Adaptive fast open-loop maneuvers for quadrocopters

We present a conceptually and computationally lightweight method for the design and iterative learning of fast maneuvers for quadrocopters. We use first-principles, reduced-order models and we do not require nor make an attempt to follow a specific state trajectory—only the initial and the final states of the vehicle are taken into account. We evaluate the adaptation scheme through experiments on quadrocopters in the ETH Flying Machine Arena that perform multi-flips and other high-performance maneuver

Performance benchmarking of quadrotor systems using time-optimal control

Frequently hailed for their dynamical capabilities, quadrotor vehicles are often employed as experimental platforms. However, questions surrounding achievable performance, influence of design parameters, and performance assessment of control strategies have remained largely unanswered. This paper presents an algorithm that allows the computation of quadrotor maneuvers that satisfy Pontryagin's minimum principle with respect to time-optimality. Such maneuvers provide a useful lower bound on the duration of maneuvers, which can be used to assess performance of controllers and vehicle design parameters. Computations are based on a two-dimensional first-principles quadrotor model. The minimum principle is applied to this model to find that time-optimal trajectories are bang-bang in the thrust command, and bang-singular in the rotational rate control. This paper presents a procedure allowing the computation of time-optimal maneuvers for arbitrary initial and final states by solving the boundary value problem induced by the minimum principle. The usage of the computed maneuvers as a benchmark is demonstrated by evaluating quadrotor design parameters, and a linear feedback control law as an example of a control strategy. Computed maneuvers are verified experimentally by applying them to quadrocopters in the ETH Zurich Flying Machine Arena testbe

Optimization-based iterative learning for precise quadrocopter trajectory tracking

Current control systems regulate the behavior of dynamic systems by reacting to noise and unexpected disturbances as they occur. To improve the performance of such control systems, experience from iterative executions can be used to anticipate recurring disturbances and proactively compensate for them. This paper presents an algorithm that exploits data from previous repetitions in order to learn to precisely follow a predefined trajectory. We adapt the feed-forward input signal to the system with the goal of achieving high tracking performance—even under the presence of model errors and other recurring disturbances. The approach is based on a dynamics model that captures the essential features of the system and that explicitly takes system input and state constraints into account. We combine traditional optimal filtering methods with state-of-the-art optimization techniques in order to obtain an effective and computationally efficient learning strategy that updates the feed-forward input signal according to a customizable learning objective. It is possible to define a termination condition that stops an execution early if the deviation from the nominal trajectory exceeds a given bound. This allows for a safe learning that gradually extends the time horizon of the trajectory. We developed a framework for generating arbitrary flight trajectories and for applying the algorithm to highly maneuverable autonomous quadrotor vehicles in the ETH Flying Machine Arena testbed. Experimental results are discussed for selected trajectories and different learning algorithm parameter

Quadcopter Aggressive Maneuvers along Singular Configurations: An Energy-Quaternion Based Approach

Automatic aggressive maneuvers with quadcopters are regarded as a highly challenging control problem. The aim is to tackle the singularities that exist in a vertical looping maneuver. Modeling singularities are resolved by writing the equations-of-motion of the quadcopter in quaternion form. Physical singularities due to underactuation are resolved by using an energy-based control. Energy-based control is utilized to overcome the uncontrollability of the quadcopter at physical singular configurations, for instance, when commanding the quadcopter to gain altitude while pitched at 90∘. Three looping strategies (circular, clothoidal, and newly developed constant thrust) are implemented on a nonlinear model of the quadcopter. The three looping strategies are discussed along with their advantages and limitations

Analysis and Control of a Variable-Pitch Quadrotor for Agile Flight

Fixed-pitch quadrotors are popular research and hobby platforms largely due to their mechanical simplicity relative to other hovering aircraft. This simplicity, however, places fundamental limits on the achievable actuator bandwidth and the possible flight maneuvers. This paper shows that many of these limitations can be overcome by utilizing variable-pitch propellers on a quadrotor. A detailed analysis of the potential benefits of variable-pitch propellers over fixed-pitch propellers for a quadrotor is presented. This analysis is supported with experimental testing to show that variable-pitch propellers, in addition to allowing for generation of reverse thrust, substantially increase the maximum rate of thrust change. A nonlinear, quaternion-based control algorithm for controlling the quadrotor is also presented with an accompanying trajectory generation method that finds polynomial minimum-time paths based on actuator saturation levels. The control law and trajectory generation algorithms are implemented on a custom variable-pitch quadrotor. Several flight tests are shown, which highlight the benefits of a variable-pitch quadrotor over a standard fixed-pitch quadrotor for performing aggressive and aerobatic maneuvers.National Science Foundation (U.S.) (0645960

