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Urban autonomous vehicles on city roads are subject to various constraints when changing lanes, and commonly used trajectory planning methods struggle to describe these conditions accurately and directly. Therefore, generating accurate and adaptable trajectories is crucial for safer and more efficient trajectory planning. This study proposes an optimal control model for local path planning that integrates dynamic vehicle constraints and boundary conditions into the optimization problem's constraint set. Using the lane-changing scenario as a basis, this study establishes environmental and collision avoidance constraints during driving and develops a performance metric that optimizes both time and turning angle. The study employs the Gauss pseudo-spectral method to continuously discretize the state and control variables, converting the optimal control problem into a nonlinear programming problem. Using numerical solutions, variable control and state trajectories that satisfy multiple constraint conditions while optimizing the performance metric are generated. The study employs two weights in the experiment to evaluate the method's performance, and the findings demonstrate that the proposed method guarantees safe obstacle avoidance, is stable, and is computationally efficient at various interpolation points compared to the Legendre pseudo-spectral method (LPM) and the Shooting method. [ABSTRACT FROM AUTHOR]

Urban autonomous vehicles on city roads are subject to various constraints when changing lanes, and commonly used trajectory planning methods struggle to describe these conditions accurately and directly. Therefore, generating accurate and adaptable trajectories is crucial for safer and more efficient trajectory planning. This study proposes an optimal control model for local path planning that integrates dynamic vehicle constraints and boundary conditions into the optimization problem’s constraint set. Using the lane-changing scenario as a basis, this study establishes environmental and collision avoidance constraints during driving and develops a performance metric that optimizes both time and turning angle. The study employs the Gauss pseudo-spectral method to continuously discretize the state and control variables, converting the optimal control problem into a nonlinear programming problem. Using numerical solutions, variable control and state trajectories that satisfy multiple constraint conditions while optimizing the performance metric are generated. The study employs two weights in the experiment to evaluate the method’s performance, and the findings demonstrate that the proposed method guarantees safe obstacle avoidance, is stable, and is computationally efficient at various interpolation points compared to the Legendre pseudo-spectral method (LPM) and the Shooting method.

In order to achieve an accurate airdrop in the actual environment, the influence of complex interferences, such as wind field and the terrain of the environment, must be taken into account. Aiming at this problem, a combined trajectory planning strategy of a parafoil system subjected to intricate conditions is proposed in this paper. This method divides the parafoil airdrop area into an obstacle area and a landing area, then, considering the terrain environment surface, a model for the parafoil system in the wind field is built in the obstacle area. The Gauss pseudo-spectral method is used to transform the complex terrain environment constraint into a series of nonlinear optimal control problems with complex constraints. Finally, the trajectory of the landing area is designed by means of multiphase homing, and the target parameters are solved by the improved marine predator algorithm. The simulation results show that the proposed method has better realizability than a single homing strategy, and the optimization results of the improved marine predator algorithm have higher accuracy.

The landing maneuver of aircraft is considered to be a feasible way to solve the problem of ultra short distance,precise landing of carrier based fixed wing aircraft. The existing researches mainly focus on aerodynamic modeling,nominal landing trajectory optimization and trajectory tracking control in the process of landing,but few on the overall analysis of the landing mission. Based on the dynamic model of aircraft longitudinal landing maneuver,the concept of landing trajectory reachable region is introduced,and the mathematical description of reachable region is given;On this basis,the Gauss pseudo-spectral method with both computational speed and accuracy is used to solve the reachable region problem,which is divided into three trajectory optimization problems. Firstly,the upper boundary of the terminal height of the perching trajectory is solved. Secondly,the nearest trajectory is solved when the terminal height is fixed. Finally,the farthest trajectory is solved when the terminal height is fixed.The simulation results show that:the model and solution method can quickly get the calculation results,the vertical landing trajectory of unpowered aircraft can reach the asymmetric region of narrow upper and wide lower,and the left and right boundary curves have good linearity.

