A flying inverted pendulum
09 May 2011-pp 763-770
TL;DR: This work extends the classic control problem of the inverted pendulum by placing the pendulum on top of a quadrotor aerial vehicle, using a ‘Virtual Body Frame’ for the time-invariant description of curved trajectories.
Abstract: We extend the classic control problem of the inverted pendulum by placing the pendulum on top of a quadrotor aerial vehicle. Both static and dynamic equilibria of the system are investigated to find nominal states of the system at standstill and on circular trajectories. Control laws are designed around these nominal trajectories. A yaw-independent description of quadrotor dynamics is introduced, using a ‘Virtual Body Frame’. This allows for the time-invariant description of curved trajectories. The balancing performance of the controller is demonstrated in the ETH Zurich Flying Machine Arena testbed. Development potential for the future is highlighted, with a focus on applying learning methodology to increase performance by eliminating systematic errors that were seen in experiments.
Citations
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TL;DR: A survey on publicly available open-source projects (OSPs) on quadrotor unmanned aerial vehicles (UAVs) finds that relatively simple structures of quadrotors has promoted interest from academia, UAV industries, and radio-control hobbyists alike.
Abstract: This article presents a survey on publicly available open-source projects (OSPs) on quadrotor unmanned aerial vehicles (UAVs). Recently, there has been increasing interest in quadrotor UAVs. Exciting videos have been published on the Internet by many research groups and have attracted much attention from the public [1][7]. Relatively simple structures of quadrotors has promoted interest from academia, UAV industries, and radio-control (RC) hobbyists alike. Unlike conventional helicopters, swashplates, which are prone to failure without constant maintenance, are not required. Furthermore, the diameter of individual rotors can be reduced as a result of the presence of four actuators [8].
287 citations
06 May 2013
TL;DR: A trajectory generation method is presented that enables finding nominal trajectories with various constraints that not only result in minimal load swing if required, but can also cause a large swing in the load for dynamically agile motions.
Abstract: A quadrotor with a cable-suspended load with eight degrees of freedom and four degrees underactuation is considered and the system is established to be a differentially-flat hybrid system. Using the flatness property, a trajectory generation method is presented that enables finding nominal trajectories with various constraints that not only result in minimal load swing if required, but can also cause a large swing in the load for dynamically agile motions. A control design is presented for the system specialized to the planar case, that enables tracking of either the quadrotor attitude, the load attitude or the position of the load. Stability proofs for the controller design and experimental validation of the proposed controller are presented.
244 citations
Additional excerpts
...With the introduction of inexpensive micro UAVs and sophisticated sensors in recent years, controllers have been designed to enable these systems to demonstrate aggressive maneuvers [8], dynamic trajectory generation [9], balancing a flying inverted pendulum [4], etc....
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TL;DR: The architecture of the Arena is described from the viewpoint of system robustness and its capability as a dual-purpose research and demonstration platform.
Abstract: The Flying Machine Arena is a platform for experiments and demonstrations with fleets of small flying vehicles. It utilizes a distributed, modular architecture linked by robust communication layers. An estimation and control framework along with built-in system protection components enable prototyping of new control systems concepts and implementation of novel demonstrations. More recently, a mobile version has been featured at several eminent public events. We describe the architecture of the Arena from the viewpoint of system robustness and its capability as a dual-purpose research and demonstration platform.
214 citations
Additional excerpts
...All rights reserved. http://dx.doi.org/10.1016/j.mechatronics.2013.11.006 ⇑ Corresponding author....
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05 Dec 2011
TL;DR: An algorithm is developed to generate an open loop trajectory guiding the vehicle to a predicted impact point - the prediction is done by integrating forward the current position and velocity estimates from a Kalman filter.
Abstract: This paper presents a method allowing a quadrocopter with a rigidly attached racket to hit a ball towards a target. An algorithm is developed to generate an open loop trajectory guiding the vehicle to a predicted impact point - the prediction is done by integrating forward the current position and velocity estimates from a Kalman filter. By examining the ball and vehicle trajectories before and after impact, the system estimates the ball's drag coefficient, the racket's coefficient of restitution and an aiming bias. These estimates are then fed back into the system's aiming algorithm to improve future performance. The algorithms are implemented for three different experiments: a single quadrocopter returning balls thrown by a human; two quadrocopters co-operatively juggling a ball back-and-forth; and a single quadrocopter attempting to juggle a ball on its own. Performance is demonstrated in the Flying Machine Arena at the ETH Zurich.
161 citations
Cites background from "A flying inverted pendulum"
...ch dancing [8]; balancing an inverted pendulum [9]; aggressive manoeuvres such as flight through windows and perching [10]; and cooperative load-carrying [11]....
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...More details about the Flying Machine Arena can be found in [8], [9] and [16]....
