Feasibility Analysis For Constrained Model Predictive Control Based Motion Cueing Algorithm

This paper deals with motion control for an 8-degree-of-freedom (DOF) high performance driving simulator. We formulate a constrained optimal control that defines the dynamical behavior of the system. Furthermore, the paper brings together various methodologies for addressing feasibility issues arising in implicit model predictive control-based motion cueing algorithms. The implementation of different techniques is described and discussed subsequently. Several simulations are carried out in the simulator platform. It is observed that the only technique that can provide ensured closed-loop stability by assuring feasibility over all prediction horizons is a braking law that basically saturates the control inputs in the constrained form

Motion Cueing Algorithm for Effective Motion Perception: A frequency-splitting MPC Approach

Model predictive control (MPC) is a promising technique for motion cueing in driving simulators, but its high computation time limits widespread real-time application. This paper proposes a hybrid algorithm that combines filter-based and MPC-based techniques to improve specific force tracking while reducing computation time. The proposed algorithm divides the reference acceleration into low-frequency and high-frequency components. The high-frequency component serves as a reference for translational motion to avoid workspace limit violations, while the low-frequency component is for tilt coordination. The total acceleration serves as a reference for combined specific force with the highest priority to enable compensation of deviations from its reference values. The algorithm uses constraints in the MPC formulation to account for workspace limits and workspace management is applied. The investigated scenarios were a step signal, a multi-sine wave and a recorded real-drive slalom maneuver. Based on the conducted simulations, the algorithm produces approximately 15% smaller root means squared error (RMSE) for the step signal compared to the state-of-the-art. Around 16% improvement is observed when the real-drive scenario is used as the simulation scenario, and for the multi-sine wave, 90% improvement is observed. At higher prediction horizons the algorithm matches the performance of a state-of-the-art MPC-based motion cueing algorithm. Finally, for all prediction horizons, the frequency-splitting algorithm produced faster results. The pre-generated references reduce the required prediction horizon and computational complexity while improving tracking performance. Hence, the proposed frequency-splitting algorithm outperforms state-of-the-art MPC-based algorithm and offers promise for real-time application in driving simulators.Comment: 8 pages, 10 figures, 3 tables, conference (DSC 2023

Evaluation of Vehicle Ride Height Adjustments Using a Driving Simulator

Testing of vehicle design properties by car manufacturers is primarily performed on-road and is resource-intensive, involving costly physical prototypes and large time durations between evaluations of alternative designs. In this paper, the applicability of driving simulators for the virtual assessment of ride, steering and handling qualities was studied by manipulating vehicle air suspension ride height (RH) (ground clearance) and simulator motion platform (MP) workspace size. The evaluation was carried out on a high-friction normal road, routinely used for testing vehicle prototypes, modelled in a driving simulator, and using professional drivers. The results showed the differences between the RHs were subjectively distinguishable by the drivers in many of the vehicle attributes. Drivers found standard and low RHs more appropriate for the vehicle in terms of the steering and handling qualities, where their performance was deteriorated, such that the steering control effort was the highest in low RH. This indicated inconsistency between subjective preferences and objective performance and the need for alternative performance metrics to be defined for expert drivers. Moreover, an improvement in drivers’ performance was observed, with a reduction of steering control effort, in larger MP configurations

Solving the Constrained Problem in Model Predictive Control Based Motion Cueing Algorithm with a Neural Network Approach

Because of the critical timing requirement, one major issue regarding model predictive control-based motion cueing algorithms is the calculation of real-time optimal solutions. In this paper, a continuous-time recurrent neural network-based gradient method is applied to compute the optimal control action in real time for an MPCbased MCA.We demonstrate that by implementing a saturation function for the constraints in the decision variables and a regulation for the energy function in the network, a constrained optimization problem can be solved without using any penalty function. Simulation results are included to compare the proposed approach and substantiate the applicability of recurrent neural networks as a quadratic programming solver. A comparison with another QP solver shows that our method can find an optimal solution much faster and with the same precision

Algorithms and Applications for Nonlinear Model Predictive Control with Long Prediction Horizon

