A fractional order proportional integral controller for path following and trajectory tracking of miniature air vehicles

In this paper, a fractional order proportional-integral controller is developed for a miniature air vehicle for rectilinear path following and trajectory tracking. The controller is implemented by constructing a vector field surrounding the path to be followed, which is then used to generate course commands for the miniature air vehicle. The fractional order proportional-integral controller is simulated using the fundamentals of fractional calculus, and the results for this controller are compared with those obtained for a proportional controller and a proportional integral controller. In order to analyze the performance of the controllers, four performance metrics, namely (maximum) overshoot, control effort, settling time and integral of the timed absolute error cost, have been selected. A comparison of the nominal as well as the robust performances of these controllers indicates that the fractional order proportional-integral controller exhibits the best performance in terms of ITAE while showing comparable performances in all other aspects.

Optimal Trajectory Generation for Convergence to a Rectilinear Path

This paper presents a strategy to determine the shortest path of a fixed-wing Miniature Air Vehicle (MAV), constrained by a bounded turning rate, to eventually fly along a given straight line, starting from an arbitrary but known initial position and orientation. Unlike the work available in the literature that solves the problem using the Pontryagin's Minimum Principle (PMP) the trajectory generation algorithm presented here considers a geometrical approach which is intuitive and easy to understand. This also computes the explicit solution for the length of the optimal path as a function of the initial configuration. Further, using a 6-DOF model of a MAV the generated optimal path is tracked by an autopilot consisting of proportional-integral-derivative (PID) controllers. The simulation results show the path generation and tracking for different cases.

Curvature-constrained trajectory generation for waypoint following for miniature air vehicle

This paper addresses trajectory generation problem of a fixed-wing miniature air vehicle, constrained by bounded turn rate, to follow a given sequence of waypoints. An extremal path, named as g-trajectory, that transitions between two consecutive waypoint segments (obtained by joining two waypoints in sequence) in a time-optimal fashion is obtained. This algorithm is also used to track the maximum portion of waypoint segments with the desired shortest distance between the trajectory and the associated waypoint. Subsequently, the proposed trajectory is compared with the existing transition trajectory in the literature to show better performance in several aspects. Another optimal path, named as loop trajectory, is developed for the purpose of tracking the waypoints as well as the entire waypoint segments. This paper also proposes algorithms to generate trajectories in the presence of steady wind to meet the same objective as that of no-wind case. Due to low computational burden and simplicity in the design procedure, these trajectory generation approaches are implementable in real time for miniature air vehicles.

Path Following Using Trajectory Shaping Guidance

Unmanned vehicle path following by pursuing a virtual target moving along the path is considered. Limitations for pure pursuit guidance are analyzed while following the virtual target on curved paths. Trajectory shaping guidance is proposed as an alternate guidance scheme for a general curvature path. It is proven that under certain tenable assumptions trajectory shaping guidance yields an identical path as that of the virtual target. By linear analysis it is shown that the convergence to the path for trajectory shaping guidance is twice as fast as pure pursuit. Simulations highlight significant improvement in position errors by using trajectory shaping guidance. Comparative simulation studies comply with analytic findings and present better performance as compared with pure pursuit and a nonlinear guidance methodology from the literature. Experimental validation supports the analytic and simulations studies as the guidance laws are implemented on a radio-controlled car in a laboratory environment.

Airblast spray in crossflow - Structure, trajectory and droplet sizing

This study reports results of an experimental investigation of airblast spray of water and ethanol in crossflow. Laser shadowgraphy and Particle/Droplet Imaging Analysis (PDIA) are used to derive spray trajectory and drop size information while Particle Tracking Velocimetry (PTV) is used to measure droplet velocities. A new phenomenon of spray bifurcation is observed for low Gas to Liquid Ratio (GLR) cases. The reasons for the spatial bifurcation can be attributed to a combination of reasons. These are (a) presence of large ligaments and droplets in the near-nozzle region for low GLRs (b) secondary breakup experienced by ligaments/droplets leading to formation of a large number of small droplets, and (c) the crossflow causing differential dispersion of the small and large droplets. A novel correlation for spray trajectory is proposed incorporating the momentum ratio and liquid surface tension. This correlation is shown to be effective in predicting the non-linear spray trajectory over a large range of conditions for not only water but ethanol and Jet-A also. It is observed that the larger droplets penetrate further into the crossflow, in the direction of injection. Thus, with increase in height of the measurement location from the injection plane, the droplet Sauter Mean Diameter (SMD) is found to increase. Moreover, as the droplets travel downstream in the crossflow direction, the droplet SMD is observed to decrease. The effect of drag is assessed by comparing velocity of different sizes of droplets at various locations. Smaller droplets are entrained into the crossflow at much lower elevations, whereas larger droplets tend to penetrate further into the crossflow. (C) 2015 Elsevier Ltd. All rights reserved.

Exploring Viral Phenomenon as an Innovative Trajectory

The viral phenomenon has garnered a great deal of attention in the recent years. Although evidence of viral success exists the underlying factors leading to the phenomenon and its measurement still remains a grey area which needs to be explored. The viral phenomenon for a product or information and its distinction based on growth curve trajectory has not been rigorously explored in the previous works. This paper aims to understand the viral phenomenon that makes products or information go viral. The viral phenomenon trajectories that distinguish the viral from a non-viral phenomenon are demonstrated. The curve fitting methodology for viral phenomenon is adopted which has not been looked into in the previous works. TED talks are analyzed to understand the diffusion pattern, essentially one or more spike, within a time period. Insights drawn indicate the characteristic viral growth trajectories and its implication on innovation.

Simulation-based optimal sensor scheduling with application to observer trajectory planning

The sensor scheduling problem can be formulated as a controlled hidden Markov model and this paper solves the problem when the state, observation and action spaces are continuous. This general case is important as it is the natural framework for many applications. The aim is to minimise the variance of the estimation error of the hidden state w.r.t. the action sequence. We present a novel simulation-based method that uses a stochastic gradient algorithm to find optimal actions. © 2007 Elsevier Ltd. All rights reserved.