Real-time model predictive control for quadrotors

This paper presents a solution to on-board trajectory tracking control of quadrotors. The proposed approach combines the standard hierarchical control paradigm that separates the control into low-level motor control, mid-level attitude dynamics control, and a high-level trajectory tracking with a model predictive control strategy. We use dynamic reduction of the attitude dynamics and dynamic extension of the thrust control along with feedback linearisation to obtain a linear system of McMillan degree three that models force controlled position and trajectory tracking for the quadrotor. Model predictive control is then used on the feedback equivalent system and its control outputs are transformed back into the inputs for the original system. The proposed structure leads to a low complexity model predictive control algorithm that is implemented in real-time on an embedded hardware. Experimental results on different position and trajectory tracking control are presented to illustrate the application of the derived linear system and controllers

Input uncertainty sensitivity enhanced non-singleton fuzzy logic controllers for long-term navigation of quadrotor UAVs

Input uncertainty, e.g., noise on the on-board camera and inertial measurement unit, in vision-based control of unmanned aerial vehicles (UAVs) is an inevitable problem. In order to handle input uncertainties as well as further analyze the interaction between the input and the antecedent fuzzy sets (FSs) of non-singleton fuzzy logic controllers (NSFLCs), an input uncertainty sensitivity enhanced NSFLC has been developed in robot operating system (ROS) using the C++ programming language. Based on recent advances in non-singleton inference, the centroid of the intersection of the input and antecedent FSs (Cen-NSFLC) is utilized to calculate the firing strength of each rule instead of the maximum of the intersection used in traditional NSFLC (Tra-NSFLC). An 8-shaped trajectory, consisting of straight and curved lines, is used for the real-time validation of the proposed controllers for a trajectory following problem. An accurate monocular keyframe-based visual-inertial simultaneous localization and mapping (SLAM) approach is used to estimate the position of the quadrotor UAV in GPS denied unknown environments. The performance of the Cen-NSFLC is compared with a conventional proportional integral derivative (PID) controller, a singleton FLC (SFLC) and a Tra-NSFLC. All controllers are evaluated for different flight speeds, thus introducing different levels of uncertainty into the control problem. Visual-inertial SLAM-based real time quadrotor UAV flight tests demonstrate that not only does the Cen-NSFLC achieve the best control performance among the four controllers, but it also shows better control performance when compared to their singleton counterparts. Considering the bias in the use of model based controllers, e.g. PID, for the control of UAVs, this paper advocates an alternative method, namely Cen-NSFLCs, in uncertain working environments

Enhanced proportional-derivative control of a micro quadcopter

ABSTRACT This paper studies the design of an enhanced proportionalderivative (PD) controller to improve the transient response of a micro quadrotor helicopter (quadcopter Introduction Micro aerial vehicles (MAVs) have a wingspan less than 0.15 m and a mass less than 0.1 kg The control of quadcopters has mostly been focused on ma

Agile load transportation systems using aerial robots

In this dissertation, we address problems that can occur during load transport using aerial robots, i.e., small scale quadrotors. First, detailed models of such transportation system are derived. These models include nonlinear models of a quadrotor, a model of a quadrotor carrying a fixed load and a model of a quadrotor carrying a suspended load. Second, the problem of quadrotor stabilization and trajectory tracking with changes of the center of gravity of the transportation system is addressed. This problem is solved using model reference adaptive control based on output feedback linearization that compensates for dynamical changes in the center of gravity of the quadrotor. The third problem we address is a problem of a swing-free transport of suspended load using quadrotors. Flying with a suspended load can be a very challenging and sometimes hazardous task as the suspended load significantly alters the flight characteristics of the quadrotor. In order to deal with suspended load flight, we present a method based on dynamic programming which is a model based offline method. The second investigated method we use is based on the Nelder-Mead algorithm which is an optimization technique used for nonlinear unconstrained optimization problems. This method is model free and it can be used for offline or online generation of the swing-free trajectories for the suspended load. Besides the swing-free maneuvers with suspended load, load trajectory tracking is another problem we solve in this dissertation. In order to solve this problem we use a Nelder-Mead based algorithm. In addition, we use an online least square policy iteration algorithm. At the end, we propose a high level algorithm for navigation in cluttered environments considering a quadrotor with suspended load. Furthermore, distributed control of multiple quadrotors with suspended load is addressed too. The proposed hierarchical architecture presented in this doctoral dissertation is an important step towards developing the next generation of agile autonomous aerial vehicles. These control algorithms enable quadrotors to display agile maneuvers while reconfiguring in real time whenever a change in the center of gravity occurs. This enables a swing-free load transport or trajectory tracking of the load in urban environments in a decentralized fashion