Coordination Control of Quadrotor VTOL Aircraft in Three-Dimensional Space

This paper presents a constructive design of distributed coordination controllers for a group of N quadrotor vertical take-off and landing (VTOL) aircraft in three-dimensional space. A combination of Euler angles and unit-quaternion for the attitude representation of the aircraft is used to result in an effective control design, and to reduce singularities in the aircraft’s dynamics. The coordination control design is based on a new bounded control design technique for second-order systems and new pairwise collision avoidance functions. The pairwise collision functions are functions of both relative positions and relative velocities between the aircraft instead of only their relative positions as in the literature. To overcome the inherent underactuation of the aircraft, the roll and pitch angles of the aircraft are considered as immediate controls. Simulations illustrate the results

Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process

This paper derives Hamilton-Jacobi equation (HJE) in Hilbert space foroptimal control of stochastic distributed parameter systems (SDPSs) governedby partial differential equations (SPDEs) subject to both state-dependent andadditive stochastic disturbances. First, nonlinear SDPSs are transformed tostochastic evolution systems (SESs), which are governed by stochastic ordinarydifferential equations (SODEs) in Hilbert space, using functional analysis.Second, the Hamilton-Jacobi equation (HJE), of which the solution resultsin an optimal control law, is derived. Third, a problem of optimal control oflinear SDPSs, which include the air pollution process, with a quadratic costfunctional is addressed as an application of the HJE. After, the control designis done, the SESs are transformed back to Euclidean space for implementation

Formation control of underactuated ships with elliptical shape approximation and limited communication ranges

Based on the recent theoretical development for formation control of multiple fully actuated agents with an elliptical shape in Do (2012), this paper develops distributed controllers that force a group of NN underactuated ships with limited communication ranges to perform a desired formation, and guarantee no collisions between any ships in the group. The ships are first fitted to elliptical disks for solving collision avoidance. A coordinate transformation is then proposed to introduce an additional control input, which overcomes difficulties caused by underactuation and off-diagonal terms in the system matrices. The control design relies on potential functions with the separation condition between elliptical disks and the smooth or pp-times differentiable step functions embedded in

Inverse optimal filtering of linear distributed parameter systems

A constructive method is developed to design inverse optimal filters to estimate the states of a class of linear distributed parameter systems (DPSs) based on the calculus of variation approach. Inverse optimality guarantees that the cost functional to be minimized is meaningful in the sense that the symmetric and positive definite weighting kernel matrix on the states is chosen after the filter design instead of being specified at the start of the filter design. Inverse optimal design enables that the Riccati nonlinear partial differential equation (PDE) can be simplified to a Bernoulli PDE, which can be solved analytically. The filter design is based on a new Green matrix formula, a new unique and bounded solution of a linear PDE, and analytical solution of a Bernoulli PDE. The inverse optimal filter design is first developed for the case where the measurements are spatially available, then is extended to the practical case where only a finite number of measurements is available

Inverse optimal control of linear distributed parameter systems

A constructive method is developed to design inverse optimal controllers for a class of linear distributed parameter systems (DPSs). Inverse optimality guarantees that the cost functional to be minimized is meaningful in the sense that the symmetric and positive definite weighting kernel matrix on the states is chosen after the control design instead of being specified at the start of the control design. Inverse optimal design enables that the Riccati nonlinear partial differential equation (PDE) can be simplified to a Bernoulli PDE, which can be solved analytically. The control design is based on a new Green matrix formula, a new unique and bounded solution of a linear PDE, and an analytical solution of a Bernoulli PDE. Both distributed and finite control problems are addressed. An example is given

Bounded Coordination Control of Second-order Dynamic Agents

This paper presents a constructive design of distributed and bounded coordination controllers that force mobile agents with second-order dynamics to track desired trajectories and to avoid collision between them. The control design is based on the new bounded control design technique for second-order systems, and new pairwise collision avoidance functions. The pair wise collision functions are functions of both the relative position and velocity of the agents instead of only the relative position as in the literature. Desired features of the proposed control design include:1) Boundedness of the control inputs by a predefined bound despite collision avoidance between the agentsconsidered,2) No collision between any agents,3) Asymptotical stability of desired equilibrium set, and4) Instability of all other undesired critical sets of the closed loop system. The proposed control design is then applied to design a coordination control system for a group of vertical take-off and landing (VTOL) aircraft

Flocking for multiple ellipsoidal agents with limited communication ranges

This paper contributes a design of distributed controllers for flocking of mobile agents with an ellipsoidal shape and a limited communication range. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise potential functions to design flocking control algorithms. The proposed flocking design results in (1) smooth controllers despite of the agents’ limited communication ranges, (2) no collisions between any agents, (3) asymptotic convergence of each agent’s generalized velocity to a desired velocity, and (4) boundedness of the flock size, defined as the sum of all distances between the agents, by a constant

Coordination control of multiple ellipsoidal agents with collision avoidance and limited sensing ranges

This paper contributes a design of cooperative controllers that force N mobile agents with an ellipsoidal shape and a limited sensing range to track desired trajectories and to avoid collision between them. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise collision avoidance functions to design coordination controllers. The proposed control design guarantees (1) smooth coordination controllers despite the agents’ limited sensing ranges, (2) no collision between any agents, (3) asymptotical stability of desired equilibrium set, and (4) instability of all other undesired critical sets of the closed loop system

Optimal sensor and actuator locations in linear distributed parameter systems

A constructive method is developed to obtain optimal sensor and actuator loca- tions for inverse optimal state estimation and control of a class of linear distributed parameter systems (DPSs). Given the inverse optimal state estimators and con- trollers for linear DPSs developed by the first author recently, it is shown that the performance index for optimal locations of sensors and actuators is the trace of the solution of the Bernoulli partial differential equations (PDEs), which are the optimal state estimation and control gain matrices. Thus, the optimal locations are designed so as to minimize the trace of the solution of the Bernoulli partial differential equations

An experimental study of flow induced vibration of a flexible model riser

This paper experimentally identifies some non-linear effects, e.g. modal coupling effect and beating motion, on a flexible model riser due to variable curvature when vortex-induced vibration (VIV) occurs. The VIV on the riser can cause enlarging dynamic stress of the body and reducing its fatigure life. This work expands existing numerical and analytical investigations on a model riser with constant curvature in shear flow condition. The results indicate that for a flexible model riser displaced in non-uniform shear flow when VIV occurred, the curvature shows substantial effects on lock-in response and multi-mode non-lock-in response. The modal coupling effect on lock-in response repeats the same effect on the structure in air, which indicates that modal coupling effect seems independent to the locking phenomenon. This experimental investigation embeds the situation when displacing a flexible rubber cable with initial caterany shape stretching its bottom end to most tensioned straight condition for varying the curvature. The effect of varying curvature on the vibration characteristics of the rubber cable is identified when displaced in air. The same effect on the structure when vortex-induced vibration occurred is taken into account through a fan produced wind loading