Autonomous driving vehicles are developing rapidly; however, the control systems for autonomous driving vehicles tracking smoothly in high speed are still challenging. This chapter develops non-linear model predictive control (NMPC) schemes for controlling autonomous driving vehicles tracking on feasible trajectories. The optimal control action for vehicle speed and steering velocity is generated online using NMPC optimizer subject to vehicle dynamic and physical constraints as well as the surrounding obstacles and the environmental side-slipping conditions. NMPC subject to softened state constraints provides a better possibility for the optimizer to generate a feasible solution as real-time subject to online dynamic constraints and to maintain the vehicle stability. Different parameters of NMPC are simulated and analysed to see the relationships between the NMPC horizon prediction length and the weighting values. Results show that the NMPC can control the vehicle tracking exactly on different trajectories with minimum tracking errors and with high comfortability.
TopIntroduction
The rapid and widespread development of advanced technologies on robotics, automation, IT and high-speed communication networks has made the application of autonomous driving vehicles growing constantly and changing the society. Autonomous vehicles have been received considerable attention in recent years and the needs are arising for the mechatronic systems to control the vehicle tracking from any given start points to any given destination points online generated from the global positioning system (GPS) and subject to the vehicle physical constraints.
This book chapter develops a real-time control system for an autonomous ground vehicle directed online from the GPS maps or/and from unmanned aerial vehicles (UAVs) images. This system can be applied for auto traveling on road or off road for unmanned ground vehicles. The system can also be used for auto parking and auto driving vehicles.
Motivation for the use of MPC is its ability to handle the constraints online within its open-loop optimal control problems while many other control techniques are conservative in handling online constraints or even try to avoid activating them, thus, losing the best performance that may be achievable. MPC can make the close loop system operating near its limits and hence, produce much better performance.
However, MPC regulator is designed for online implementation, any infeasible solution of the optimization problems cannot be allowed. To improve the system’s stability once some constraints are violated, some kinds of softened constraints or tolerant regions can be developed whereas the output constraints are not strictly imposed and can be violated somewhat during the evolution of the performance.
To deal with the system uncertainties and the model-plant mismatches, robust MPC algorithms can be built accounting for the modelling errors at the controller design. Robust MPC can forecast all possible models in the plant uncertainty set and the optimal actions then can be determined through the min-max optimization.
The reference feasible trajectories can be generated online using solver for ordinary differential equations (ODEs) with the flatness or polynomial equations presented in (Minh V.T, 2013). Algorithms for robust MPC tracking set points are referred in Minh V.T and Hashim F.B (2011), where the system’s uncertainties are demonstrated by a set of multiple models via a tree trajectory and its branches and the robust MPC problem is to find the optimal control actions that, once implemented, cause all branches to converge to a robust control invariant set.
Application of MPC in controlling vehicle speed and engine torque is referred to in Minh V.T and Hashim F.B (2012), where a real time transition strategy with MPC is achieved for quick and smooth clutch engagements. Essential knowledge on vehicle handling and steering calculations is referred to in Minh V.T (2012), in chapter 8 and chapter 9, where the vehicle dynamic behaviours are analysed and applied for designing a fee-error feedback controller for its autonomous tracking.
Robust MPC schemes for input saturated and softened state constraints are referred from Minh V.T and Afzulpurkar N (2005), where uncertain systems are used with linear matrix inequalities (LMIs) subject to input and output saturated constraints. Nonlinear MPC (NMPC) algorithms are referred to in Minh V.T and Afzulpurkar N (2006), where three NMPC regulators of zero terminal region, quasi-infinite horizon, and softened state constraints are presented and compared. In NMPC, all solution for the regulator is implemented for close-lope control by solving on-line the ODEs repeatedly.
Control of vehicle tracking with MPC can be referred to in some several latest research papers. However, the idea of an MPC for online tracking optimal trajectories generated from flatness or polynomial equations is still not available. Some of MPC schemes for autonomous ground vehicle can be seen in Falcon P. et al (2008), where an initial frame work based on MPC for a simplified vehicle is presented. However, the research has ignored the real-time solving of the vehicle ODEs equations and failed to generate the optimal controlled inputs for the vehicle linear velocity and its steering velocity. Similarly, another recent paper on optimal MPC for path tracking of autonomous vehicles by Lei L. et al (2011) is presented where the vehicle’s equations of motion are approximately linearized by the vehicle coordinates and the heading angle. The paper failed to include the steering angle in its equations.