基于微分几何的蛇板系统动力学建模与运动规划

A Gauss pseudospectral method is proposed in this study to solve the optimal trajectory-planning problem for satellite rapid large-angle maneuvers. In order to meet the requirement of rapid maneuver capability of agile small satellites, Single Gimbal Control Moment Gyros (SGCMGs) are adopted as the actuators for the attitude control systems (ACS). Because the singularity problem always exists for SGCMGs during the large-angle maneuvering of the satellites, a trajectory optimization method for the gimbal rates is developed based on the Gauss pseudospectral method. This method satisfies the control requirement of satellite rapid maneuvers and evades the singularity problem of SGCMGs. The method treats the large-angle maneuver problem as an optimization problem, which meets the boundary condition and a series of the physical constraints including the gimbal angle constraint, the gimbal rates constraint, the singularity index constraint, and some other performance criteria. This optimization problem is discretized as a nonlinear programming problem by the Gauss pseudospectral method. The optimal nonsingularity gimbal angle trajectory is obtained by the sequence of quadratic programming (SQP). This approach avoids the difficulties in solving the boundary value problem. The simulations reveal that the Gauss pseudospectral method effectively plans an optimal trajectory and satisfies all the constraints within a short time.

This paper considers the optimal control problem of continuously targeting for extinguishing a moving fire source with a quadrotor. It aims to enhance computational time-efficiency, and real-time targeting performance compared with generic optimizers onboard, even suffering from severe nonlinearities. To this end, an efficient strategy is proposed for this optimal control problem. First, the Gauss Pseudospectral Method is utilized to transform the optimal control problem into a nonlinear constrained quadratic programming problem. Then, via the Sequential Quadratic Programming (SQP) algorithm, the control input can be generated analytically. To further improve the computational efficiency, the techniques, separation of variables and prior gradient calculation, are applied. Through comparative simulations, it is verified that the proposed method has excellent targeting performance and high computing efficiency. Further analysis demonstrate that the proposed efficient strategy can complete the control plan in approximately 0.5 ms, which is 20 times faster than the generic optimizers.

Multidisciplinary design optimization (MDO) was performed on a helicopter rotor blade. The blade was modeled as a rigid flapping blade for dynamics; Blade Element Theory (BET) was the analysis approach to model the aerodynamic loading, and a simple linearly elastic hollowed rectangular section was the main structural component. MATLAB was used to solve the flapping differential equations and its Sequential Quadratic Programming (SQP) and Genetic Algorithm (GA) were used for the optimization. A Particle Swarm Optimization (PSO) routine was also tested. The optimization process consisted of three cases. The first case was a simple cantilever beam under centrifugal and an assumed bending loads. The optimization was performed using the SQP, GA, and PSO algorithms. The SQP resulted in the superior design with 75.45 compared to the GA's 87.1 and the PSO's 79.2, but a local minimum was present. The second case was an expansion of the first case by turning it into multidisciplinary problem. Aerodynamics was included in the design variables and objective function. Only the SQP algorithm was used and there was a reduction in hub vertical shear by 33.6%. The blade mass increased by 36.84%. The last case was an improvement to the second by creating a multiobjective problem by including the hub radial shear and the results were improved significantly by reducing the hub vertical shear by 34.06% and radial shear by 17.87% with a reduction of blade mass by 23.86%.

A safe and rapid formation generation is of great importance for the cooperation performance of the multiple unmanned helicopters. The trajectory optimization and control is the key problem in the process of the formation generation. To achieve this goal, a novel safe formation generation strategy is proposed through trajectory optimization and tracking control. First, the rapidly-exploring random tree (RRT) algorithm is applied to obtain the initial guess to satisfy the requirement of rapid solution. Then, the Gauss pseudospectral method is used to transform the optimal control problem to the nonlinear programming (NLP) problem and the sequence quadratic programming (SQP) method is utilized to gain the optimal trajectory combined with the initial guess. Second, a finite-time sliding mode controller is proposed to ensure the finite time trajectory tracking in the presence of model parameter uncertainties and unknown external disturbances. Finally, the numerical simulation is provided to show the effectiveness of the proposed formation generation strategy for unmanned helicopters formation.

