Re-entry trajectory optimization using a multiple- interval Radau pseudospectral method

Aiming at increasing the calculation efficiency of the pseudospectral methods, a multiple- interval Radau pseudospectral method （RPM） is presented to generate a reusable launch vehicle （RLV） ＇s optimal re-entry trajectory. After dividing the optimal control problem into many intervals, the state and control variables are approximated using many fixed- and low-degree Lagrange polyno- mials in each interval. Convergence of the numerical discretization is then achieved by increasing the number of intervals. With the application of the proposed method, the normal nonlinear program- ming （NLP） problem transcribed from the optimal control problem can avoid being dense because of the low-degree approximation polynomials in each interval. Thus, the NLP solver can easily compute a solution. Finally, simulation results show that the optimized re-entry trajectories satisfy the path constraints and the boundary constraints successfully. Compared with the single interval RPM, the multiple-interval RPM is significantly faster and has higher calculation efficiency. The results indicate that the multiple-interval RPM can be applied for real-time trajectory generation due to its high effi- ciency and high precision.

Joint Optimization of Resource Allocation and Trajectory Based on User Trajectory for UAV-Assisted Backscatter Communication System

The Backscatter communication has gained widespread attention from academia and industry in recent years. In this paper, A method of resource allocation and trajectory optimization is proposed for UAV-assisted backscatter communication based on user trajectory. This paper will establish an optimization problem of jointly optimizing the UAV trajectories, UAV transmission power and BD scheduling based on the large-scale channel state signals estimated in advance of the known user trajectories, taking into account the constraints of BD data and working energy consumption, to maximize the energy efficiency of the system. The problem is a non-convex optimization problem in fractional form, and there is nonlinear coupling between optimization variables.An iterative algorithm is proposed based on Dinkelbach algorithm, block coordinate descent method and continuous convex optimization technology. First, the objective function is converted into a non-fractional programming problem based on Dinkelbach method,and then the block coordinate descent method is used to decompose the original complex problem into three independent sub-problems. Finally, the successive convex approximation method is used to solve the trajectory optimization sub-problem. The simulation results show that the proposed scheme and algorithm have obvious energy efficiency gains compared with the comparison scheme.

THREE-DIMENSIONAL TRAJECTORY OPTIMIZATION WITH DIRECT METHOD

The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And capabilities of flight and propulsion systems are considered also. Combined with digital terrain map technique, the direct method is applied to the three dimensional trajectory optimization for low altitude penetration, and simplex algorithm is used to solve the parameters in optimization. For the small number of parameters, the trajectory can be optimized in real time on board.

Max-Min Adaptive Ant Colony Optimization Approach to Multi-UAVs Coordinated Trajectory Replanning in Dynamic and Uncertain Environments

Multiple Uninhabited Aerial Vehicles (multi-UAVs) coordinated trajectory replanning is one of the most complicated global optimum problems in multi-UAVs coordinated control. Based on the construction of the basic model of multi-UAVs coordinated trajectory replanning, which includes problem description, threat modeling, constraint conditions, coordinated function and coordination mechanism, a novel Max-Min adaptive Ant Colony Optimization (ACO) approach is presented in detail. In view of the characteristics of multi-UAVs coordinated trajectory replanning in dynamic and uncertain environments, the minimum and maximum pheromone trails in ACO are set to enhance the searching capability, and the point pheromone is adopted to achieve the collision avoidance between UAVs at the trajectory planner layer. Considering the simultaneous arrival and the air-space collision avoidance, an Estimated Time of Arrival (ETA) is decided first. Then the trajectory and flight velocity of each UAV are determined. Simulation experiments are performed under the complicated combating environment containing some static threats and popup threats. The results demonstrate the feasibility and the effectiveness of the proposed approach.

Reentry trajectory rapid optimization for hypersonic vehicle satisfying waypoint and no-fly zone constraints

To rapidly generate a reentry trajectory for hypersonic vehicle satisfying waypoint and no-fly zone constraints, a novel optimization method, which combines the improved particle swarm optimization （PSO） algorithm with the improved Gauss pseudospectral method （GPM）, is proposed. The improved PSO algorithm is used to generate a good initial value in a short time, and the mission of the improved GPM is to find the final solution with a high precision. In the improved PSO algorithm, by controlling the entropy of the swarm in each dimension, the typical PSO algorithm＇s weakness of being easy to fall into a local optimum can be overcome. In the improved GPM, two kinds of breaks are introduced to divide the trajectory into multiple segments, and the distribution of the Legendre-Gauss （LG） nodes can be altered, so that all the constraints can be satisfied strictly. Thereby the advan- tages of both the intelligent optimization algorithm and the direct method are combined. Simulation results demonstrate that the proposed method is insensitive to initial values, and it has more rapid convergence and higher precision than traditional ones.