The rapid developments of artificial intelligence in the last decade are influencing aerospace engineering to a great extent and research in this context is proliferating. In this paper, the trajectory optimization of a three-stage launch vehicle in the powering phase subject to the sun-synchronous orbit is considered. To solve the optimal control problem, the Gauss pseudo-spectral method (GPM) is used to transform the optimization model to a nonlinear programming (NLP) problem and sequential quadratic programming is applied to find the optimal solution. However, the sensitivity of the initial guess may cost the solver significant time to do the Newton iteration or even lead to the local minimum. Aiming at this issue, a good initial guess generated by combination of harmony search and GPM is introduced to help the optimizer to faster and better solve the sun-synchronous orbit (SSO) trajectory optimization. Comparative simulation tests are conducted with the proposed algorithm and popular approaches, the results indicate that with the optimized initial guess, the proposed method could achieve better performance in terms of convergence ability and convergence rate. [ABSTRACT FROM AUTHOR]

In order to achieve an accurate airdrop in the actual environment, the influence of complex interferences, such as wind field and the terrain of the environment, must be taken into account. Aiming at this problem, a combined trajectory planning strategy of a parafoil system subjected to intricate conditions is proposed in this paper. This method divides the parafoil airdrop area into an obstacle area and a landing area, then, considering the terrain environment surface, a model for the parafoil system in the wind field is built in the obstacle area. The Gauss pseudo-spectral method is used to transform the complex terrain environment constraint into a series of nonlinear optimal control problems with complex constraints. Finally, the trajectory of the landing area is designed by means of multiphase homing, and the target parameters are solved by the improved marine predator algorithm. The simulation results show that the proposed method has better realizability than a single homing strategy, and the optimization results of the improved marine predator algorithm have higher accuracy. [ABSTRACT FROM AUTHOR]

The trajectory of the near space hypersonic target interceptor is designed and verified. Firstly, this paper discusses the necessity of the trajectory design of the near space hypersonic target interceptor. Taking the high throw-reentry-glide trajectory scheme of the near space hypersonic as the reference trajectory, the whole trajectory is divided into active phase and glide phase. Secondly, the active phase takes the longest range as the performance index, and the glide phase takes the maximum terminal velocity as the performance index. According to the constraints of flight process analysis, it establishes the optimal control model of trajectory optimization. Lastly, the Gauss pseudo-spectral method is used to plan the trajectory of the active and gliding phases. The simulation results show that the obtained trajectory characteristics are consistent with the high-throw-reentry-glide trajectory scheme, and the flight parameters satisfy the constraints. This study can provide some reference for the trajectory planning of the near-space interceptor.

Orbital perturbations caused by the space environment will induce deviations compared with the prescribed motion trajectory or dynamic performance of the tethered satellite system (TSS). To comprehensively investigate the effects of the orbital perturbations on the TSS, a precise variable-length element that can describe the large deformation and flexibility of the tether is adopted in this paper to predict the deployment dynamics considering orbital perturbations, including atmospheric drag, solar pressure, lunisolar gravitation, and J2 perturbation. To this end, the variable-length element using arbitrary LagrangianEulerian (ALE) description in the frame work of absolute nodal coordinate formulation (ANCF) is developed firstly. Subsequently, the dynamic governing equations for the TSS are established in the context of ANCF with the employment of ANCF reference node (ANCF-RN). Effects of orbital perturbations including atmospheric drag, solar pressure, lunisolar gravity and J2 perturbation on the dynamics of an optimal deployment are analyzed numerically. It is shown that the orbital perturbations except the J2 perturbation will induce the out-of-plane motion of the TSS. Additionally, the tether tension is less affected by the orbital perturbations. By contrast, the lunisolar gravitation will induce a deviation on the motion path of satellite, which should be considered in the design phase of the TSS.

