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 testbed. Electronic supplementary materialThe online version of this article (

This paper presents a method for enabling a fleet of circularly arranged quadrocopters to throw and catch balls with a net. Based on a first-principles model of the net forces, nominal inputs for all involved vehicles are derived for arbitrary target trajectories of the net. Two algorithms that generate open-loop trajectories for throwing and catching a ball are also introduced. A set of throws and catches is demonstrated in the ETH Zurich Flying Machine Arena testbed.

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This paper introduces a method for carrying a flexible payload with multiple attached flying vehicles. A model for a particular class of flexible structures is presented, and an estimator is derived that observes the pose of the structure in space as well as the magnitude of some characteristic deformation modes. A control strategy that controls the flexible payload to a desired pose while also controlling the deformations to zero is introduced. The presented methods are validated in the ETH Zurich Flying Machine Arena by flying with a thin, flexible ring that is carried by six quadrocopters.