Page - (000102) - in Autonomes Fahren - Technische, rechtliche und gesellschaftliche Aspekte

Implementable Ethics for Autonomous Vehicles90 In a classic optimal control problem, the goal of the system is expressed in the form of a cost function that the controller should seek to maximize or minimize. For instance, the goal of steering a vehicle to a desired path can be described as minimizing the error between the path taken by the vehicle and the desired path over a certain time horizon. For a given vehicle path, the cost associated with that path could be calculated by choosing a number of points in time (for instance, N), predicting the error between this path and the desired path at each of these points and summing the squared error (Figure 5.2). The control input would therefore be the steering command that minimized this total error or cost function, J, over the time horizon: J C e i i N = ∑ ( ) = 1 1 2 (5.1) Other desired objectives can be achieved by adding additional elements to the cost function. Often, better tracking performance can be achieved by rapidly moving the inputs (for ex- ample, the steering) to compensate for any errors. This, however, reduces the smoothness of the system operation and may cause additional wear on the steering actuators. The costs associated with using the input can be captured by placing an additional cost on changing the steering angle, į, between time steps: J C e i C j j i N j N = ∑ ( ) + ∑ +( )− ( ) = = − 1 1 2 2 1 1 1δ δ (5.2) The choice of the weights, C1 and C2, in the cost function has a large impact on the system performance. Increasing the weight on steering angle change, C2, in the example above will produce a controller that tolerates some deviation from the path in order to keep the steering command quite gentle. Decreasing the weight on steering has the opposite effect, tracking more tightly even if large steering angle changes are needed to do so. Thus the weights can be chosen to reflect actual costs related to the system operation or used as tuning knobs to more qualitatively adjust the system performance across different objectives. Fig. 5.2 Generating a cost from the difference between a desired path (black) and the vehicle’s actual path (blue)