Fast implementations of NMPC are important when addressing real-time control of systems exhibiting features like fast dynamics, large dimension, and long prediction horizon, as in such situations the computational burden of the NMPC may limit the achievable control bandwidth. For that purpose, this thesis addresses both algorithms and applications. First, fast NMPC algorithms for controlling continuous-time dynamic systems using a long prediction horizon have been developed. A bridge between linear and nonlinear MPC is built using partial linearizations or sensitivity update. In order to update the sensitivities only when necessary, a Curvature-like measure of nonlinearity (CMoN) for dynamic systems has been introduced and applied to existing NMPC algorithms. Based on CMoN, intuitive and advanced updating logic have been developed for different numerical and control performance. Thus, the CMoN, together with the updating logic, formulates a partial sensitivity updating scheme for fast NMPC, named CMoN-RTI. Simulation examples are used to demonstrate the effectiveness and efficiency of CMoN-RTI. In addition, a rigorous analysis on the optimality and local convergence of CMoN-RTI is given and illustrated using numerical examples. Partial condensing algorithms have been developed when using the proposed partial sensitivity update scheme. The computational complexity has been reduced since part of the condensing information are exploited from previous sampling instants. A sensitivity updating logic together with partial condensing is proposed with a complexity linear in prediction length, leading to a speed up by a factor of ten. Partial matrix factorization algorithms are also proposed to exploit partial sensitivity update. By applying splitting methods to multi-stage problems, only part of the resulting KKT system need to be updated, which is computationally dominant in on-line optimization. Significant improvement has been proved by giving floating point operations (flops). Second, efficient implementations of NMPC have been achieved by developing a Matlab based package named MATMPC. MATMPC has two working modes: the one completely relies on Matlab and the other employs the MATLAB C language API. The advantages of MATMPC are that algorithms are easy to develop and debug thanks to Matlab, and libraries and toolboxes from Matlab can be directly used. When working in the second mode, the computational efficiency of MATMPC is comparable with those software using optimized code generation. Real-time implementations are achieved for a nine degree of freedom dynamic driving simulator and for multi-sensory motion cueing with active seat

Autonomous Collision Avoidance Using MPC with LQR-Based Weight Transformation

Model predictive control (MPC) is a multi-objective control technique that can handle system constraints. However, the performance of an MPC controller highly relies on a proper prioritization weight for each objective, which highlights the need for a precise weight tuning technique. In this paper, we propose an analytical tuning technique by matching the MPC controller performance with the performance of a linear quadratic regulator (LQR) controller. The proposed methodology derives the transformation of a LQR weighting matrix with a fixed weighting factor using a discrete algebraic Riccati equation (DARE) and designs an MPC controller using the idea of a discrete time linear quadratic tracking problem (LQT) in the presence of constraints. The proposed methodology ensures optimal performance between unconstrained MPC and LQR controllers and provides a sub-optimal solution while the constraints are active during transient operations. The resulting MPC behaves as the discrete time LQR by selecting an appropriate weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. In this paper, the effectiveness of the proposed technique is investigated in the application of a novel vehicle collision avoidance system that is designed in the form of linear inequality constraints within MPC. The simulation results confirm the potency of the proposed MPC control technique in performing a safe, feasible and collision-free path while respecting the inputs, states and collision avoidance constraints

Enhancing human motion perception in model predictive motion cueing algorithm

In this research, the predictive motion cueing algorithm has been optimized for improving a human driver sensation based on the mathematical model. The Model Predictive Control cost function and the prediction and control horizons are optimized. The future trajectory is predicted by artificial intelligence and the related control actions are applied beforehand in real-time

