Efficient Numerical Optimal Control for Motion Planning and Control of Mobile Robots

Robotics holds high promises contributing solutions to our future society's challenges by taking over dangerous, physically intense work or fill up the lack of skilled labor resulting from population aging. To fulfill these promises, robots will need to solve increasingly complex tasks, requiring more versatile hardware designs with more degrees of freedom. Paired with fast development cycles, this poses a major challenge for robotic motion planning and control. In traditional approaches, reasoning about the structure of the task and the robot itself has led to impressive performance. However, this involves manually re-engineering solutions almost entirely from scratch when the robot design or the given task changes. Therefore, there is a strong need for transferable methods. Ideally, the task or desired motion is specified on a high level and the planners and controllers then reason about the dynamics and kinematics of the robot to find a solution. In the first part of this work, we aim at creating such a general, transferable motion planning and control framework by using Numerical Optimal Control. We verify our method on three entirely different classes of robots namely walking, flying and ground robots. In order for our approach to leverage the full potential of each of the robots, we use full dynamic models of all systems. This allows us for solving complex motion planning tasks such as flying an Unmanned Aerial Vehicle through a narrow, tilted window or discovering different gait patterns on a quadruped robot. In contrast to many state-of-the-art approaches, we execute our planners and controllers on the physical systems and verify them with rigorous hardware experiments. Running Numerical Optimal Control online comes with several practical challenges such as limited computation time, model mismatches between simulation and hardware as well as estimating the state of the robot in its workspace. In the second part of this work, we address these application issues. We speed up our Numerical Optimal Control approach by applying Automatic Differentiation, a programming technique to obtain gradients of our systems more efficiently. We further investigate why off-the-shelf simulators perform poorly in evaluating feedback control performance. Lastly, we propose a lightweight, cost efficient estimation system which localizes a mobile robot relatively to its workspace. Both parts of this thesis constitute a significant contribution in applying Numerical Optimal Control to physical systems. This work underlines the potential and versatility of such approaches by demonstrating them in hardware experiments on vastly different systems and tasks. Enabled by the efforts of an efficient implementation, we can run our Numerical Optimal Control solver online or even in Model Predictive Control fashion. Our approach outperforms state-of-the-art methods with respect to significantly lower computational time