Tiauw Hiong Go

Quadcopter formation flight control combining MPC and robust feedback linearization

Abstract This paper presents an integrated and practical control strategy to solve the leader–follower quadcopter formation flight control problem. To be specific, this control strategy is designed for the follower quadcopter to keep the specified formation shape and avoid the obstacles during flight. The proposed control scheme uses a hierarchical approach consisting of model predictive controller (MPC) in the upper layer with a robust feedback linearization controller in the bottom layer. The MPC controller generates the optimized collision-free state reference trajectory which satisfies all relevant constraints and robust to the input disturbances, while the robust feedback linearization controller tracks the optimal state reference and suppresses any tracking errors during the MPC update interval. In the top-layer MPC, two modifications, i.e. the control input hold and variable prediction horizon, are made and combined to allow for the practical online formation flight implementation. Furthermore, the existing MPC obstacle avoidance scheme has been extended to account for small non-apriorily known obstacles. The whole system is proved to be stable, computationally feasible and able to reach the desired formation configuration in finite time. Formation flight experiments are set up in Vicon motion-capture environment and the flight results demonstrate the effectiveness of the proposed formation flight architecture.

Analytical theory of three-degree-of-freedom aircraft wing rock

Multiple-degree-of-freedom wing-rock cases are usually studied using numerical methods because of the complexity of the problem. Recently, a methodology combining the Multiple Time Scales method, center manifold reduction principle, and bifurcation theory has been developed for obtaining an accurate representation of the two-degree-of-freedom wing-rock dynamics in a parametric form. Such solutions offer an advantage over numerical solutions in that the interdependence of the important parameters affecting the dynamic properties of the system can be easily seen. Also, the fast and slow dynamics of the system are systematically separated, leading to more insight into the complex dynamics of the aircraft. This paper extends the methodology to the more difficult case of wing rock on an aircraft having three rotational degrees of freedom. The excellent accuracy of the analytical solution is then demonstrated by comparison with the numerical result.

Waypoint Navigation of Small-Scale UAV incorporating Dynamic Soaring

The latest attempts at improving small scale autonomously guided Uninhabited Aerial Vehicles (UAVs) have concentrated around the increase of range and speed. One of these ways is to incorporate dynamic slope soaring manoeuvres as part of the flight path. This is in contrast to most conventional path-planning algorithms where waypoint guidance is merged with terrain avoidance or contour following capability. Additionally, current trajectory optimization techniques are iterative and so have a considerable computational load. The proposed algorithm is based on Dubins curves, and is therefore optimal by definition. Being non-iterative, it is comparatively a more efficient algorithm. Hence, a key advantage of the proposed technique is that the desired trajectory is generated quickly in real time with minimum computational load while satisfying the spatial constraints of dynamic slope soaring.

Reconfiguration Control with Collision Avoidance Framework for Unmanned Aerial Vehicles in Three-Dimensional Space

AbstractThis work concerns a collision-free fixed-time formation reconfiguration control method for unmanned aerial vehicles (UAVs). The reconfiguration to the new formation in three-dimensional space is specified based on the target final states of each UAV. A reference reconfiguration trajectory is generated from a Bolza optimization solution of simplified dynamics of the vehicle. A sliding controller is then utilized to track the reconfiguration trajectory. Collision avoidance is achieved by modeling the detection region of each UAV as a potential field. Such a field generates control signals that are inversely proportional to the square of the distance between the UAV and a moving or stationary object within its detection region. Altered optimal trajectories are generated online as the UAV avoids collision with another UAV or other obstacles. Simulations confirm that the control scheme developed is able to produce satisfactory results. This paper examines the stability (in the sense of Lyapunov) and p...

