lateral position error, and Lyapunov stability. To mitigate the online calculation burden, the continuation/ generalized minimal residual (C/GMRES) algorithm is adopted. The deadzone penalty functions are employed for handling the inequality constraints and holding the smoothness of solution. Moreover, the varying predictive duration is utilized in this paper so as to fast gain the good initial solution by numerical algorithm. Finally, the simulation validations are carried out, which yields that the proposed strategy can achieve desirable path following and vehicle stability efficacy, while greatly reducing the computational burden compared with the NMPC controllers by active set algorithm or interior point algorithm

The predictive functional control and the management of constraints in GUANAY II autonomous underwater vehicle actuators

Autonomous underwater vehicle control has been a topic of research in the last decades. The challenges addressed vary depending on each research group's interests. In this paper, we focus on the predictive functional control (PFC), which is a control strategy that is easy to understand, install, tune, and optimize. PFC is being developed and applied in industrial applications, such as distillation, reactors, and furnaces. This paper presents the rst application of the PFC in autonomous underwater vehicles, as well as the simulation results of PFC, fuzzy, and gain scheduling controllers. Through simulations and navigation tests at sea, which successfully validate the performance of PFC strategy in motion control of autonomous underwater vehicles, PFC performance is compared with other control techniques such as fuzzy and gain scheduling control. The experimental tests presented here offer effective results concerning control objectives in high and intermediate levels of control. In high-level point, stabilization and path following scenarios are proven. In the intermediate levels, the results show that position and speed behaviors are improved using the PFC controller, which offers the smoothest behavior. The simulation depicting predictive functional control was the most effective regarding constraints management and control rate change in the Guanay II underwater vehicle actuator. The industry has not embraced the development of control theories for industrial systems because of the high investment in experts required to implement each technique successfully. However, this paper on the functional predictive control strategy evidences its easy implementation in several applications, making it a viable option for the industry given the short time needed to learn, implement, and operate, decreasing impact on the business and increasing immediacy.Peer ReviewedPostprint (author's final draft

Flatness-based control in successive loops for robotic manipulators and autonomous vehicles

The control problem for the multivariable and nonlinear dynamics of robotic manipulators and autonomous vehicles is solved with the use of a flatness-based control approach which is implemented in successive loops. The state-space model of these robotic systems is separated into two subsystems, which are connected between them in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearised flat systems. The state variables of the second subsystem become virtual control inputs for the first subsystem. In turn, exogenous control inputs are applied to the first subsystem. The whole control method is implemented in two successive loops and its global stability properties are also proven through Lyapunov stability analysis. The validity of the control method is confirmed in two case studies: (a) control of a 3-DOF industrial rigid-link robotic manipulator and (b) control of a 3-DOF autonomous underwater vessel. The novel control method can simplify significantly the solution of the nonlinear control problem for robotic manipulators and vehicles. Unlike global linearisation-based control schemes, the proposed flatness-based method in successive loops does not need any changes in state variables of complicated state-space model transformations.Partially supported by Grant Ref. ‘CSP_contract_040322’ – ‘Intelligent control for electric power systems and electric vehicles’ of the Unit of Industrial Automation of the Industrial Systems Institute

Shifting strategy for efficient block-based nonlinear model predictive control using real-time iterations

Nonlinear Model Predictive Control (NMPC) requires the use of efficient solutions and strategies for its implementation in fast/real-time systems. A popular approach for this is the Real Time Iteration (RTI) Scheme which uses a shifting strategy, namely the Initial Value Embedding (IVE), that shifts the solution from one sampling time to the next. However, this strategy together with other efficient strategies such as Move Blocking, present a recursive feasibility problem. This paper proposes a novel modified shifting strategy which preserve both recursive feasibility and stability properties, as well as achieves a significant reduction in the computational burden associated with the optimisation. The proposed approach is validated through a simulation of an inverted pendulum where it clearly outperforms other standard solutions in terms of performance and recursive feasibility properties. Additionally, the approach was tested on two computing platforms: a laptop with an i7 processor and a Beaglebone Blue Linux-based computer for robotic systems, where computational gains compared to existing approaches are shown to be as high as 100 times faster

Feasible, Robust and Reliable Automation and Control for Autonomous Systems

The Special Issue book focuses on highlighting current research and developments in the automation and control field for autonomous systems as well as showcasing state-of-the-art control strategy approaches for autonomous platforms. The book is co-edited by distinguished international control system experts currently based in Sweden, the United States of America, and the United Kingdom, with contributions from reputable researchers from China, Austria, France, the United States of America, Poland, and Hungary, among many others. The editors believe the ten articles published within this Special Issue will be highly appealing to control-systems-related researchers in applications typified in the fields of ground, aerial, maritime vehicles, and robotics as well as industrial audiences

Design, testing and validation of model predictive control for an unmanned ground vehicle

