Safe Controller Optimization for Quadrotors with Gaussian Processes

One of the most fundamental problems when designing controllers for dynamic systems is the tuning of the controller parameters. Typically, a model of the system is used to obtain an initial controller, but ultimately the controller parameters must be tuned manually on the real system to achieve the best performance. To avoid this manual tuning step, methods from machine learning, such as Bayesian optimization, have been used. However, as these methods evaluate different controller parameters on the real system, safety-critical system failures may happen. In this paper, we overcome this problem by applying, for the first time, a recently developed safe optimization algorithm, SafeOpt, to the problem of automatic controller parameter tuning. Given an initial, low-performance controller, SafeOpt automatically optimizes the parameters of a control law while guaranteeing safety. It models the underlying performance measure as a Gaussian process and only explores new controller parameters whose performance lies above a safe performance threshold with high probability. Experimental results on a quadrotor vehicle indicate that the proposed method enables fast, automatic, and safe optimization of controller parameters without human intervention.Comment: IEEE International Conference on Robotics and Automation, 2016. 6 pages, 4 figures. A video of the experiments can be found at http://tiny.cc/icra16_video . A Python implementation of the algorithm is available at https://github.com/befelix/SafeOp

Safe Learning of Quadrotor Dynamics Using Barrier Certificates

To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach.Comment: Submitted to ICRA 2018, 8 page

Barrier Functions in Cascaded Controller: Safe Quadrotor Control

Safe control for inherently unstable systems such as quadrotors is crucial. Imposing multiple dynamic constraints simultaneously on the states for safety regulation can be a challenging problem. In this paper, we propose a quadratic programming (QP) based approach on a cascaded control architecture for quadrotors to enforce safety. Safety regions are constructed using control barrier functions (CBF) while explicitly considering the nonlinear underactuated dynamics of the quadrotor. The safety regions constructed using CBFs establish a non-conservative forward invariant safe region for quadrotor navigation. Barriers imposed across the cascaded architecture allows independent safety regulation in quadrotor's altitude and lateral domains. Despite barriers appearing in a cascaded fashion, we show preservation of safety for quadrotor motion in SE(3). We demonstrate the feasibility of our method on a quadrotor in simulation with static and dynamic constraints enforced on position and velocity spaces simultaneously.Comment: Submitted to ACC 2020, 8 pages, 7 figure

AutoTune: Controller Tuning for High-Speed Flight

Due to noisy actuation and external disturbances, tuning controllers for high-speed flight is very challenging. In this paper, we ask the following questions: How sensitive are controllers to tuning when tracking high-speed maneuvers? What algorithms can we use to automatically tune them? To answer the first question, we study the relationship between parameters and performance and find out that the faster the maneuver, the more sensitive a controller becomes to its parameters. To answer the second question, we review existing methods for controller tuning and discover that prior works often perform poorly on the task of high-speed flight. Therefore, we propose AutoTune, a sampling-based tuning algorithm specifically tailored to high-speed flight. In contrast to previous work, our algorithm does not assume any prior knowledge of the drone or its optimization function and can deal with the multi-modal characteristics of the parameters' optimization space. We thoroughly evaluate AutoTune both in simulation and in the physical world. In our experiments, we outperform existing tuning algorithms by up to 90\% in trajectory completion. The resulting controllers are tested in the AirSim Game of Drones competition, where we outperform the winner by up to 25\% in lap-time. Finally, we show that AutoTune improves tracking error when flying a physical platform with respect to parameters tuned by a human expert.Comment: Video: https://youtu.be/m2q_y7C01So; Code: https://github.com/uzh-rpg/mh_autotun