Real-Time Unified Trajectory Planning and Optimal Control for Urban Autonomous Driving Under Static and Dynamic Obstacle Constraints

Trajectory planning and control have historically been separated into two modules in automated driving stacks. Trajectory planning focuses on higher-level tasks like avoiding obstacles and staying on the road surface, whereas the controller tries its best to follow an ever changing reference trajectory. We argue that this separation is (1) flawed due to the mismatch between planned trajectories and what the controller can feasibly execute, and (2) unnecessary due to the flexibility of the model predictive control (MPC) paradigm. Instead, in this paper, we present a unified MPC-based trajectory planning and control scheme that guarantees feasibility with respect to road boundaries, the static and dynamic environment, and enforces passenger comfort constraints. The scheme is evaluated rigorously in a variety of scenarios focused on proving the effectiveness of the optimal control problem (OCP) design and real-time solution methods. The prototype code will be released at https://github.com/WATonomous/control

Integrated trajectory planning and control for obstacle avoidance manoeuvre using nonlinear vehicle model-predictive algorithm

In the current literature, model-predictive (MP) algorithm is widely applied in autonomous vehicle trajectory planning and control but most of the current studies only apply the linear tyre model, which cannot accurately present the tyre non-linear characteristic. Furthermore, most of these studies separately consider the trajectory planning and trajectory control of the autonomous vehicle and few of them have integrated the trajectory planning and trajectory control together. To fill in above research gaps, this study proposes the integrated trajectory planning and trajectory control method using a non-linear vehicle MP algorithm. To fully utilise the advantages of four-wheel-independent-steering and four-wheel-independent-driving vehicle, the MP algorithm is proposed based on four-wheel dynamics model and non-linear Dugoff tyre model. This study also proposes the mathematical modelling of the static obstacle and dynamic obstacle for the obstacle avoidance manoeuvre of the autonomous vehicle. Finally, simulation results have been presented to show the effectiveness of the proposed control method

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 real-time nonlinear model predictive control strategy for stabilisation of an electric vehicle at the limits of handling

In this paper, we propose a real-time nonlinear model predictive control (NMPC) strategy for stabilization of a vehicle near the limit of lateral acceleration using the rear axle electric torque vectoring configuration of an electric vehicle. A nonlinear four-wheel vehicle model that neglects the wheel dynamics is coupled with a nonlinear tire model to design three MPC strategies of different levels of complexity that are implementable online: one that uses a linearized version of the vehicle model and then solves the resulting quadratic program problem to compute the necessary longitudinal slips on the rear wheels, a second one that employs the real-time iteration scheme on the NMPC problem, and a third one that applies the primal dual interior point method on the NMPC problem instead until convergence. Then, a sliding mode slip controller is used to compute the necessary torques on the rear wheels based on the requested longitudinal slips. After analyzing the relative tradeoffs in performance and computational cost between the three MPC strategies by comparing them against the optimal solution in a series of simulation studies, we test the most promising solution in a high-fidelity environment

High-Speed Obstacle Avoidance at the Dynamic Limits for Autonomous Ground Vehicles