Model-Based Control Techniques for Automotive Applications

Two different topics are covered in the thesis. Model Predictive Control applied to the Motion Cueing Problem In the last years the interest about dynamic driving simulators is increasing and new commercial solutions are arising. Driving simulators play an important role in the development of new vehicles and advanced driver assistance devices: in fact, on the one hand, having a human driver on a driving simulator allows automotive manufacturers to bridge the gap between virtual prototyping and on-road testing during the vehicle development phase; on the other hand, novel driver assistance systems (such as advanced accident avoidance systems) can be safely tested by having the driver operating the vehicle in a virtual, highly realistic environment, while being exposed to hazardous situations. In both applications, it is crucial to faithfully reproduce in the simulator the driver's perception of forces acting on the vehicle and its acceleration. This has to be achieved while keeping the platform within its limited operation space. Such strategies go under the name of Motion Cueing Algorithms. In this work, a particular implementation of a Motion Cueing algorithm is described, that is based on Model Predictive Control technique. A distinctive feature of such approach is that it exploits a detailed model of the human vestibular system, and consequently differs from standard Motion Cueing strategies based on Washout Filters: such feature allows for better implementation of tilt coordination and more efficient handling of the platform limits. The algorithm has been evaluated in practice on a small-size, innovative platform, by performing tests with professional drivers. Results show that the MPC-based motion cueing algorithm allows to effectively handle the platform working area, to limit the presence of those platform movements that are typically associated with driver motion sickness, and to devise simple and intuitive tuning procedures. Moreover, the availability of an effective virtual driver allows the development of effective predictive strategies, and first simulation results are reported in the thesis. Control Techniques for a Hybrid Sport Motorcycle Reduction of the environmental impact of transportation systems is a world wide priority. Hybrid propulsion vehicles have proved to have a strong potential to this regard, and different four-wheels solutions have spread out in the market. Differently from cars, and even if they are considered the ideal solution for urban mobility, motorbikes and mopeds have not seen a wide application of hybrid propulsion yet, mostly due to the more strict constraints on available space and driving feeling. In the thesis, the problem of providing a commercial 125cc motorbike with a hybrid propulsion system is considered, by adding an electric engine to its standard internal combustion engine. The aim for the prototype is to use the electrical machine (directly keyed on the drive shaft) to obtain a torque boost during accelerations, improving and regularizing the supplied power while reducing the emissions. Two different control algorithms are proposed 1) the first is based on a standard heuristic with adaptive features, simpler to implement on the ECU for the prototype; 2) the second is a torque-split optimal-control strategy, managing the different contributions from the two engines. A crucial point is the implementation of a Simulink virtual environment, realized starting from a commercial tool, VI-BikeRealTime, to test the algorithms. The hybrid engine model has been implemented in the tool from scratch, as well as a simple battery model, derived directly from data-sheet characteristics by using polynomial interpolation. The simulation system is completed by a virtual rider and a tool for build test circuits. Results of the simulations on a realistic track are included, to evaluate the different performance of the two strategies in a closed loop environment (thanks to the virtual rider). The results from on-track tests of the real prototype, using the first control strategy, are reported too

Real Coded Mixed Integer Genetic Algorithm for Geometry Optimization of Flight Simulator Mechanism Based on Rotary Stewart Platform

Featured Application Low-cost flight simulators with electric rotary actuators and optimized geometry for flight simulation. Designing the motion platform for the flight simulator is closely coupled with the particular aircraft's flight envelope. While in training, the pilot on the motion platform has to experience the same feeling as in the aircraft. That means that flight simulators need to simulate all flight cases and forces acting upon the pilot during flight. Among many existing mechanisms, parallel mechanisms based on the Stewart platform are suitable because they have six degrees of freedom. In this paper, a real coded mixed integer genetic algorithm (RCMIGA) is applied for geometry optimization of the Stewart platform with rotary actuators (6-RUS) to design a mechanism with appropriate physical limitations of workspace and motion performances. The chosen algorithm proved that it can find the best global solution with all imposed constraints. At the same time, the obtained geometry can be manufactured because integer solutions can be mapped to available discrete values. Geometry is defined with a minimum number of parameters that fully define the mechanism with all constraints. These geometric parameters are then optimized to obtain custom-tailored geometry for aircraft flight simulation

Driving Simulator Motion Cueing Assessment: A Platform Design Perspective

The overall aim of this thesis was to study the effects of a simulator’s motion system on vestibular motion cueing fidelity in different contexts, evaluated in terms of drivers’ perception and behaviour, in low and high road friction conditions. The effects of manipulating the motion cueing algorithm (MCA), was found to be a function of the vehicle motion in a manoeuvre, and significant effects were observed. The applicability of simulators for the assessment of vehicle driven attribute qualities such as ride, steering and handling were studied by manipulating vehicle ride height (RH). The differences between the RHs were subjectively distinguishable by the drivers in the simulator. Incongruities between the subjective preferences and objective performances were observed in both of the independent comparisons of the MCAs and RHs. The effects of motion platform (MP) workspace size were found to be dependent on the manoeuvres and road friction level. In the low-friction condition, with the increase of MP size, two opposite effects were observed on drivers’ preferences and their performances, depending on the manoeuvre. In high-friction, in most of the handling and steering qualities, a direct relation was found between the MP size and appropriate vehicle RH. Furthermore, the optimal tuning of the MCAs and optimisation of the MP workspace size was introduced. A conservative motion cueing fidelity criteria was defined. A multi-layered optimisation method was developed that uses the optimal setting of the MCA, to address the MP translational workspace size, and to meet the fidelity criteria; applicable for different manoeuvres. This method was tested on the drivers’ performance data collected from the experiments in the simulator