Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

In this paper, we present a comprehensive and detailed review of dynamic soaring process, and in particular, its application to unmanned aerial vehicles (UAVs). We start by explaining the biological inspiration that comes from soaring birds and how researchers have tried to utilize the dynamic soaring phenomenon/maneuver and apply it to UAVs. We present and discuss the fundamentals of wind shear models in both the linear and nonlinear cases. Moreover, a comprehensive parametric characterization of the key performance parameters for the dynamic soaring maneuver is given. Numerical methods for nonlinear trajectory optimization are summarized and methodologies capable of generating rapid solutions suitable for real-time implementation, are presented. Additionally, the paper introduces mathematical modeling and procedure to generate the optimized dynamic soaring trajectory. Through this paper, a consolidated platform is built, which not only covers technical aspects of advancements made over the passage of time, but also identifies and discusses the existing challenges. These challenges which are encountered by UAVs curtail the potential utility of dynamic soaring. Integrating dynamic soaring with morphology and inclusion of nonlinear control theory in the flight control system are introduced as a possible future research directions that may overcome the existing limitations.

Review of dynamic soaring: technical aspects, nonlinear modeling perspectives and future directions

Three-dimensional terminal angle constrained robust guidance law with autopilot lag consideration

Under harsh geographical conditions where manned flight is not possible, the ability of the unmanned aerial vehicle (UAV) to successfully carry out the payload hold–release mission by avoiding obstacles depends on the optimal path planning and tracking performance of the UAV. The ability of the UAV to plan and track the path with minimum energy and time consumption is possible by using the flight parameters. This study performs the optimum path planning and tracking using Harris hawk optimization (HHO)–grey wolf optimization (GWO), a hybrid metaheuristic optimization algorithm, to enable the UAV to actualize the payload hold–release mission avoiding obstacles. In the study, the hybrid HHO–GWO algorithm, which stands out with its avoidance of local minima and speed convergence, is used to successfully obtain the feasible and effective path. In addition, the effect of the mass change uncertainty of the UAV on optimal path planning and tracking performance is determined. The effectiveness of the proposed approach is tested by comparing it with the metaheuristic swarm optimization algorithms such as particle swarm optimization (PSO) and GWO. The experimental results obtained indicate that the proposed algorithm generates a fast and safe optimal path without becoming stuck with local minima, and the quadcopter tracks the generated path with minimum energy and time consumption.

/pdf/metaheuristic-optimization-based-path-planning-and-tracking-2enc1t9z.pdf

Metaheuristic Optimization-Based Path Planning and Tracking of Quadcopter for Payload Hold-Release Mission

This paper deals with the optimization of the ascent trajectory of a multistage launch vehicle, from liftoff to the payload injection into the target orbit, considering inverse-square gravity accel...

Convex Approach to Three-Dimensional Launch Vehicle Ascent Trajectory Optimization

Efficient ascent trajectory optimization using convex models based on the Newton–Kantorovich/Pseudospectral approach

Space maneuverings of the space vehicle require the capability of onboard trajectory planning. Convex programming based optimization strategy gets much attention in the design of trajectory planning methods with deterministic convergence properties. Due to the nonlinear dynamics, space-trajectory planning problems are always non-convex and difficult to be solved by the convex programming approach directly. This paper presents a Newton–Kantorovich/convex programming (N–K/CP) approach, based on the combination of the convex programming and the Newton–Kantorovich (N–K) method, to solve the nonlinear and non-convex space-trajectory planning problem. This trajectory planning problem is formulated as a nonlinear optimal control problem. By linearization and relaxation techniques, the nonlinear optimal control problem is convexified as a convex programming problem, which can be solved efficiently with convex programming solvers. For the linearized convex optimization problem, N–K method is introduced to design an iterative solving algorithm, the solution of which approximates the original trajectory planning problem with high accuracy. The convergence of the proposed N–K/CP approach is proved, and the effectiveness is demonstrated by numerical experiments and comparisons with other state-of-the-art methods.

Autonomous trajectory planning for space vehicles with a Newton–Kantorovich/convex programming approach

https://www.research.manchester.ac.uk/portal/files/68333757/2018AESCTE_2_.pdf

Robust finite-time guidance against maneuverable targets with unpredictable evasive strategies

Graph-based path decision modeling for hypersonic vehicles with no-fly zone constraints

Efficient energy management for the solid rocket is very important to exhaust excess energy and to meet the various terminal constraints. Based on the online planning of the velocity capability curve, a Double-arcs Energy Management (DAEM) guidance algorithm is proposed in this paper. In the DAEM, the velocity capability curve is designed with two tangential arcs. By using the elegant geometric characteristic of the arcs, the closed-loop guidance problem is transformed as a problem of solving a system of nonlinear equations about the parameters (radius and center position) of the two arcs, and the nonlinear equations can be solved in real time. The main advantages of this algorithm are that the height increment constraint, which is difficult to be satisfied in traditional energy management methods, can be satisfied theoretically, and the convergence of the solution of the DAEM is quadratic. The effectiveness and advantages of the proposed DAEM algorithm are demonstrated by simulations and comparisons with other energy management algorithms.

Huifeng Li

Papers

Efficient ascent trajectory optimization using convex models based on the Newton–Kantorovich/Pseudospectral approach

Autonomous trajectory planning for space vehicles with a Newton–Kantorovich/convex programming approach

Robust finite-time guidance against maneuverable targets with unpredictable evasive strategies

Graph-based path decision modeling for hypersonic vehicles with no-fly zone constraints

An ascent guidance algorithm for the energy management of solid rockets.