Application of Differential Game Theory for Vehicle Collision Avoidance

With respect to autonomous driving, recent advances in the innovative application of robotics have highlighted the importance of interaction between different actors, as robots are no longer confined to specific environments such as factory floors, but face a complex world with many other actors. Therefore, rational interaction between different actors is required to avoid conflicts. Autonomous actors must take into account the decisions of other actors when making decisions themselves. In the present work, the approach adopted is to use discrete control functions instead of continuous control functions as generally used in differential games. The reason for this is that in a differential game with two or more players, the computation of Nash Equilibria is time consuming and complex calculations have to be performed. For the different discrete control variables of the discrete control functions, the reachability analysis was used to define the different reachable states of the player, which also allows uncertainties for the initial state and the strategies of the players to be taken into account. Based on the reachable states, the cost for each player could be estimated and it is possible through the discrete control functions to consider and solve games in normal form instead of the complex and time-consuming solution process of differential games. Based on the defined reachable states, the individual costs for each player were estimated. The reachability analysis also allows to take into account the uncertainties in the initial state and in the strategy of the players. In order to be able to determine the costs for each player, two groups of cost functions were defined in this work, one containing cost functions that are intended to prevent collisions and the other containing running costs that take into account the speed and comfort of the occupant. In addition, the worst cases were estimated for each pair of controls included in the reachable states. Depending on the cost function, the cost functions were optimized with respect to the maximum or minimum. As part of the nonlinear optimization of the cost functions, optimization functions were defined in which the respective cost functions were adjusted with respect to the worst case. These defined cost functions were simulated using three defined driving scenarios, which include different driving maneuvers and evaluated with respect to their relevance. The simulation results have generally shown that the defined cost functions are reasonable and comprehensible cost functions that can be used in games with two players. A cost function that calculates costs related to collisions energy in the event of a possible collision did not provide the expected results due to the consideration of points as states. Since an exact intersection of points is unlikely due to different parameters, complexity and defined uncertainties, this is reflected in the simulation results. Further work could address this problem and consider other geometric bodies instead of points, so that comprehensible results can be simulated.