Avoidance maneuvers at normal driving speed or higher are demanding driving situations that force the vehicle to the limit of tire-road friction in critical situations. To study and develop control for these situations, dynamic optimization has been in growing use in research. One idea to handle such optimization computations effectively is to divide the total maneuver into a sequence of sub-maneuvers and to associate a segmented optimization problem to each sub-maneuver. Here, the alternating augmented Lagrangian method is adopted, which like many other optimization methods benefits strongly from a good initialization, and to that purpose a method with motion candidates is proposed to get an initially feasible motion. The two main contributions are, firstly, the method for computing an initially feasible motion that is found to use obstacle positions and progress of vehicle variables to its advantage, and secondly, the integration with a subsequent step with segmented optimization showing clear improvements in paths and trajectories. Overall, the combined method is able to handle driving scenarios at demanding speeds.

To allow future autonomous passenger vehicles to be used in the same driving situations and conditions as ordinary vehicles are used by human drivers today, the control systems must be able to perform automated emergency maneuvers. In such maneuvers, vehicle dynamics, tire–road interaction, and limits on what the vehicle is capable of performing are key factors to consider. After detecting a static or moving obstacle, an avoidance maneuver or a sequence of lane changes are common ways to mitigate the critical situation. For that purpose, motion planning is important and is a primary task for autonomous-vehicle control subsystems. Optimization-based methods and algorithms for such control subsystems are the main focus of this thesis.

Vehicle-dynamics models and road obstacles are included as constraints to be fulfilled in an optimization problem when finding an optimal control input, while the available freedom in actuation is utilized by defining the optimization criterion. For the criterion design, a new proposal is to use a lane-deviation penalty, which is shown to result in well-behaved maneuvers and, in comparison to minimum-time and other lateral-penalty objective functions, decreases the time that the vehicle spends in the opposite lane.

It is observed that the final phase of a double lane-change maneuver, also called the recovery phase, benefits from a dedicated treatment. This is done in several steps with different criteria depending on the phase of the maneuver. A theoretical redundancy analysis of wheel-torque distribution, which is derived independently of the optimization criterion, complements and motivates the suggested approach.

With a view that a complete maneuver is a sequence of two or more sub-maneuvers, a decomposition approach resulting in maneuver segments is proposed. The maneuver segments are shown to be possible to determine with coordinated parallel computations with close to optimal results. Suitable initialization of segmented optimizations benefits the solution process, and different initialization approaches are investigated. One approach is built upon combining dynamically feasible motion candidates, where vehicle and tire forces are important to consider. Such candidates allow addressing more complicated situations and are computed under dynamic constraints in the presence of body and wheel slip. 

To allow a quick reaction of the vehicle control system to moving obstacles and other sudden changes in the conditions, a feedback controller capable of replanning in a receding-horizon fashion is developed. It employs a coupling between motion planning using a friction-limited particle model and a novel low-level controller following the acceleration-vector reference of the computed plan. The controller is shown to have real-time performance.

A controller for critical vehicle maneuvering is proposed that avoids obstacles and keeps the vehicle on the road while achieving heavy braking. It operates at the limit of friction and is structured in two main steps: a motion-planning step based on receding-horizon planning to obtain acceleration-vector references, and a low-level controller for following these acceleration references and transforming them into actuator commands. The controller is evaluated in a number of challenging scenarios and results in a well behaved vehicle with respect to, e.g., the steering angle, the body slip, and the path. It is also demonstrated that the controller successfully balances braking and avoidance such that it really takes advantage of the braking possibilities. Specifically, for a moving obstacle, it makes use of a widening gap to perform more braking, which is a clear advantage of the online replanning capability if the obstacle should be a moving human or animal. Finally, real-time capabilities are demonstrated. In conclusion, the controller performs well, both from a functional perspective and from a real-time perspective.

Segmenting a motion-planning problem into smaller subproblems could be beneficial in terms of computational complexity. This observation is used as a basis for a new sub-maneuver decomposition approach investigated in this paper in the context of optimal evasive maneuvers for autonomous ground vehicles. The recently published alternating augmented Lagrangianmethod is adopted and leveraged on, which turns out to fit the problem formulation with several attractive properties of the solution procedure. The decomposition is based on moving the coupling constraints between the sub-maneuvers into a separate coordination problem, which is possible to solve analytically. The remaining constraints and the objective function are decomposed into subproblems, one for each segment, which means that parallel computation is possible and benecial. The method is implemented and evaluated in a safety-critical double lane-change scenario. By using the solution of a low-complexity initialization problem and applying warm-start techniques in the optimization, a solution is possible to obtain after just a few alternating iterations using the developed approach. The resulting computational time is lower than solving one optimization problem for the full maneuver.

This thesis studies motion planning for future autonomous vehicles with main focus on passenger cars. By having automatic steering and braking together with information about the environment, such as other participants in the traffic or obstacles, it would be possible to perform autonomous maneuvers while taking limitations of the vehicle and road–tire interaction into account. Motion planning is performed to find such maneuvers that bring the vehicle from the current state to a desired future state, here by formulating the motion-planning problem as an optimal control problem. There are a number of challenges for such an approach to motion planning; some of them are how to formulate the criterion in the motion planning (objective function in the corresponding optimal control problem), and how to make the solution of motion-planning problems efficient to be useful in online applications. These challenges are addressed in this thesis.

As a criterion for motion-planning problems of passenger vehicles on doublelane roads, it is investigated to use a lane-deviation penalty function to capture the observation that it is dangerous to drive in the opposing lane, but safe to drive in the original lane after the obstacle. The penalty function is augmented with certain additional terms to address also the recovery behavior of the vehicle. The resulting formulation is shown to provide efficient and steady maneuvers and gives a lower time in the opposing lane compared to other objective functions. Under varying parameters of the scenario formulation, the resulting maneuvers are changing in a way that exhibits structured characteristics.

As an approach to improve efficiency of computations for the motion-planning problem, it is investigated to segment motion planning of the full maneuver into several smaller maneuvers. A way to extract segments is considered from a vehicle dynamics point of view, and it is based on extrema of the vehicle orientation and the yaw rate. The segmentation points determined using this approach are observed to allow efficient splitting of the optimal control problem for the full maneuver into subproblems.

Having a method to segment maneuvers, this thesis further studies methods to allow parallel computation of these maneuvers. One investigated method is based on Lagrange relaxation and duality decomposition. Smaller subproblems are formulated, which are governed by solving a low-complexity coordination problem. Lagrangian relaxation is performed on a subset of the dynamic constraints at the segmentation points, while the remaining variables are predicted. The prediction is possible because of the observed structured characteristics resulting from the used lane-deviation penalty function. An alternative approach is based on adoption of the alternating augmented Lagrangian method. Augmentation of the Lagrangian allows to apply relaxation for all dynamic constraints at the segmentation points, and the alternating approach makes it possible to decompose the full problem into subproblems and coordinating their solutions by analytically solving an overall coordination problem. The presented decomposition methods allow computation of maneuvers with high correspondence and lower computational times compared to the results obtained for solving the full maneuver in one step.

To decrease the complexity of motion-planning optimizations, a segmentation and merging strategy for maneuvers is proposed. Maneuvers that are at-the-limit of friction are of special interest since they appear in many critical situations. The segmentation pointsare used to set constraints for several smaller optimizations for parts of the full maneuver, which later are merged and compared withoptimizations of the full maneuver. The technique is illustrated for a double lane-change maneuver.