Study of trajectory optimization using terminal-node adaptive-altered spline algorithm

The advantage of using a spline function to evaluate the trajectory parameters optimization is discussed. A new method that using adaptive varied terminal-node spline interpolation for solving trajectory optimization is proposed. And it is validated in optimizing the trajectory of guided bombs and extended range guided munitions （ERGM）. The solutions are approximate to the real optimization results. The advantage of this arithmetic is that it can be used to solve the trajectory optimization with complex models. Thus, it is helpful for solving the practical engineering optimization problem.

Joint Trajectory and Passive Beamforming Optimization in IRS-UAV Enhanced Anti-Jamming Communication Networks

This paper investigates the anti-jamming communication scenario where an intelligent reflecting surface(IRS)is mounted on the unmanned aerial vehicle(UAV)to resist the malicious jamming attacks.Different from existing works,we consider the dynamic deployment of IRS-UAV in the environment of the mobile user and unknown jammer.Therefore,a joint trajectory and passive beamforming optimization approach is proposed in the IRS-UAV enhanced networks.In detail,the optimization problem is firstly formulated into a Markov decision process(MDP).Then,a dueling double deep Q networks multi-step learning algorithm is proposed to tackle the complex and coupling decision-making problem.Finally,simulation results show that the proposed scheme can significantly improve the anti-jamming communication performance of the mobile user.

Smart Gait:A Gait Optimization Framework for Hexapod Robots

The current gait planning for legged robots is mostly based on human presets,which cannot match the flexible characteristics of natural mammals.This paper proposes a gait optimization framework for hexapod robots called Smart Gait.Smart Gait contains three modules:swing leg trajectory optimization,gait period&duty optimization,and gait sequence optimization.The full dynamics of a single leg,and the centroid dynamics of the overall robot are considered in the respective modules.The Smart Gait not only helps the robot to decrease the energy consumption when in locomotion,mostly,it enables the hexapod robot to determine its gait pattern transitions based on its current state,instead of repeating the formalistic clock-set step cycles.Our Smart Gait framework allows the hexapod robot to behave nimbly as a living animal when in 3D movements for the first time.The Smart Gait framework combines offline and online optimizations without any fussy data-driven training procedures,and it can run efficiently on board in real-time after deployment.Various experiments are carried out on the hexapod robot LittleStrong.The results show that the energy consumption is reduced by 15.9%when in locomotion.Adaptive gait patterns can be generated spontaneously both in regular and challenge environments,and when facing external interferences.

Earth-moon Trajectory Optimization Using Solar Electric Propulsion

The optimization of the Earth-moon trajectory using solar electric propulsion is presented. A feasible method is proposed to optimize the transfer trajectory starting from a low Earth circular orbit （500 km altitude） to a low lunar circular orbit （200 km altitude）. Due to the use of low-thrust solar electric propulsion, the entire transfer trajectory consists of hundreds or even thousands of orbital revolutions around the Earth and the moon. The Earth-orbit ascending （from low Earth orbit to high Earth orbit） and lunar descending （from high lunar orbit to low lunar orbit） trajectories in the presence of J2 perturbations and shadowing effect are computed by an analytic orbital averaging technique. A direct/indirect method is used to optimize the control steering for the trans-lunar trajectory segment, a segment from a high Earth orbit to a high lunar orbit, with a fixed thrust-coast-thrust engine sequence. For the trans-lunar trajectory segment, the equations of motion are expressed in the inertial coordinates about the Earth and the moon using a set of nonsingular equinoctial elements inclusive of the gravitational forces of the sun, the Earth, and the moon. By way of the analytic orbital averaging technique and the direct/indirect method, the Earth-moon transfer problem is converted to a parameter optimization problem, and the entire transfer trajectory is formulated and optimized in the form of a single nonlinear optimization problem with a small number of variables and constraints. Finally, an example of an Earth-moon transfer trajectory using solar electric propulsion is demonstrated.

A Stable Analytical Solution Method for Car-Like Robot Trajectory Tracking and Optimization

In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.