Optimization of Hover-to-Cruise Transition Maneuver Using Variable-Incidence Wing

A = disc area of the propeller D = drag g = acceleration due to gravity J = cost/objective function L = lift L=W = lift-to-weight ratio m = mass of the aircraft T = thrust Tmax = maximum thrust T=W = thrust-to-weight ratio T=W max = maximum thrust-to-weight ratio u = horizontal velocity u = control variable vector ut = terminal horizontal velocity V = freestream velocity wi = ith weight coefficient vt = terminal vertical velocity W = weight w = induced velocity aft of the propeller x = horizontal acceleration yi = altitude at ith discretized calculation instant z = vertical acceleration fus = fuselage and inboard wing angle of attack prop = angle of attack of the propeller wing = outboard wing angle of attack _ wing = rate of change of outboard wing angle of attack = flight-path angle = air density _ = rate of change of variable , d dt

Robust Decentralized Formation Flight Control

Motivated by the idea of multiplexed model predictive control (MMPC), this paper introduces a new framework for unmanned aerial vehicles (UAVs) formation flight and coordination. Formulated using MMPC approach, the whole centralized formation flight system is considered as a linear periodic system with control inputs of each UAV subsystem as its periodic inputs. Divided into decentralized subsystems, the whole formation flight system is guaranteed stable if proper terminal cost and terminal constraints are added to each decentralized MPC formulation of the UAV subsystem. The decentralized robust MPC formulation for each UAV subsystem with bounded input disturbances and model uncertainties is also presented. Furthermore, an obstacle avoidance control scheme for any shape and size of obstacles, including the nonapriorily known ones, is integrated under the unified MPC framework. The results from simulations demonstrate that the proposed framework can successfully achieve robust collision-free formation flights.

Lateral-Directional Aircraft Dynamics Under Static Moment Nonlinearity

T HIS Note specifically focuses on the aircraft lateraldirectional dynamics in the presence of nonlinearity in lateral moments with respect to sideslip (static lateral moments). Such nonlinearity is often encountered during flight in the regimes in which the aerodynamic properties are nonlinear: for example, during high-angle-of-attack flight. In the previous works by the author [1–3], which focus on the multiple-degree-of-freedom wing-rock dynamics at high angles of attack, the results imply that by itself, the nonlinearity in the static lateral moments [such as that considered here (cubic polynomial with respect to sideslip)] does not lead to wing rock. Those analyses, however, consider only the situation in which the nonlinearity is relatively weak. In [4], cubic nonlinearity of static lateral moments with respect to sideslip is shown to cause wing rock in a multimode system in certain conditions. Because of these seemingly discrepant findings, the topic is revisited here. This Note presents detailed analysis of the lateral-directional motion when the cubic type of static lateral moment nonlinearity is present in the system. The equations of motion as derived in [3] are used as the basis for the analysis. To gain physical insight into the problem, an analytical approach using the multiple-time-scales (MTS) method is used (see, for example, [5,6]). Both weak and strong nonlinearity cases are considered.

Formation Flight Control Using Model Predictive Approach

A leader-follower formation flight control using Model Predictive Control (MPC) approach is investigated in this paper. In this formation control scheme, the changes in the leader motion are considered as measured disturbances and the commands to the wing aircraft are considered as manipulated variables. A cost function for the formation flight control problem is obtained and the input and output constraints are included. The control stability is established by adding a terminal state region to the optimization constraints. In the closed-loop system, commanded separation trajectories are asymptotically tracked by each wing aircraft while the lead aircraft is maneuvering. A sliding mode approach is incorporated in order to compensate the effects generated by the vortex of the adjacent lead aircraft. The applications of the controller to the formation flight of multiple aircrafts are then simulated. The results show that the MPC controller can successfully maintain the formation of the flight with only the leader is commanded by the Ground Control Station (GCS).

Analysis of Wing Rock Due to Rolling-Moment Hysteresis

This paper examines the single-degree-of-freedom wing-rock dynamic characteristics due to the presence of hysteresis in the static rolling-moment coefficient with respect to the sideslip angle. Two simplified hysteresis cases are considered: one represents full hysteresis and the other represents partial hysteresis. The approach used for analyzing the problem is analytical, using the multiple-time-scales method. Using such an approach, approximate solutions for the wing-rock amplitudes and frequencies as functions of the hysteresis parameters are obtained. These analytical solutions, which lead to considerable insight into the aerodynamic hysteresis effect on wing rock, are demonstrated to be in good agreement with the numerical results. It is also shown that, unlike the case involving the nonhysteretic type of nonlinearity, in the presence of the hysteresis, wing rock can occur before the loss of the dynamic roll-damping derivative.