Automatic generation of feasible trajectory is one of the key technologies for autonomous flying of unmanned aerial vehicles (UAVs). The existing path planning methods, such as swarm intelligence algorithm and graph-based algorithm, cannot incorporate the flying time and UAV dynamic model into evolution. To overcome such disadvantages, a hierarchical trajectory optimization scheme consisted by improved particle swarm optimization (PSO) and Gauss pseudo-spectral method (GPM) is investigated in this paper. Firstly, considering that traditional GPM is sensitive to initial values, we design an improved PSO for path planning in the first layer. By introducing adaptive parameter adjustment strategy and position mutation updating strategy, the rapidity and optimality of the improved PSO is enhanced. Then in the second layer, a fitted curve based on the path waypoints generated by improved PSO is constructed and served as the initial values for GPM. Comparing with random initial values, the designed curve can significant improve GPM efficiency. A multi-segment strategy is also put forward to further improve the efficiency. Finally, with the consideration of dynamic model and state constraints, the time minimum trajectory planning for quadrotor UAVs is solved. Plenty of simulations are carried out and the results illustrate that the proposed scheme guarantees much better efficiency.

Based on the characteristics of the configuration and flight of the micro gliding air vehicle (MGAV), an analysis and optimization for general gliding path of different mission demands is carried out. Firstly, an overall design method and parameters are summarized. Secondly, the equilibrium glide launching parameters are determined based on the general aircraft re-entry equation. The real launching parameter are also developed by considering the real launching facility. Furthermore, the un-controlled maximum-range-towards path characteristics for the real and equilibrium glide are compared and analyzed. The range in equilibrium glide is 5 km larger than real glide. Then, two potential flight demand are explained and the Gauss pseudo-spectral method is adopted to solve the maximum endurance and the maximum endurance and range with the process constraint and final constraint. The first target is 8 minutes longer than the original glide path but the range is 20 km less compared to the maximum range. The second target could keep the maximum range and at the meantime, the endurance could be increased 2 minutes. Finally, the control variables are substituted into the dynamic equations to validate the results. The result shows that the Gauss pseudo-spectral method is an effective and feasible way to solve the optimum gliding path.

Vehicle-infrastructure cooperative systems can potentially enhance both traffic safety and efficiency by conducting coordinated control through the interactive strategy between the vehicles and the infrastructure. In this study, the interactive strategy of a vehicle infrastructure cooperative system is designed. Lane change maneuver is a conventional behavior in driving. Thus, this paper proposes a trajectory planning algorithm based on a Gauss pseudo-spectral method that is applied to the intelligent vehicle-infrastructure cooperative system in the lane change scenario. A road side unit calculates the planning trajectory using collected vehicle information and sensor data and then sends the trajectory planning advice to the designated vehicle. The Gauss pseudo-spectral method is used to obtain the planning trajectory, which effectively helps solve the discontinuous optimization problems in partial conditions. It transforms the optimal control problem of dynamic systems into a nonlinear programming problem using the orthogonal collocation method to discretize the objective function and various constraints of the optimization problem. Furthermore, the ssuential quadratic programming method is used to solve the problem numerically. The effectiveness of the proposed method and interactive strategy are demonstrated through simulations and experimental results. [ABSTRACT FROM AUTHOR]

Periodic cruise has the potential to improve the fuel efficiency of a hypersonic vehicle. However, the optimization of periodic cruise is very difficult and can only be performed inefficiently through trial-and-error due to the parameterized form. In this paper, we systematically optimized the hypersonic periodic cruise using the pseudo-spectral method (PSM) scheme. We specify the main variables as the given forms of periodic functions and parameterize the periodic guidance. The characteristic parameters can then be considered as augmented states to generate augmented dynamics. Therefore, periodic cruise optimization can be directly obtained by using GPOPS (Gauss Pseudo-spectral OPtimization Software). The numerical results demonstrate the effectiveness of the proposed method. The approach in this case study can be generalized to solve similar trajectory optimization problems that can be parameterized in a unified manner. [ABSTRACT FROM AUTHOR]

