We address the controller design and the trajectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5–10 body lengths/second) in three-dimensional slalom courses.

Minimum snap trajectory generation and control for quadrotors

We study the problem of designing dynamically feasible trajectories and controllers that drive a quadrotor to a desired state in state space. We focus on the development of a family of trajectories defined as a sequence of segments, each with a controller parameterized by a goal state or region in state space. Each controller is developed from the dynamic model of the robot and then iteratively refined through successive experimental trials in an automated fashion to account for errors in the dynamic model and noise in the actuators and sensors. We show that this approach permits the development of trajectories and controllers enabling such aggressive maneuvers as flying through narrow, vertical gaps and perching on inverted surfaces with high precision and repeatability.

Trajectory generation and control for precise aggressive maneuvers with quadrotors

In the last five years, advances in materials, electronics, sensors, and batteries have fueled a growth in the development of microunmanned aerial vehicles (MAVs) that are between 0.1 and 0.5 m in length and 0.1-0.5 kg in mass [1]. A few groups have built and analyzed MAVs in the 10-cm range [2], [3]. One of the smallest MAV is the Picoftyer with a 60-mmpropellor diameter and a mass of 3.3 g [4]. Platforms in the 50-cm range are more prevalent with several groups having built and flown systems of this size [5]-[7]. In fact, there are severalcommercially available radiocontrolled (PvC) helicopters and research-grade helicopters in this size range [8].

The GRASP Multiple Micro-UAV Testbed

We present a novel, deeply embedded robotics middleware and programming environment. It uses a multithreaded, publish-subscribe design pattern and provides a Unix-like software interface for micro controller applications. We improve over the state of the art in deeply embedded open source systems by providing a modular and standards-oriented platform. Our system architecture is centered around a publish-subscribe object request broker on top of a POSIX application programming interface. This allows to reuse common Unix knowledge and experience, including a bash-like shell. We demonstrate with a vertical takeoff and landing (VTOL) use case that the system modularity is well suited for novel and experimental vehicle platforms. We also show how the system architecture allows a direct interface to ROS and to run individual processes either as native ROS nodes on Linux or nodes on the micro controller, maximizing interoperability. Our microcontroller-based execution environment has substantially lower latency and better hardware connectivity than a typical Robotics Linux system and is therefore well suited for fast, high rate control tasks.

/pdf/px4-a-node-based-multithreaded-open-source-robotics-50m35kksn5.pdf

PX4: A node-based multithreaded open source robotics framework for deeply embedded platforms

This brief describes the application of direct and indirect model reference adaptive control to a lightweight low-cost quadrotor unmanned aerial vehicle platform. A baseline trajectory tracking controller is augmented by an adaptive controller. The approach is validated using simulations and flight tested in an indoor test facility. The adaptive controller is found to offer increased robustness to parametric uncertainties. In particular, it is found to be effective in mitigating the effects of a loss-of-thrust anomaly, which may occur due to component failure or physical damage. The design of the adaptive controller is presented, followed by a comparison of flight test results using the existing linear and augmented adaptive controllers.

Adaptive Control of Quadrotor UAVs: A Design Trade Study With Flight Evaluations

We describe a simple and intuitive policy gradient method for improving parametrized quadrocopter multi-flips by combining iterative experiments with information from a first-principles model. We start by formulating an N-flip maneuver as a five-step primitive with five adjustable parameters. Optimization using a low-order first-principles 2D vertical plane model of the quadrocopter yields an initial set of parameters and a corrective matrix. The maneuver is then repeatedly performed with the vehicle. At each iteration the state error at the end of the primitive is used to update the maneuver parameters via a gradient adjustment. The method is demonstrated at the ETH Zurich Flying Machine Arena testbed on quadrotor helicopters performing and improving on flips, double flips and triple flips.

/pdf/a-simple-learning-strategy-for-high-speed-quadrocopter-multi-44e94sran5.pdf

A simple learning strategy for high-speed quadrocopter multi-flips

In this paper, an optimization-based iterative learning control approach is presented. Given a desired trajectory to be followed, the proposed learning algorithm improves the system performance from trial to trial by exploiting the experience gained from previous repetitions. Taking advantage of the a-priori knowledge about the systems dominating dynamics, a data-based update rule is derived which adapts the feedforward input signal after each trial. By combining traditional model-based optimal filtering methods with state-of-the-art optimization techniques such as convex programming, an effective and computationally highly efficient learning strategy is obtained. Moreover, the derived formalism allows for the direct treatment of input and state constraints. Different (nonlinear) performance objectives can be specified defining the overall learning behavior. Finally, the proposed algorithm is successfully applied to the benchmark problem of swinging up a pendulum using open-loop control only.

/pdf/optimization-based-iterative-learning-control-for-trajectory-2s2eig3yx0.pdf

Optimization-based iterative learning control for trajectory tracking

This paper presents a quadrocopter flying in rhythm to music. The quadrocopter performs a periodic side-to-side motion in time to a musical beat. Underlying controllers are designed that stabilize the vehicle and produce a swinging motion. Synchronization is then achieved by using concepts from phase-locked loops. A phase comparator combined with a correction algorithm eliminate the phase error between the music reference and the actual quadrocopter motion. Experimental results show fast and effective synchronization that is robust to sudden changes in the reference amplitude and frequency. Changes in frequency and amplitude are tracked precisely when adding an additional feedforward component, based on an experimentally determined look-up table.

/pdf/synchronizing-the-motion-of-a-quadrocopter-to-music-165kjtaep7.pdf

Synchronizing the motion of a quadrocopter to music

The Flying Machine Arena (FMA) is an indoor research space built specifically for the study of autonomous systems and aerial robotics. In this video, we give an overview of this testbed and some of its capabilities. We show the FMA infrastructure and hardware, which includes a fleet of quadrocopters and a motion capture system for vehicle localization. The physical components of the FMA are complemented by specialized software tools and components that facilitate the use of the space and provide a unified framework for communication and control. The flexibility and modularity of the experimental platform is highlighted by various research projects and demonstrations.

http://www.flyingmachinearena.org/wp-content/uploads/2012/fma-publications/TheFlyingMachine%20ArenaAsOf2010.pdf

The Flying Machine Arena as of 2010

This paper describes a method for checking the feasibility of quadrocopter motions. The approach, meant as a validation tool for preprogrammed quadrocopter performances, is based on first principles models and ensures that a desired trajectory respects both vehicle dynamics and motor thrust limits. We apply this method towards the eventual goal of using parameterized motion primitives for expressive quadrocopter choreographies. First, we show how a large class of motion primitives can be formulated as truncated Fourier series. We then show how the feasibility check can be applied to such motions by deriving explicit parameter constraints for two particular parameterized primitives. The predicted feasibility constraints are compared against experimental results from quadrocopters in the ETH Flying Machine Arena.

/pdf/feasiblity-of-motion-primitives-for-choreographed-2i5o090gu5.pdf

Angela Schollig

Papers

A simple learning strategy for high-speed quadrocopter multi-flips

Optimization-based iterative learning control for trajectory tracking

Synchronizing the motion of a quadrocopter to music

The Flying Machine Arena as of 2010

Feasiblity of motion primitives for choreographed quadrocopter flight