Aerodynamic Estimation of Annular Wings Based on Leading-Edge Suction Analogy

A NNULAR wings belong to the class of nonplanar wing configurations and have gained significant popularity recently [1–5] among the designers of unmanned air vehicles (UAVs) and micro air vehicles (MAVs). The lift increment of the annular wing from any planar configuration of same aspect ratio is well known. Moreover, for small aspect ratios, a significant improvement in L∕D max is observed. Not surprisingly, the increased popularity of annular wings has been driven by their application in ducted-fan UAVs. Annular shroud around the fan helps to increase the static and dynamic thrusts produced, and when the shroud is designed as an annular wing, it also acts as a lifting surface in the forward flight. Typical examples of UAVs with annular wings are the Honeywell MAV by AVID, LLC [1,2], the Singapore Technologies (ST) fantail system [3], and the GoldenEye UAV [4]. The application of the annular wing on passenger aircraft has also been conceptualized. Although the work related to annular wings can be traced back to [6] in 1947, the generic theoretical aerodynamic models of such wings have not been fully studied and have not received significant attention from technology protagonists beside its recognized advantages. Ribner [6] analytically derived the lift characteristics of annular wings and concluded that their lift-curve slope is twice that of the flatplate elliptical wings of the same aspect ratio. The seminalwork in [7] represented the first formal experimental investigations on annular wings by a varying aspect ratio and comparing their lift-curve slope with various theoretical models. The investigation included the longitudinal aerodynamic characteristics of five annular wings of aspect ratio AR 1∕3, 2∕3, 1.0, 1.5, and 3.0 with equal projected areas and theClark-Yairfoil cross section (thickness-to-chord ratio of 11.7%). The Reynolds numbers of the experiment varied, Re 0.704–2.11 million, due to the variation in the root chords of the wings. The results indicated that the lift-curve slopes of the annular wings were about twice that of the lift-curve slopes for planar rectangular wings having the same aspect ratio, which confirmed the findings of [6]. Recently, Traub [5] has revisited the topic by carrying out the experimental investigation on the baseline annular wing aerodynamics and studied the effects of gap and aspect ratio. The findings for aspect ratio variation coincide with the results in [7], but no analytical approximation of the lift behavior is attempted. Demasi [8] has developed a theoretical model of the minimum-induced drag prediction for annular wings based on the lifting line theory and the small perturbation acceleration method. A simplified concept of leading-edge suction analogy was proposed in [9] for the low-aspect ratio planforms (specifically delta wings) in the late 1960s. The aerodynamic surfaces at moderate angles of attack suffer from flow separation at or near leading edge, which significantly alters the pressure distribution on the upper surface. The approach assumes that the total lift in the prestall regime can be calculated as the sum of the component of lift from potential flow (based on fully attached pressure distribution) and the other component associated with the separated leading-edge vortices. The total force on the wings (prior to stall) associated with the pressure required to stabilize the separated vortices is equivalent to the leading-edge suction force to keep the flow around the wings attached. This theory was extended in [10] to other planform shapes, such as rectangular wings in subsonic and supersonic regimes. Suction analogy for the side-edge vortices was also proposed in this work. Recently, this approach has been used to study the aerodynamic characteristics of different low-aspect ratio planform shapes at the low Reynolds numbers in [11,12]. Specifically, the aerodynamic effect of pressure-induced forces and vortex-induced forces are parameterized and can be observed explicitly for various planform shapes and aspect ratios. The vortex generated from leading-edge flow separation is also observed in the annular wings. In [5], during the surface flow visualization, a significant region of separation is observedon topof the annular wingwith an increasing angle of attack. The lower surface also showed evidence of large scale separation in the vicinity of the stall. Such separation leads tovortex generation and, consequently, a suction force that will contribute to lift as in the planar wing. Therefore, the influence of leading-edge separation on overall pressure distribution can be approached similarly using the Polhamus-like method. The key factor in the development of the Polhamus-like formulation for the annular wings is to properlymodel the division of overall lift contribution from fully attached (potential) flow and vortex-induced flow. This is achieved by comparing a set of different theoretical models to the experimental data of the annular wing with Received 22 February 2012; revision received 2 July 2012; accepted for publication 25 August 2012; published online 26 November 2012 Copyright