A novel time-optimal memetic whale optimization algorithm (WOA) integrating the Gauss pseudo-spectral methods (GPM), is proposed in this paper for the hypersonic vehicle entry trajectory optimization problem with no-fly zones. The WOA is featured with the strong global search ability and non-sensitive to the initial values, but also shows poor searching convergence speed around the global optimum. Conversely, GPM may be sensitive to the initial solution and easily trapped in a local optimum, but it also possesses more rapid convergence speed around the optimum and higher searching accuracy. Thus, a memetic optimization algorithm which contains a two-stage approach mechanism is proposed for searching the global optimum. The first searching stage, which is driven by an improved WOA (IWOA), works as an initializer of the entire searching due to its strong global search ability and non-sensitive to the initial values. The local optimum reservation and adaptive amplitude factor updating strategy are established to improve the convergent speed and the global search ability of the WOA. Once the changing of fitness value satisfies the predefined criterion, the next searching stage driven by GPM will take the place of the IWOA to expedite the search process around optimum and to obtain a precise global optimal solution. By this hybrid way, the proposed optimization algorithm may find an optimum more quickly and accurately. Simulation results show the proposed algorithm possesses faster convergence speed, higher accuracy, and stronger robustness for the hypersonic vehicle entry trajectory optimization. [ABSTRACT FROM AUTHOR]

The takeoff-mass of a two-stage-to-orbit Rocket-Based Combined Cycle Engine-Rocket (RBCC-RKT) launch vehicle is a crucial factor in its comprehensive performance. This paper optimizes the takeoff-mass together with the trajectory by reformulating it to a nonlinear optimal control problem. The range of the second stage rocket mass is considered as a process constraint. When the scopes of initial and terminal states are specified, the problem can be solved by using the Gauss pseudo-spectral method (GPM). In order to reduce the convergent difficulty caused by using table data, the data in different stages are utilized by employing an integrated interpolation strategy through the optimization. Simulation results show that the mass can be effectively optimized to meet the inertia mass ratio constraint of the first-stage, and the separation of Mach number and altitude can be optimized at the same time. [ABSTRACT FROM AUTHOR]

Periodic cruise has the potential to improve the fuel efficiency of a hypersonic vehicle. However, the optimization of periodic cruise is very difficult and can only be performed inefficiently through trial-and-error due to the parameterized form. In this paper, we systematically optimized the hypersonic periodic cruise using the pseudo-spectral method (PSM) scheme. We specify the main variables as the given forms of periodic functions and parameterize the periodic guidance. The characteristic parameters can then be considered as augmented states to generate augmented dynamics. Therefore, periodic cruise optimization can be directly obtained by using GPOPS (Gauss Pseudo-spectral OPtimization Software). The numerical results demonstrate the effectiveness of the proposed method. The approach in this case study can be generalized to solve similar trajectory optimization problems that can be parameterized in a unified manner.

In this paper, a hybrid optimization strategy using particle swarm optimization and Gauss pseudo-spectral method is proposed to generate the optimal entry trajectory of Mars pin-point landing mission. This hybrid optimization strategy merges global optimization with local optimization. Coarse optimization is first conducted to provide a global relative suitable initial guess for subsequent local accurate optimization, which can greatly improve optimization efficiency and robustness and produce the optimal Mars atmospheric entry trajectory from the present position to the designed terminal state satisfying the path constraints. The validity of the hybrid optimization strategy developed in this paper is confirmed by computer simulation in the presence of aerodynamics uncertainties. [ABSTRACT FROM AUTHOR]

In a low energy moon return mission, due to the weak stability of the orbit, it is necessary to implement an accurate orbital maneuver to guarantee a successful return. During the process of getting the optimal thrust control with these two kinds of methods, it is hard to guess the initial value of the co-states in the indirect method while a large amount of calculation is needed to insure the precision in the direct method. To solve the problem, in this paper a combined method is given which has the merit of both direct and indirect methods. In this method, the virtual satellite method (VSM) and the Gauss pseudo-spectral method (GPM) are applied, while the fuel optimal control strategy is computed with GPM to carry out a soft rendezvous between the spacecraft and a hypothetical virtual satellite running on the nominal low energy return orbit so that the spacecraft will enter the return orbit accurately. Compared with the direct and indirect methods, this combined method can avoid guessing the initial value of the co-states and the complexity of calculation is acceptable. According to the simulation results, the spacecraft is inserted to the target return orbit with a high accuracy and also the optimization is very effective. [ABSTRACT FROM AUTHOR]

