Ran Dai

Optimal topology design for dynamic networks

In this paper, we examine optimization-based methods for designing the network topology when the desired topology should have certain global variational properties, such as minimal power consumption for information exchange links, or supporting fast convergence of consensus-based distributed protocols. We first classify the optimization-based methodology for three distinct categories, namely, for construction of optimal non-geometric networks, time-invariant geometric networks, and time-varying geometric networks. We then proceed to propose optimization-based algorithms for each class of problems that aim to allocate the limited resources, e.g., communication ranges, in the most efficient way while achieving optimal performance. Examples and applications of the developed methodology are also examined.

Path Planning and State Estimation for Unmanned Aerial Vehicles in Hostile Environments

U NMANNED aerial vehicles (UAVs) are now widely used in antiterrorism activities and intelligence gathering to enhance mission performance and maximize safety. The susceptibility of these UAVs in hostile environments raises requirements for flight path planning. Path planning strategies in hostile environments are normally composed of two phases [1,2]. The first phase is a Voronoi graph search, which will generate polygonal graphs and will optimize a safety performance index. The second is to use the virtual forces emanated from the virtual field of each surveillance radar site to refine the generated Voronoi graphs. These virtual forces provide information that can be used to reduce the vertices of the Voronoi polygonal and greatly improve the UAV performance. But the curvature continuity of the refined graphs, which plays an important role in the stability of the UAVs’ turning maneuvers, often does not meet the requirements for a continuously flyable path. Many kinds of curves have been studied and designed for UAVs to accomplish their mission [3–5]. Dubins curves, first applied in robotics path planning, are curves along which the UAV can move forward. This kind of circle–line–circle curve has a jump discontinuity in curvature at the connection points between the circle and the line that will cause a robot to stop at these connection points when traveling through the whole path. Other curves, such as the Reeds– Shepp curves [6,7], also have curvature discontinuities at their joint points. An alternative choice, the composite clothoid–line–clothoid curves, can be well designed with curvature being zero at the joint points to eliminate the discontinuities. This allows one to generate a continuous-curvature path by using different kinds of simply shaped curves, although, under most circumstances, we are expecting more flexibility in the curve shape that will allow more space for change. Shanmugavel et al. [3–5]. proposed quintic Pythagorean hodograph (PH) curves for a flyable path, with ten parameters representing each curve. The PH curves are flexible in design and their curvatures are expressed in continuous polynomials. The parameter calculation of a PH curve is an iterative process in order to satisfy different constraints. Such kinds of curves can be further simplified with fewer parameters and a more efficient optimization algorithm. All the methods discussed leave room for improvement in the area of continuous-curvature path planning. The Cornu sprial (CS) [8,9], also known as a clothoid or Euler’s spiral, has wide application in highway and railroad construction, since it can be used to design gradual and smooth transitions in highway entrances or exits. Kelly and Nagy [10] used a parametric CS model to generate real-time nonholonomic trajectories for robotics to minimize the terminal posture error. Here, we consider this CSmodel for use in UAV path planning and investigate how this parametric CS curve works under different constraints. To generate a flyable and safe path with given starting and ending points for UAVs passing through areas covered, at least partially, by several radar sites, the path constraints considered here include 1) minimum accumulative exposure to all radar sites; 2) continuous curvature throughout its length, which will ensure a flyable path’ 3) maximum curvature corresponding to the maximum achievable lateral turn rate; and 4) initial and final boundary constraints. Unlike other path planning problems, including that of moving objects finding the final path, which normally result in motion planning or trajectory planning with system dynamics [11], the path considered here is in a static object environment without dynamic constraints. The work in this paper is based on the developed Voronoi graph; it refines the graph by proposing a generalized CS curve along with a simplified parameter-identification procedure. Most papers on the topic of path planning do not include the information about dynamic state variables of UAVs flying along the planned path. For control purposes, it is beneficial to estimate these state variables to construct complete information of the flight. Kalman filtering [12] has been widely used as an efficient tool in optimal filtering and prediction, especially in the field of state estimation of UAVs performing designated missions [13–17]. For example, Grillo and Vitrano [13] used an extended Kalman filter (EKF) to estimate the state variables and wind velocity for a nonlinear UAV model with Global Positioning System (GPS) measurements. Abdelkrim et al. [14] used an EKF and an H1filter to estimate the localization of UAVs for which the position, velocity, and attitude aremeasured by an inertial navigation system. Campbell andOusingsawat [15] used two different estimators to provide online state and parameter estimation for path planning in uncertain environments. The state estimations in these studies have a commonality, because the UAVs in both cases have sensors or other instruments to provide useful measurement information. If all of the Voronoi points on the initial path are fixed and expected to be followed as closely as possible, they can be assumed asmeasurement points. The generated CS curve is then treated as the reference solution so that the state variables can be estimated by the EKF. The following sections present the procedure for the pathinformation construction in three parts. The first part is the initial rough path of the Voronoi graph and the dynamic programming search algorithm. In the second part, CS curve expression and properties are introduced and different constraints and their mathematical expression are explained. This is followed by the systematicsolution nonlinear programming (NLP) solver. In the last part, the state variables are estimated based on the generated Voronoi points and the refined reference path generated in the first two parts. Simulation results are presented in each part separately.

Optimal path planning and power allocation for a long endurance solar-powered UAV

In this paper the problem of optimal path planning and power allocation for an Unmanned Aerial Vehicle (UAV) is explored. The UAV is equipped with photovoltaic cells on top of its wings and its energy sources are solar power and rechargeable batteries. The Sun incidence angle on the photovoltaic cells, which subsequently affects energy harvesting, is determined by the attitude of the UAV and the Sun position. The desired optimal path between two given boundary points, is aimed at increasing the amount of energy storage at the final point. Meanwhile, the charging state of the battery, resulting from the power allocation, needs to be determined along with the path planning procedure. Two approaches, nonlinear programming and model reduction, are proposed and their corresponding simulation results are presented and compared.