A DNN based trajectory optimization method for intercepting non-cooperative maneuvering spacecraft

Current successes in artificial intelligence domain have revitalized interest in neural networks and demonstrated their potential in solving spacecraft trajectory optimization problems. This paper presents a data-free deep neural network(DNN) based trajectory optimization method for intercepting noncooperative maneuvering spacecraft, in a continuous low-thrust scenario. Firstly, the problem is formulated as a standard constrained optimization problem through differential game theory and minimax principle. Secondly, a new DNN is designed to integrate interception dynamic model into the network and involve it in the process of gradient descent, which makes the network endowed with the knowledge of physical constraints and reduces the learning burden of the network. Thus, a DNN based method is proposed, which completely eliminates the demand of training datasets and improves the generalization capacity. Finally, numerical results demonstrate the feasibility and efficiency of our proposed method.

A CALCULATION OF OPTIMAL FLIGHT TRAJECTORY USING THE PARAMETERIZED OPTIMIZATION METHOD

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Receding-Horizon Trajectory Planning for Under-Actuated Autonomous Vehicles Based on Collaborative Neurodynamic Optimization

This paper addresses a major issue in planning the trajectories of under-actuated autonomous vehicles based on neurodynamic optimization.A receding-horizon vehicle trajectory planning task is formulated as a sequential global optimization problem with weighted quadratic navigation functions and obstacle avoidance constraints based on given vehicle goal configurations.The feasibility of the formulated optimization problem is guaranteed under derived conditions.The optimization problem is sequentially solved via collaborative neurodynamic optimization in a neurodynamics-driven trajectory planning method/procedure.Simulation results with under-actuated unmanned wheeled vehicles and autonomous surface vehicles are elaborated to substantiate the efficacy of the neurodynamics-driven trajectory planning method.

Analysis of Controlled Trajectory Optimization for Canard Trajectory Correction Fuze

The optimization method of the canard trajectory correction fuze's controlled trajectory phase is researched by using the aerodynamics of aerocraft and the optimal control theory, the trajectory parameters of the controlled trajectory phase based on the least energy cost are determined. On the basis of determining the control starting point and the target point, the optimal trajectory and the variation rule of the normal overload with the least energy cost are provided, when there is no time restriction in the simulation process. The results provide a theoretical basis for the structure design of the canard mechanism.

Multi-objectives nonlinear structure optimization for actuator in trajectory correction fuze subject to high impact loadings

This paper presents an actuator used for the trajectory correction fuze,which is subject to high impact loadings during launch.A simulation method is carried out to obtain the peak-peak stress value of each component,from which the ball bearings are possible failures according to the results.Subsequently,three schemes against impact loadings,full-element deep groove ball bearing and integrated raceway,needle roller thrust bearing assembly,and gaskets are utilized for redesigning the actuator to effectively reduce the bearings’stress.However,multi-objectives optimization still needs to be conducted for the gaskets to decrease the stress value further to the yield stress.Four gasket’s structure parameters and three bearings’peak-peak stress are served as the four optimization variables and three objectives,respectively.Optimized Latin hypercube design is used for generating sample points,and Kriging model selected according to estimation result can establish the relationship between the variables and objectives,representing the simulation which is time-consuming.Accordingly,two optimization algorithms work out the Pareto solutions,from which the best solutions are selected,and verified by the simulation to determine the gaskets optimized structure parameters.It can be concluded that the simulation and optimization method based on these components is effective and efficient.

An Energy-Efficient UAV Deployment Scheme for Emergency Communications in Air-Ground Networks with Joint Trajectory and Power Optimization

The space-air-ground integrated network(SAGIN)has gained widespread attention from academia and industry in recent years.It is widely applied in many practical fields such as global observation and mapping,intelligent transportation systems,and military missions.As an information carrier of air platforms,the deployment strategy of unmanned aerial vehicles(UAVs)is essential for communication systems’performance.In this paper,we discuss a UAV broadcast coverage strategy that can maximize energy efficiency(EE)under terrestrial users’requirements.Due to the non-convexity of this issue,conventional approaches often solve with heuristics algorithms or alternate optimization.To this end,we propose an iterative algorithm by optimizing trajectory and power allocation jointly.Firstly,we discrete the UAV trajectory into several stop points and propose a user grouping strategy based on the traveling salesman problem(TSP)to acquire the number of stop points and the optimization range.Then,we use the Dinkelbach method to dispose of the fractional form and transform the original problem into an iteratively solvable convex optimization problem by variable substitution and Taylor approximation.Numerical results validate our proposed solution and outperform the benchmark schemes in EE and mission completion time.

