We analyze patterns of gene presence and absence in a maximum likelihood framework with rate parameters for gene gain and loss. Standard methods allow independent gains and losses in different parts of a tree. While losses of the same gene are likely to be frequent, multiple gains need to be considered carefully. A gene gain could occur by horizontal transfer or by origin of a gene within the lineage being studied. If a gene is gained more than once, then at least one of these gains must be a horizontal transfer. A key parameter is the ratio of gain to loss rates, a/v We consider the limiting case known as the infinitely many genes model, where a/v tends to zero and a gene cannot be gained more than once. The infinitely many genes model is used as a null model in comparison to models that allow multiple gains. Using genome data from cyanobacteria and archaea, it is found that the likelihood is significantly improved by allowing for multiple gains, but the average a/v is very small. The fraction of genes whose presence/absence pattern is best explained by multiple gains is only 15% in the cyanobacteria and 20% and 39% in two data sets of archaea. The distribution of rates of gene loss is very broad, which explains why many genes follow a treelike pattern of vertical inheritance, despite the presence of a significant minority of genes that undergo horizontal transfer.

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Quadrotors have been applied to collect information for traffic, weather monitoring, surveillance and aerial photography. In order to accomplish their mission, quadrotors have to follow specific trajectories. This paper presents proportional-integral-derivative (PID) cascade control of a quadrotor for path tracking problem when velocity and acceleration are small. It is based on near hover controller for small attitude angles. The integral of time-weighted absolute error (ITAE) criterion is used to determine the PID gains as a function of quadrotor modeling parameters. The controller is evaluated in three-dimensional environment in Simulink. Overall, the tracking performance is found to be excellent for small velocity condition. IntroductionRecently, a growing interest in unmanned aerial vehicles (UAVs) has been shown among the research community. Quadcopters are flying vehicles that can be equipped with cameras and sensors to perform many complex tasks. Due to their high maneuverability and small size, quadrotors have been widely used. Their potential applications include search-and-rescue, homeland security, military surveillance, and earth sciences [1][2][3]. In general, quadrotors are naturally unstable, under-actuated, under damped, coupled and nonlinear systems that need to be controlled. Several control techniques can be utilized to control a quadrotor including proportional-integral-derivative (PID) [4,5], linear quadratic regulator (LQR) [6], and backstepping and sliding mode control [7,8]. Because of its simple structure and good stability, PID plays an important role in quadrotor control.In this study, a PID controller is used for attitude and position control. Assuming small acceleration and small attitude angles, the corresponding control laws are derived. A Simulink model is developed where the performance of the controller is tested for different path-tracking cases.

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Parrot Mambo mini-drone is a readily available commercial quadrotor platform to understand and analyze the behavior of a quadrotor both in indoor and outdoor applications. This study evaluates the performance of three alternative controllers on a Parrot Mambo mini-drone in an interior environment, including Proportional–Integral–Derivative (PID), Linear Quadratic Regulator (LQR), and Model Predictive Control (MPC). To investigate the controllers’ performance, initially, the MATLAB®/Simulink™ environment was considered as the simulation platform. The successful simulation results finally led to the implementation of the controllers in real-time in the Parrot Mambo mini-drone. Here, MPC surpasses PID and LQR in ensuring the system’s stability and robustness in simulation and real-time experiment results. Thus, this work makes a contribution by introducing the impact of MPC on this quadrotor platform, such as system stability and robustness, and showing its efficacy over PID and LQR. All three controllers demonstrate similar tracking performance in simulations and experiments. In steady state, the maximal pitch deviation for the PID controller is 0.075 rad, for the LQR, it is 0.025 rad, and for the MPC, it is 0.04 rad. The maximum pitch deviation for the PID-based controller is 0.3 rad after the take-off impulse, 0.06 rad for the LQR, and 0.17 rad for the MPC.

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