Optimal Trajectory Generation for Establishing Connectivity in Proximity Networks

We examine the problem of designing optimal trajectories to establish connectivity in a network of initially scattered dynamic agents, specifically minimizing the squared integral of the total control effort. The network edges are modeled by proximity relationships between endpoint agents, leading to a dynamic state-dependent network topology. We formulate an optimal control problem with specified initial states, linear dynamics, and a connectivity constraint on the final induced topology. Our approach utilizes the Hamiltonian and resultant Euler-Lagrange equations to restructure the optimal control formulation as a parameter optimization problem based on final agent states. We provide both a heuristic approach and an iterative semidefinite programming (SDP) relaxation to efficiently approximate a solution of the resulting combinatorial optimization problem. Simulation results for double integrator agent dynamics are first provided to demonstrate feasibility for both approaches, and the results are compared with those obtained from exhaustive global search and random sampling. Additional simulation is performed for a specific spacecraft formation problem requiring the design of a stable connected network between a collection of fractionated spacecraft modules to illustrate the practicability and indicate the range of applications of the proposed approaches.

Optimal path planning for solar-powered UAVs based on unit quaternions

In this paper, we examine a unit quaternion based method to design the optimal paths with maximum sun exposure for unmanned aerial vehicles (UAVs) equipped with photovoltaic cells on their wings. The mission of traveling between two specified boundary points with fixed flying time and constant speed is considered. Since the solar power is the sole source of energy for these UAVs during the flight, we consider the problem of maximizing the incoming solar radiation throughout their trajectory. As the attitude of the UAV directly determines solar intensity normal to the vertical surface of the wing, we use a unit quaternion based method to control the attitude maneuver during the flight interval. Subsequently, the aircraft kinematics are expressed as quadratic functions in terms of unit quaternions which can be solved by a branch and bound approach. Simulation results in two and three dimensions are presented.

Path planning for multiple unmanned aerial vehicles by parameterized cornu-spirals

In this paper, a group of cooperative planning paths for simultaneous starting and arriving Unmanned Aerial Vehicles (UAVs) are generated by parameterized Cornu-Spirals (CSs). The continuity and smoothness requirements for the designed flyable paths are achieved by the continuous curvature characteristics of CSs. The final curves are minimized in length with the least number of parameters representing the polynomial expression of the path curvature, while satisfying the maximum curvature constraints, equal length constraints, and collision avoidance constraints. The paths are integrated from initial points to final points by a trapezoidal integration algorithm. A nonlinear programming solver is used to calculate the optimized parameters. Simulation results for four simultaneous UAV paths are presented with designated initial and final positions and attitudes.

Path Planning of Spatial Rigid Motion with Constrained Attitude

This paper presents a general quadratic optimization methodology for autonomous path planning of spatial rigid motion with constrained attitude. The motion to be planned has six degrees of freedom and is assumed under constant velocity in the body frame. The objective is to determine the motion orientation (or attitude), handled as control variables, along the planned paths. A procedure is discussed to transform the rotational constraints and attitude constraints as quadratic functions in terms of unit quaternions, and the path-planning problem is reformulated as a general, quadratically constrained, quadratic programming problem. A semidefinite relaxation method is then applied to obtain a bound on the global optimal value of the nonconvex, quadratically constrained, quadratic programming problem. Subsequently, an iterative rank minimization approach is proposed to find the optimal solution. Application examples of aircraft path-planning problems are presented using the proposed method and compared with ...

Distributed Motion Estimation of Space Objects Using Dual Quaternions

This paper examines the motion estimation problem for space objects using multiple image sensors in a connected network. The objective is to increase the estimation precision of relative translational and rotational motions based on integrated dual quaternion representations and cooperation between connected sensors. The relative motion of space objects is rst formulated using dual elements to express its kinematics and dynamics. Two modular optimization approaches, namely dual decomposition and distributed Newton methods, for decomposing this cooperative estimation problem among the sensors is then proposed. Simulation results from single sensor estimation and two distributed estimation frameworks are provided and compared.

B-Splines Based Optimal Control Solution

A fast convergent optimization algorithm is proposed in this paper to calculate sequential optimal trajectories for pursuing a moving target or under dynamically changing environments. The changing boundary conditions or perturbations in such problems require an efficient algorithm to update the optimal trajectories with appropriate time steps. Concepts of a uniform B-spline and differentially flat system are introduced to map the system equations to a lower dimensional space with least number of variables as necessary. The initial trajectory starts from quadratic uniform B-splines and then is refined by increasing the spline degree level to generate smooth trajectories with higher accuracy. Solution of all levels is transformed to a unit time interval. The whole procedure is schemed to be applicable to most of the classical Bolza problems. Finally, simulation results are compared to those solved by trapezoidal and pseudospectral discretization methods.

Path planning of solar-powered unmanned aerial vehicles at low altitude

In this paper, the path planning strategy for solar powered UAVs at low altitude is examined including the weather factor in energy harvesting. The designed path will maximize the difference between the collected energy and the consumed energy, named net gain of energy, when flying from the specified initial point to the final point. A weather map providing information such as regional precipitation is utilized to predict the solar spectral density for the concerned areas. We propose a graph based approach which divides the concerned areas into small grids to evaluate the solar spectral density corresponding to the local weather and then build the energy intensity distribution map as a function of coordinates. The Bellman-Ford algorithm is utilized to find the optimal path which yields maximum net gain of energy at terminal point. Simulation results for level flight are presented.