Learning-Supported Approximated Optimal Control for Autonomous Vehicles in the Presence of State Dependent Uncertainties

The control and operation of autonomous systems often involve different decision layers. The higher control levels are responsible for the planning and perception and operate on a slow time scale. To achieve good performance and disturbance rejection, often additional lower level controllers are used, which act on a fast time scale. Designing lower level controllers for autonomous systems is often challenged by the available, typically limited computational power. Furthermore, for safety and reliability reasons the low level controllers need to be verified, need to guarantee constraint satisfaction and correct operation under all circumstances. We consider the problem of low level continuous time controller design for autonomous systems subject to state dependent uncertainties. The main idea is to derive offline an approximated explicit solution of an optimal feedback law based on a series expansion via Al'brekht`s Method. To decrease the impact of state dependent uncertainties, the controller is parametrized in terms of disturbance parameters, which are adapted - learned online. As shown, the proposed strategy can be implemented in real-time even on computationally limited embedded platforms. We outline local stability results of the explicit solution for polynomial systems. The effectiveness and robustness of the proposed strategy to learn and mitigate the effect of the external disturbances are validated via simulation results for a quadcopter with different uncertainty scenarios.