In the last decade, research studies on parking planning mainly focused on path planning rather than trajectory planning. The results of trajectory planning are more instructive for a practical parking process. Therefore, this paper proposes a trajectory planning method in which the optimal autonomous valet parking (AVP) trajectory is obtained by solving an optimal control problem. Additionally, a vehicle kinematics model is established with the consideration of dynamic obstacle avoidance and terminal constraints. Then the parking trajectory planning problem is modeled as an optimal control problem, while the parking time and driving distance are set as the cost function. The homotopic method is used for the expansion of obstacle boundaries, and the Gauss pseudospectral method (GPM) is utilized to discretize this optimal control problem into a nonlinear programming (NLP) problem. In order to solve this NLP problem, sequential quadratic programming is applied. Considering that the GPM is insensitive to the initial guess, an online calculation method of vertical parking trajectory is proposed. In this approach, the offline vertical parking trajectory, which is calculated and stored in advance, is taken as the initial guess of the online calculation. The selection of an appropriate initial guess is based on the actual starting position of parking. A small parking lot is selected as the verification scenario of the AVP. In the validation of the algorithm, the parking trajectory planning is divided into two phases, which are simulated and analyzed. Simulation results show that the proposed algorithm is efficient in solving a parking trajectory planning problem. The online calculation time of the vertical parking trajectory is less than 2 s, which meets the real-time requirement.

The objective of this paper is to investigate a reliable method to generate optimal ascent trajectory for hypersonic air-breathing vehicles. When solving optimal trajectories in endo-atmospheric flight, most of traditional indirect methods suffer from difficulties in finding an appropriate initial guess and getting a convergent solution for the two point boundary value problem (TPBVP). With improvements on on-board computer performance, direct methods such as pseudospectral method show promising potential for real-time optimal guidance. It removes the need for computing analytical gradients of aerodynamic coefficients, and remains high accurate solution similar to indirect methods. In this work, optimal ascent trajectory generation problem was formulated as a fuel-optimal control problem. Gauss pseudospectral method (GPM) was presented to generate the optimal ascent trajectories. Optimal solutions from GPM were compared with an indirect method based on finite difference method (FDM). Numerical simulations were studied with various initial conditions to investigate the optimal trajectory characteristics for hypersonic air-breathing vehicles. The results verified the validity and accuracy of GPM for ascent trajectory optimization.

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.

Optimal spacecraft formation establishment and reconfiguration propelled by the geomagnetic Lorentz force

Optimal aeroassisted symmetric transfer between coplanar elliptical orbits

Trajectory optimization is an important problem in the field of aircraft design. Effective trajectory optimization is critical to the tactical flight of an aircraft. Based on previous research, this paper further studies trajectory optimization of an unpowered gliding vehicle. The goal is to maximize its range and to analyze the influence of different initial conditions on trajectory optimization. In this paper, the trajectory optimization model involving all kinds of state constraints and control constraints was established and aerodynamic coefficient was calculated by CFD software. Finally Gauss Pseudo-spectral Method program was run to calculate the flight path of the gliding vehicle and to seek trajectory with maximum range. The simulation data shows that results of Gauss Pseudo-spectral Method are realistic and prove its practical operability. The use of Gauss Pseudo-spectral Method for trajectory optimization has a good effect.

Path planning and obstacle avoidance of Unmanned Surface Vehicle (USV) is one of the hottest research topics in modem national defense and ocean engineering. Considering the issue of obstacle-free path planning of USV, this paper focuses on a 3-DoF USV and develops an algorithm design. We adopt Gauss pseudo-spectral method to discretize control model and make use of a hybrid algorithm to optimize which combines the advantage of genetic algorithm and sequential quadratic programming algorithm. Simulation results show that this method can quickly explore a high-precision route in an unknown environment which meets the mobility requirement of USV without setting the initial value artificially.

Comparison of SQP and AL algorithms for deterministic constrained production optimization of hydrocarbon reservoirs

The sequential quadratic programming and genetic algorithms are finely tuned on the optimal design of a brushless DC wheel motor. Combining both methods, a hybrid approach is tested. Multiobjective optimizations are performed using Nondominated Sorting Genetic Algorithm, Strength Pareto Evolutionary Algorithm, and a variable weighted sum of objectives with the sequential quadratic programming. The Pareto fronts are compared in term of accuracy, uniformity, and coverage criteria using some quality indicators.

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration

Recently, with the wide adoption of electric vehicles, transportation network has shown different characteristics and been further developed. In this paper, we present a new time-flow impedance function, which may be more realistic than the existing time-flow impedance functions. Based on this new impedance function, we present an optimization model for a mixed-mode traffic network in which battery electric vehicles (BEVs) and gasoline vehicles (GVs) are chosen. We suggest two approaches to handle the model: One is to use the interior point (IP) algorithm and the other is to employ the sequential quadratic programming (SQP) algorithm. Three numerical examples are presented to illustrate the efficiency of these approaches. In particular, our numerical results show that more travelers prefer to choosing BEVs when the distance limit of BEVs is long enough and the unit operating cost of GVs is higher than that of BEVs, and the SQP algorithm is faster than the IP algorithm.