The rapid increase in designing, manufacturing, and using autonomous robots has attracted numerous researchers and industries in recent decades. The logical motivation behind this interest is the wide range of applications. For instance, perimeter surveillance, search and rescue missions, agriculture, and construction. In this thesis, motion planning and control based on model predictive control (MPC) for unmanned ground vehicles (UGVs) is tackled. In addition, different variants of MPC are designed, analysed, and implemented for such non-holonomic systems. It is imperative to focus on the ability of MPC to handle constraints as one of the motivations. Furthermore, the proliferation of computer processing enables these systems to work in a real-time scenario. The controller's responsibility is to guarantee an accurate trajectory tracking process to deal with other specifications usually not considered or solved by the planner. However, the separation between planner and controller is not necessarily defined uniquely, even though it can be a hybrid process, as seen in part of this thesis. Firstly, a robust MPC is designed and implemented for a small-scale autonomous bulldozer in the presence of uncertainties, which uses an optimal control action and a feed-forward controller to suppress these uncertainties. More precisely, a linearised variant of MPC is deployed to solve the trajectory tracking problem of the vehicle. Afterwards, a nonlinear MPC is designed and implemented to solve the path-following problem of the UGV for masonry in a construction context, where longitudinal velocity and yaw rate are employed as control inputs to the platform. For both the control techniques, several experiments are performed to validate the robustness and accuracy of the proposed scheme. Those experiments are performed under realistic localisation accuracy, provided by a typical localiser. Most conspicuously, a novel proximal planning and control strategy is implemented in the presence of skid-slip and dynamic and static collision avoidance for the posture control and tracking control problems. The ability to operate in moving objects is critical for UGVs to function well. The approach offers specific planning capabilities, able to deal at high frequency with context characteristics, which the higher-level planner may not well solve. Those context characteristics are related to dynamic objects and other terrain details detected by the platform's onboard perception capabilities. In the control context, proximal and interior-point optimisation methods are used for MPC. Relevant attention is given to the processing time required by the MPC process to obtain the control actions at each actual control time. This concern is due to the need to optimise each control action, which must be calculated and applied in real-time. Because the length of a prediction horizon is critical in practical applications, it is worth looking into in further detail. In another study, the accuracies of robust and nonlinear model predictive controllers are compared. Finally, a hybrid controller is proposed and implemented. This approach exploits the availability of a simplified cost-to-go function (which is provided by a higher-level planner); thus, the hybrid approach fuses, in real-time, the nominal CTG function (nominal terrain map) with the rest of the critical constraints, which the planner usually ignores. The conducted research fills necessary gaps in the application areas of MPC and UGVs. Both theoretical and practical contributions have been made in this thesis. Moreover, extensive simulations and experiments are performed to test and verify the working of MPC with a reasonable processing capability of the onboard process

Efficient Real-Time Solutions for Nonlinear Model Predictive Control with Applications

Nonlinear Model Predictive Control is an advanced optimisation methodology widely used for developing optimal Feedback Control Systems that use mathematical models of dynamical systems to predict and optimise their future performance. Its popularity comes from its general ability to handle a wide range of challenges present when developing control systems such as input/output constraints, complex nonlinear dynamics multi-variable systems, dynamic systems with significant delays as well as handling of uncertainty, disturbances and fault-tolerance. One of the main and most important challenges is the computational burden associated with the optimisation, particularly when attempting to implement the underlying methods in fast/real-time systems. To tackle this, recent research has been focused on developing efficient real-time solutions or strategies that could be used to overcome this problem. In this case, efficiency may come in various different ways from mathematical simplifications, to fast optimisation solvers, special algorithms and hardware, as well as tailored auto-generated coding tool-kits which help to make an efficient overall implementation of these type of approaches. This thesis addresses this fundamental problem by proposing a wide variety of methods that could serve as alternatives from which the final user can choose from depending on the requirements specific to the application. The proposed approaches focus specifically of developing efficient real-time NMPC methods which have a significantly reduced computational burden whilst preserving desirable properties of standard NMPC such as nominal stability, recursive feasibility guarantees, good performance, as well as adequate numeric conditioning for their use in platforms with reduced numeric precision such as ``floats'' subject to certain conditions being met. One of the specific aims of this work is to obtain faster solutions than the popular ACADO toolkit, in particular when using condensing-based NMPC solutions under the Real-Time Iteration Scheme, considered for all practical purposes the state-of-the-art standard real-time solution to which all the approaches will be bench-marked against. Moreover, part of the work of this thesis uses the concept of ``auto-generation'' for developing similar tool-kits that apply the proposed approaches. To achieve this, the developed tool-kits were supported by the Eigen 3 library which were observed to result in even better computation times than the ACADO toolkit. Finally, although the work undertaking by this thesis does not look into robust control approaches, the developed methods could be used for improving the performance of the underlying ``online'' optimisation, eg. by being able to perform additional iterations of the underlying SQP optimisation, as well as be used in common robust frameworks where multi-model systems must be simultaneously optimised in real-time. Thus, future work will look into merging the proposed methods with other existing strategies to give an even wider range of alternatives to the final user