Time-to-go weighted optimal trajectory shaping guidance law

For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based on the time-to-go weighted function. Based on the same cost function, the closed-form solutions of the guidance law were derived when the initial displacement of missile, final impact angle, heading error and target maneuver was introduced into the lag-free guidance system. To validate the closed-form solutions, the simulation of the lag-free system was done and the simulation results exactly matched the closed-form solutions and only when the exponent is greater than zero, the final acceleration approaches to zero.

Trajectory shaping guidance law based on virtual angle with terminal constraints

A trajectory shaping guidance law based on virtua angle （TSGLBVA） is proposed for a re-entry vehicle with the constraints of terminal impact angles and their time derivatives. In the view of differential properties of the maneuvering trajectory, a virtual angle and a virtual radius are defined. Also, the shaping trajectory of the vehicle is established by the polynomials of the virtual angle. Then, four optimized parameters are selected according to the theorem of parameters transformation presented in this paper. Finally, a convergent variant of the Nelder-Mead algorithm is adopted to obtain the reference trajectory, and a trajectory feedback tracking guidance law is designed. The simulation results demonstrate that the TSGLBVA ensures the re-entry vehicle to impact a target precisely from a specified direction with smal terminal load factor command, as well as to obtain a maximum or constrained terminal velocity according to various requirements.

Trajectory shaping guidance law with terminal impact angle constraint

In order to strike hard targets underground or warships and tanks with expected impact angle by missiles or guided bombs, trajectory shaping guidance law with terminal position and impact angle constraints is derived based on linear quadratic optimal control theory. The required accelera- tion expressed by impact angle and heading error is obtained in lag-free guidance system in order to find the optimal relationship of those angles in terminal phase. The adjoint systems of miss distance and impact angle error of first-order guidance system are established based on statistical linearization adjoint method （SLAM） in order to study the impact performances of the guidance law. Simulation results show that the miss distance and impact angle error of trajectory shaping guidance law are both according with the impact position and angle constraint and the required acceleration at impact can be decreased by an optimal relationship of impact angle and heading error.

Extended trajectory shaping guidance law considering a first-order autopilot lag

To satisfy the terminal position and impact angel constraints,an optimal guidance problem was discussed for homing missiles. For a stationary or a slowly moving target on the ground,an extended trajectory shaping guidance lawconsidering a first-order autopilot lag（ ETSG L-C FAL） was proposed. To derive the ETSG L-C FAL,a time-to-go- nth power weighted objection function was adopted and three different derivation methods were demonstrated while the Schwartz inequality method was mainly demonstrated.The performance of the ETSG L-C FAL and the ETSG L guidance laws was compared through simulation.Simulation results showthat although a first-order autopilot is introduced into the ETSG L-C FAL guidance system,the position miss distance and terminal impact angle error induced by the impact angle is zero for different guidance time.

Optimal guidance of extended trajectory shaping

To control missile＇s miss distance as well as terminal impact angle, by involving the timeto-go-nth power in the cost function, an extended optimal guidance law against a constant maneuvering target or a stationary target is proposed using the linear quadratic optimal control theory.An extended trajectory shaping guidance（ETSG） law is then proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small. For a lag-free ETSG system, closed-form solutions for the missile＇s acceleration command are derived by the method of Schwartz inequality and linear simulations are performed to verify the closed-form results. Normalized adjoint systems for miss distance and terminal impact angle error are presented independently for stationary targets and constant maneuvering targets, respectively. Detailed discussions about the terminal misses and impact angle errors induced by terminal impact angle constraint, initial heading error, seeker zero position errors and target maneuvering, are performed.

A fast scanning strategy based on trajectory shaping for atomic force microscopy

To improve the scanning speed of an atomic force microscopy(AFM),a smooth scanning pattern is elaborately devised via trajectory shaping in this paper,so as to achieve fast imaging without hardware modification.Specifically,in the proposed scanning method,the piezoelectric actuator tracks a well-designed smooth periodic signal in x-direction,and simultaneously tracks a step signal in y-direction.The advantage of the proposed method is that it does not require additional data reprocessing to construct the morphology of the sample surface,while significantly increasing the scanning bandwidth restricted by the raster scanning method.Particularly,to directly utilize the height data collected by scanning to produce the sample morphology,the forward process in the common raster scanning mode is retained in the proposed method,the tracking signal in the forward process is thus set to a ramp function in x-direction.In addition,to ensure the continuity and smoothness of the entire tracking signal in x-direction,a segment of a sine curve is uniquely determined as the backward tracking signal by position and acceleration constraints,so as to ensure that the forward and backward curves are continuous and acceleration-continuous at the intersection point.Moreover,the frequency spectrum analysis of the designed smooth signal is carried out to exhibit the depressed amplitudes of high-frequency components,which demonstrates that the proposed method is able to reduce the resonance in AFM high-speed scanning,so as to improve the capacity of rapidly generating high-quality images.Finally,convincing comparison experiments are implemented to verify the imaging performance of the designed scanning algorithm.

Complex human activities recognition using interval temporal syntactic model

A novel method based on interval temporal syntactic model was proposed to recognize human activities in video flow. The method is composed of two parts: feature extract and activities recognition. Trajectory shape descriptor, speeded up robust features(SURF) and histograms of optical flow(HOF) were proposed to represent human activities, which provide more exhaustive information to describe human activities on shape, structure and motion. In the process of recognition, a probabilistic latent semantic analysis model(PLSA) was used to recognize sample activities at the first step. Then, an interval temporal syntactic model, which combines the syntactic model with the interval algebra to model the temporal dependencies of activities explicitly, was introduced to recognize the complex activities with a time relationship. Experiments results show the effectiveness of the proposed method in comparison with other state-of-the-art methods on the public databases for the recognition of complex activities.

Composite impact vector control based on Apollo descent guidance

A new three-dimensional missile guidance law to control the impact vector against a stationary target is proposed.The composite guidance law has two well-known components:Apollo descent guidance and trajectory shaping guidance.These respectively linear and planar guidance laws are combined to achieve a specified impact direction.The main idea is to define an impact plane and to steer the missile onto this plane using Apollo descent guidance while concurrently performing trajectory shaping with reference to the impact plane.The resulting guidance law is expressed by a single equation in vector form,which is straightforward to implement.Because it originates from an optimal formulation,the performance of the proposed technique is expected to be satisfactory.This is confirmed by comparative simulation runs,which also involve the method known as generalized explicit guidance.