The trend of more advanced driver-assistance features and the development toward autonomous vehicles enable new possibilities in the area of active safety. With more information available in the vehicle about the surrounding traffic and the road ahead, there is the possibility of improved active-safety systems that make use of this information for stability control in safety-critical maneuvers. Such a system could adaptively make a trade-off between controlling the longitudinal, lateral, and rotational dynamics of the vehicle in such a way that the risk of collision is minimized. To support this development, the main aim of this licentiate thesis is to provide new insights into the optimal behavior for autonomous vehicles in safety-critical situations. The knowledge gained have the potential to be used in future vehicle control systems, which can perform maneuvers at-the-limit of vehicle capabilities.

Stability control of a vehicle in autonomous safety-critical at-the-limit maneuvers is analyzed by the use of optimal control. Since analytical solutions of the studied optimal control problems are intractable, they are discretized and solved numerically. A formulation of an optimization criterion depending on a single interpolation parameter is introduced, which results in a continuous family of optimal coordinated steering and braking patterns. This formulation provides several new insights into the relation between different braking patterns for vehicles in at-the-limit maneuvers. The braking patterns bridge the gap between optimal lane-keeping control and optimal yaw control, and have the potential to be used for future active-safety systems that can adapt the level of braking to the situation at hand. A new illustration named attainable force volumes is introduced, which effectively shows how the trajectory of a vehicle maneuver relates to the attainable forces over the duration of the maneuver. It is shown that the optimal behavior develops on the boundary surface of the attainable force volume. Applied to lane-keeping control, this indicates a set of control principles similar to those analytically obtained for friction-limited particle models in earlier research, but is shown to result in vehicle behavior close to the globally optimal solution also for more complex models and scenarios.

Without a driver to fall back on, a fully self-driving car needs to be able to handle any situation it can encounter. With the perspective of future safety systems, this research studies autonomous maneuvering at the tire-road friction limit. In these situations, the dynamics is highly nonlinear, and the tire-road parameters are uncertain.

To gain insights into the optimal behavior of autonomous safety-critical maneuvers, they are analyzed using optimal control. Since analytical solutions of the studied optimal control problems are intractable, they are solved numerically. An optimization formulation reveals how the optimal behavior is influenced by the total amount of braking. By studying how the optimal trajectory relates to the attainable forces throughout a maneuver, it is found that maximizing the force in a certain direction is important. This is like the analytical solutions obtained for friction-limited particle models in earlier research, and it is shown to result in vehicle behavior close to the optimal also for a more complex model.

Based on the insights gained from the optimal behavior, controllers for autonomous safety maneuvers are developed. These controllers are based on using acceleration-vector references obtained from friction-limited particle models. Exploiting that the individual tire forces tend to be close to their friction limits, the desired tire slip angles are determined for a given acceleration-vector reference. This results in controllers capable of operating at the limit of friction at a low computational cost and reduces the number of vehicle parameters used. For straight-line braking, ABS can intervene to reduce the braking distance without prior information about the road friction. Inspired by this, a controller that uses the available actuation according to the least friction necessary to avoid a collision is developed, resulting in autonomous collision avoidance without any estimation of the tire–road friction.

Investigating time-optimal lane changes, it is found that a simple friction-limited particle model is insufficient to determine the desired acceleration vector, but including a jerk limit to account for the yaw dynamics is sufficient. To enable a tradeoff between braking and avoidance with a more general obstacle representation, the acceleration-vector reference is computed in a receding-horizon framework.

The controllers developed in this thesis show great promise with low computational cost and performance not far from that obtained offline by using numerical optimization when evaluated in high-fidelity simulation.