The design parameters of high-altitude solar-powered aircraft are highly correlative with its flight trajectory. However, it is not an easy work to jointly optimize them in the concept design stage. This paper considers the joint optimization problem of battery mass and flight trajectory for high-altitude solar-powered aircraft. The system model including the aircraft dynamic model, aerodynamic parameters, and thrust model is presented. Then the problem to be optimized is formulated and a new optimization method, which uses the particle swarm optimization and Gauss pseudo-spectral method, is proposed. The Gauss pseudo-spectral method is employed to generate the minimal power consumed by following the flight trajectory in the given configuration of high-altitude solar-powered aircraft, while the particle swarm optimization is used to calculate the optimal battery mass of aircraft. The simulation result shows that the proposed joint optimization method can reduce the battery mass of high-altitude solar-powered aircraft from 16 kg to 13.6 kg, which is equivalent to enhancing its energy density by 19.7%. It can be also seen that the proposed optimization method connects each parameter in a logically clear way and hence provide a perspective for understanding the optimization problem. [ABSTRACT FROM PUBLISHER]

There is a greatly persistent wind shear in the upper atmosphere, especially at the altitude of 10–20 km. For the idea of dynamic soaring, the wind shear can be treated as a kind of energy resource for aircraft if the aircraft is flying in a proper manner. Based on the above facts, the influence of wind shear to the performance of high-altitude solar-powered aircraft from a new prospect is systemically studied: The wind shear in the upper atmosphere is treated as a kind of energy resource for aircraft, and to be used to compensate the energy consumed by drag. The results of simulations show that the energy extracted from wind shear can compensate about 30–50% of the energy consumed by drag in climbing and 20–40% in descending for high-altitude aircraft when the strength of wind shear is greater than 0.005 s−1 and smaller than 0.01 s−1. This is a valuable conclusion for the high-altitude aircraft, since the strength of wind shear between 10 km and 20 km has fallen into this interval. By defining the dynamic soaring parameter, it has been found that the dynamic soaring parameter is possibly greater than 1 in the place that great enough strength of wind shear can be found, which implies that it is possible for high-altitude aircraft to perform unpowered flight by dynamic soaring if the wind shear can be unitized properly. [ABSTRACT FROM PUBLISHER]

Gravitational gliding during night without electric power is an efficient method to enhance the endurance of high-altitude solar-powered unmanned aerial vehicles. The properties of the maximum endurance path of gravitational gliding are studied in this article. The maximum endurance path problem is formulated as the problem of the maximum endurance can be sustained by unit altitude difference with the constraints of dynamic equations and aerodynamic parameters. The maximum endurance path is generated by Gauss pseudo-spectral method, and a new way to estimate co-state variables in Hamiltonian is proposed. In order to analyze the sensitivity of initial altitude and velocity of solar unmanned aerial vehicles with its endurance performance, the lift coefficient in the interval [0.4, 1.2] and flight envelopes between 0 and 30 km are investigated. The results are as follows: first, the broad range of lift coefficients can improve solar aircrafts’ long-endurance performance; second, the lower the initial altitude, the longer the gliding endurance can be sustained by unit altitude difference; third, it is possible for a solar-powered unmanned aerial vehicle to keep aloft during the whole night just by gravitational potential energy storage, but the issues with turbulence and wind would render this mode of unlimited endurance unfeasible. Thus, gravitational gliding by potential energy storage can only be partly used instead of electric energy storage in application now. [ABSTRACT FROM PUBLISHER]

A Gauss pseudo-spectral method is proposed to solve optimal control problem for satellite rapid orbital maneuver, in which only one axis thruster is provided under the finite thrust. The concept of "virtual satellite" transforms the orbital maneuver of satellite into the soft rendezvous of the satellite and virtual satellite. The relative motion equations are then formulated and the maneuver time is selected as cost function for the optimal control problem, which is transformed to a nonlinear programming problem by using the Gauss pseudo-spectral method. This approach avoids the difficulties in solving boundary value problem. Finally, the optimal trajectory is solved by using MATLAB optimization toolbox. The results show that the Gauss pseudo- spectral method is very effective for solving the multiple constrained nonlinear strongly coupled equations, and it isn't very sensitive to initial data and has certain robustness. [ABSTRACT FROM AUTHOR]