Trajectory online optimization for unmanned combat aerial vehicle using combined strategy

This paper presents a combined strategy to solve the trajectory online optimization problem for unmanned combat aerial vehicle (UCAV). Firstly, as trajectory directly optimizing is quite time costing, an online trajectory functional representation method is proposed. Considering the practical requirement of online trajectory, the 4-order polynomial function is used to represent the trajectory, and which can be determined by two independent parameters with the trajectory terminal conditions; thus, the trajectory online optimization problem is converted into the optimization of the two parameters, which largely lowers the complexity of the optimization problem. Furthermore, the scopes of the two parameters have been assessed into small ranges using the golden section ratio method. Secondly, a multi-population rotation strategy differential evolution approach (MPRDE) is designed to optimize the two parameters; in which, 'current-to-best/1/bin', 'current-to-rand/1/bin' and 'rand/2/bin' strategies with fixed parameter settings are designed, these strategies are rotationally used by three subpopulations. Thirdly, the rolling optimization method is applied to model the online trajectory optimization process. Finally, simulation results demonstrate the efficiency and real-time calculation capability of the designed combined strategy for UCAV trajectory online optimizing under dynamic and complicated environments.

UAVs cooperative task assignment and trajectory optimization with safety and time constraints

This paper proposes new methods and strategies for Multi-UAVs cooperative attacks with safety and time constraints in a complex environment.Delaunay triangle is designed to construct a map of the complex flight environment for aerial vehicles.Delaunay-Map,Safe Flight Corridor(SFC),and Relative Safe Flight Corridor(RSFC)are applied to ensure each UAV flight trajectory's safety.By using such techniques,it is possible to avoid the collision with obstacles and collision between UAVs.Bezier-curve is further developed to ensure that multi-UAVs can simultaneously reach the target at the specified time,and the trajectory is within the flight corridor.The trajectory tracking controller is also designed based on model predictive control to track the planned trajectory accurately.The simulation and experiment results are presented to verifying developed strategies of Multi-UAV cooperative attacks.

Optimal Trajectory Generation for Aircraft Engine-Off Taxi Towing System Under Stochastic Constraints

The novel aircraft engine-off taxi towing system featuring aircraft power integration has demonstrated significant advantages,including reduced energy consumption,diminished emissions,and enhanced efficiency.However,the aircraft engine-off taxi towing system lacks the consideration of attendant constraints in the trajectory generation process,which can potentially lead to ground accidents and constrain the improvement of traction speed.Addressing this challenge,the present work investigates the optimal control problem of trajectory generation for the taxiing traction system in the complex stochastic environment in the airport flight area.For the stochastic constraints,a strategy of deterministic processing is proposed to describe the stochastic constraints using random constraints.Furthermore,an adaptive pseudo-spectral method is introduced to transform the optimal control problem into a nonlinear programming problem,enabling its effective resolution.Simulation results substantiate that the generated trajectory can efficiently handle the stochastic constraints and accomplish the given task towards the time-optimization objective,thereby effectively enhancing the stability and efficiency of the taxiing traction system,ensuring the safety of the aircraft system,and improving the ground access capacity and efficiency of the airport.

Novel integrated optimization algorithm for trajectory planning of robot manipulators based on integrated evolutionary programming

Optimal trajectory planning for robot manipulators plays an important role in implementing the high productivity for robots. The performance indexes used in optimal trajectory planning are classified into two main categories: optimum traveling time and optimum mechanical energy of the actuators. The current trajectory planning algorithms are designed based on one of the above two performance indexes. So far, there have been few planning algorithms designed to satisfy two performance indexes simultaneously. On the other hand, some deficiencies arise in the existing integrated optimi2ation algorithms of trajectory planning. In order to overcome those deficiencies, the integrated optimization algorithms of trajectory planning are presented based on the complete analysis for trajectory planning of robot manipulators. In the algorithm, two object functions are designed based on the specific weight coefficient method and ' ideal point strategy. Moreover, based on the features of optimization problem, the intensified evolutionary programming is proposed to solve the corresponding optimization model. Especially, for the Stanford Robot,the high-quality solutions are found at a lower cost.