Model predictive contouring control for autonomous ground vehicles

Increment in the car accidents and energy wasted inefficiently makes the field of the autonomous vehicles more attractive for automotive companies such as Tesla, Volvo and Mercedes also attract academic researcher's attention due to competitive structure of the problem of autonomy, because it is open to development and testing of the new and advanced control methods and field of autonomous vehicles has unpredictable problems in its nature. Numerious methods have been proposed for autonomous vehicle control. At the beginning classical methods applied to this problem. But classical methods do not have constraint handling such as keeping the vehicle always on track or not exceeding pre-defined speed in a systematic way and do not have preferable objective achievement such as minimizing the traveling time, minimizing the amount of wasted energy, or maximizing the safety in their nature, so the method used in this field must have constraint handling in a systematic way that is always achievable and objective achievement in an intuitive way by predicting the all possible situations from the model of the vehicle and from the road like human driver does. Briefly, it is appropriate to use model predictive control which is a subtopic of the optimal control theory in autonomous vehicles and in this thesis model predictive control is used to make a car autonomous with capability of constraint handling and with an adjustable objective in an intuitive way such as tuning the weighting factors in the optimization problem. Road information is needed to be able to take the border constraints in account and there should be a path that will be followed by minimizing the positional errors between the vehicle and road or at least there should be a path that defines the progress taken by the vehicle. One of the model predictive control approaches applied into the autonomous vehicles is defining a path that achieves a pre-defined objective such as least curvature, minimum lap time, maximum path accuracy, and then following this path using the controller, so before tracking, 1d path must be planned on 2d road, this is a two-layer approach consists of high level path planner and low level path tracking controller, but the calculation of the optimal path is a hard task due to its non-convex nature. The other model predictive control approach is to make planning and tracking at the same time, this is called one-layer approach and one of them is "model predictive contouring control". In model predictive contouring control approach, first, a path is chosen for only progress indication, then traveled distance of the projection of the vehicle on this pre-chosen path is maximized so even if the vehicle is not onto this path, it completes the lap, this is called progress of the vehicle and as stated it is measured by the projection of the car on the path. Generally, this path defines progress is chosen as center line of the 2d road. At the same time with the progress maximization, the error between the vehicle and its projection which is called contouring error is minimized but projection is itself an optimization problem, the result is optimization in an optimization problem and this is too complex to do in real time. To overcome this issue, projection approximation is used, and this approximated projection of the vehicle on the path is dedicated as a new optimization variable, and called path variable. It is controlled by the virtual input. Approximation is valid only when the longitudinal error between real projection and approximated projection is almost zero, this longitudinal error is called lag error. Path variable and its virtual control variable are added to the optimization problem so that maximization of the progress and the minimization of the contouring and lag errors can be achieved by tuning three weighting factors in an intuitive way. If speed is desired then the weighting on lag error is increased, if the accuracy is more essential then the weighting on contouring error is increased. In order to follow just one known road function in the prediction horizan at time step k, the road is divided into known functions and function areas in which center line of the road is currently followed road function. When the vehicle enters a next road function area, then in the whole prediction horizon, this road function is used as the progress path. The joining these independent road paths is the problem for this thesis, there must be a switching to change the road function. As switching, intersection of the currently followed road and the next road is used. When the vehicle enters the intersection area, it suddenly follows the next road function and kept into the new borders. Intersection area provides switching before projection arrives end point of the currently followed line, and this decrease the possibility of the infeasibilty at the turnings. In summary, effect of the weighting factor in the model predictive control approach and the new proposed intersection area method for turnings are tested in this thesis.