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01 Dec 2013
TL;DR: This paper investigates tracking controls for an arbitrary number of cooperating quadrotor unmanned aerial vehicles with a suspended load, developed in a coordinate-free fashion to avoid singularities and complexities associated with local parameterizations.
Abstract: This paper investigates tracking controls for an arbitrary number of cooperating quadrotor unmanned aerial vehicles with a suspended load. Assuming that a point mass is connected to multiple quadrotors by rigid massless links, control systems for quadrotors are constructed such that the point mass asymptotically follows a given desired trajectory and quadrotors maintain a prescribed formation, either relative to the point mass or with respect to the inertial frame. These are developed in a coordinate-free fashion to avoid singularities and complexities associated with local parameterizations. The desirable features are illustrated by several numerical examples, including a flying inverted spherical pendulum on a quadrotor.
143 citations
References
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Book•
01 May 1995TL;DR: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization.
Abstract: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning.
10,834 citations
TL;DR: The authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model with a model-based fuzzy controller design utilizing the concept of the so-called "parallel distributed compensation" and presents a design methodology for stabilization of a class of nonlinear systems.
Abstract: Presents a design methodology for stabilization of a class of nonlinear systems. First, the authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called "parallel distributed compensation" is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMIs. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart.
2,534 citations
"A flying inverted pendulum" refers background in this paper
...in reinforcement learning [6], neural networks [14], and fuzzy control [13]....
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TL;DR: The new algorithm, least-squares policy iteration (LSPI), learns the state-action value function which allows for action selection without a model and for incremental policy improvement within a policy-iteration framework.
Abstract: We propose a new approach to reinforcement learning for control problems which combines value-function approximation with linear architectures and approximate policy iteration. This new approach is motivated by the least-squares temporal-difference learning algorithm (LSTD) for prediction problems, which is known for its efficient use of sample experiences compared to pure temporal-difference algorithms. Heretofore, LSTD has not had a straightforward application to control problems mainly because LSTD learns the state value function of a fixed policy which cannot be used for action selection and control without a model of the underlying process. Our new algorithm, least-squares policy iteration (LSPI), learns the state-action value function which allows for action selection without a model and for incremental policy improvement within a policy-iteration framework. LSPI is a model-free, off-policy method which can use efficiently (and reuse in each iteration) sample experiences collected in any manner. By separating the sample collection method, the choice of the linear approximation architecture, and the solution method, LSPI allows for focused attention on the distinct elements that contribute to practical reinforcement learning. LSPI is tested on the simple task of balancing an inverted pendulum and the harder task of balancing and riding a bicycle to a target location. In both cases, LSPI learns to control the pendulum or the bicycle by merely observing a relatively small number of trials where actions are selected randomly. LSPI is also compared against Q-learning (both with and without experience replay) using the same value function architecture. While LSPI achieves good performance fairly consistently on the difficult bicycle task, Q-learning variants were rarely able to balance for more than a small fraction of the time needed to reach the target location.
1,405 citations
"A flying inverted pendulum" refers background in this paper
...in reinforcement learning [6], neural networks [14], and fuzzy control [13]....
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TL;DR: In the last five years, advances in materials, electronics, sensors, and batteries havefueled a growth in the development of microunmanned aerial vehicles (MAVs) that are between 0.1 and 0.5 m in length and0.1-0.5 kg in mass.
Abstract: 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].
806 citations
"A flying inverted pendulum" refers background in this paper
...Other complex maneuvers, including flight through windows and perching have been demonstrated [8]....
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TL;DR: The main components and architecture of RAVEN are described and recent flight test results are presented illustrating the applications discussed above.
Abstract: To investigate and develop unmanned vehicle systems technologies for autonomous multiagent mission platforms, we are using an indoor multivehicle testbed called real-time indoor autonomous vehicle test environment (RAVEN) to study long-duration multivehicle missions in a controlled environment. Normally, demonstrations of multivehicle coordination and control technologies require that multiple human operators simultaneously manage flight hardware, navigation, control, and vehicle tasking. However, RAVEN simplifies all of these issues to allow researchers to focus, if desired, on the algorithms associated with high-level tasks. Alternatively, RAVEN provides a facility for testing low-level control algorithms on both fixed- and rotary-wing aerial platforms. RAVEN is also being used to analyze and implement techniques for embedding the fleet and vehicle health state (for instance, vehicle failures, refueling, and maintenance) into UAV mission planning. These characteristics facilitate the rapid prototyping of new vehicle configurations and algorithms without requiring a redesign of the vehicle hardware. This article describes the main components and architecture of RAVEN and presents recent flight test results illustrating the applications discussed above.
452 citations
"A flying inverted pendulum" refers background in this paper
...[5], and references therein), a growing community is working on using the full dynamical potential of these vehicles....
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