Enabling autonomy of passenger-size and larger vehicles is becoming increasingly important in both military and commercial applications. For large autonomous ground vehicles (AGVs), the vehicle dynamics are critical to consider to ensure vehicle safety during obstacle avoidance maneuvers especially at high speeds. This research is concerned with large-size high-speed AGVs with high center of gravity that operate in unstructured environments. The term `unstructured' in this context denotes that there are no lanes or traffic rules to follow. No map of the environment is available a priori. The environment is perceived through a planar light detection and ranging sensor. The mission of the AGV is to move from its initial position to a given target position safely and as fast as possible. In this dissertation, a model predictive control (MPC)-based obstacle avoidance algorithm is developed to achieve the objectives through an iterative simultaneous optimization of the path and the corresponding control commands. MPC is chosen because it offers a rigorous and systematic approach for taking vehicle dynamics and safety constraints into account. Firstly, this thesis investigates the level of model fidelity needed for an MPC-based obstacle avoidance algorithm to be able to safely and quickly avoid obstacles even when the vehicle is close to its dynamic limits. Five different representations of vehicle dynamics models are considered. It is concluded that the two Degrees-of-Freedom (DoF) representation that accounts for tire nonlinearities and longitudinal load transfer is necessary for the MPC-based obstacle avoidance algorithm to operate the vehicle at its limits within an environment that includes large obstacles. Secondly, existing MPC formulations for passenger vehicles in structured environments do not readily apply to this context. Thus, a novel nonlinear MPC formulation is developed. First, a new cost function formulation is used that aims to find the shortest path to the target position. Second, a region partitioning approach is used in conjunction with a multi-phase optimal control formulation to accommodate the complicated forms of obstacle-free regions from an unstructured environment. Third, the no-wheel-lift-off condition is established offline using a fourteen DoF vehicle dynamics model and is included in the MPC formulation. The formulation can simultaneous optimize both steering angle and reference longitudinal speed commands. Simulation results show that the proposed algorithm is capable of safely exploiting the dynamic limits of the vehicle while navigating the vehicle through sensed obstacles of different size and number. Thirdly, in the algorithm, a model of the vehicle is used explicitly to predict and optimize future actions, but in practice, the model parameter values are not exactly known. It is demonstrated that using nominal parameter values in the algorithm leads to safety issues in about one fourth of the evaluated scenarios with the considered parametric uncertainty distributions. To improve the robustness of the algorithm, a novel double-worst-case formulation is developed. Results from simulations with stratified random scenarios and worst-case scenarios show that the double-worst-case formulation considering both the most likely and less likely worst-case scenarios renders the algorithm robust to all uncertainty realizations tested. The trade-off between the robustness and the task completion performance of the algorithm is also quantified. Finally, in addition to simulation-based validation, preliminary experimental validation is also performed. These results demonstrate that the developed algorithm is promising in terms of its capability of avoiding obstacles. Limitations and potential improvements of the algorithm are discussed.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135770/1/ljch_1.pd

Trajectory Planning for Autonomous High-Speed Overtaking in Structured Environments using Robust MPC

Automated vehicles are increasingly getting mainstreamed and this has pushed development of systems for autonomous manoeuvring (e.g., lane-change, merge, overtake, etc.) to the forefront. A novel framework for situational awareness and trajectory planning to perform autonomous overtaking in high-speed structured environments (e.g., highway, motorway) is presented in this paper. A combination of a potential field like function and reachability sets of a vehicle are used to identify safe zones on a road that the vehicle can navigate towards. These safe zones are provided to a tube-based robust model predictive controller as reference to generate feasible trajectories for combined lateral and longitudinal motion of a vehicle. The strengths of the proposed framework are: (i) it is free from nonconvex collision avoidance constraints, (ii) it ensures feasibility of trajectory even if decelerating or accelerating while performing lateral motion, and (iii) it is real-time implementable. The ability of the proposed framework to plan feasible trajectories for highspeed overtaking is validated in a high-fidelity IPG CarMaker and Simulink co-simulation environment

Evaluation of model predictive control method for collision avoidance of automated vehicles

Indiana University-Purdue University Indianapolis (IUPUI)Collision avoidance design plays an essential role in autonomous vehicle technology. It's an attractive research area that will need much experimentation in the future. This research area is very important for providing the maximum safety to automated vehicles, which have to be tested several times under diFFerent circumstances for safety before use in real life. This thesis proposes a method for designing and presenting a collision avoidance maneuver by using a model predictive controller with a moving obstacle for automated vehicles. It consists of a plant model, an adaptive MPC controller, and a reference trajectory. The proposed strategy applies a dynamic bicycle model as the plant model, adaptive model predictive controller for the lateral control, and a custom reference trajectory for the scenario design. The model was developed using the Model Predictive Control Toolbox and Automated Driving Toolbox in Matlab. Builtin tools available in Matlab/Simulink were used to verify the modeling approach and analyze the performance of the system. The major contribution of this thesis work was implementing a novel dynamic obstacle avoidance control method for automated vehicles. The study used validated parameters obtained from previous research. The novelty of this research was performing the studies using a MPC based controller instead of a sliding mode controller, that was primarily used in other studies. The results obtained from the study are compared with the validated models. The comparisons consisted of the lateral overlap, lateral error, and steering angle simulation results between the models. Additionally, this study also included outcomes for the yaw angle. The comparisons and other outcomes obtained in this study indicated that the developed control model produced reasonably acceptable results and recommendations for future studies