Page - (000103) - in Autonomes Fahren - Technische, rechtliche und gesellschaftliche Aspekte

915.3 Cost Functions and Consequentialism In the past, the limitations of computational power restricted the form and complexity of cost functions that could be used in systems that require real-time computation of control inputs. Linear quadratic functions of a few variables and simplified problems for which closed-form solutions exist became the textbook examples of the technique. In recent years, however, the ability to efficiently solve certain optimization problems has rapidly expand- ed the applicability of these techniques to a broad range of systems [6]. 5.3 Cost Functions and Consequentialism The basic approach of optimal control – choosing the set of inputs that will optimize a cost function – is directly analogous to consequentialist approaches in philosophy. If the ethical implications of an action can be captured in a cost function, as preference utilitarianism attempts to do, the control inputs that optimize that function produce the ideal outcome in an ethical sense. Since the vehicle can re-evaluate its control inputs, or acts, to produce the best possible result for any given scenario, the optimal controller operates according to the principles of act consequentialism in philosophy. As a conceptual example, suppose that all objects in the environment can be weighted in terms of the hazard or risk they present to the vehicle. Such a framework was proposed by Gibson and Crooks [7] as a model for human driving based on valences in the environ- ment and has formed the basis for a number of approaches to autonomous driving or driver assistance. These include electrical field analogies for vehicle motion developed by Reichardt and Schick [8], the mechanical potential field approach of Gerdes and Rossetter [9], the virtual bumpers of Donath and colleagues [10] and the work by Nagai and Raksin- charoensak on autonomous vehicle control based on risk potentials [11]. If the hazard in the environment can be described in such a way, the ideal path through the environment (at least from the standpoint of the single vehicle being controlled) minimizes the risk or hazard experienced. The task of the control algorithm then becomes determining com- mands to the engine, brakes and steering that will move the vehicle along this path. In both engineering and philosophy, the fundamental challenge with such approaches lies in developing an appropriate cost function. The simple example above postulates a cost function in terms of risk to a single vehicle but a more general approach would consider a broader societal perspective. One possible solution would be to estimate the damage to different road users and treat this as the cost to be reduced. The cost could include proper- ty damage, injury or even death, depending upon the situation. Such a calculation would require massive amounts of information about the objects in the environment and a means of estimating the potential outcomes in collision scenarios, perhaps by harnessing statistical data from prior crashes. Leaving aside for the moment the demands this consequentialist approach places on information, the behavior arising from such a cost function itself raises some challenges. Assuming such a cost could be reasonably defined or approximated, the car would seek to minimize damage in a global sense in the event of a dilemma situation, thereby reducing the