Search Results (13)

This study proposes an NSL-GWO-hpRPM framework for constrained glide trajectory optimization of guided projectiles. The method combines an improved Grey Wolf Optimizer with the hp-adaptive Radau pseudospectral method to reduce the dependence of hpRPM on initial guesses and improve global search performance. In the improved GWO, Sobol low-discrepancy sequence initialization is used to enhance population diversity, a nonlinear convergence strategy is introduced to balance exploration and exploitation, and Levy flight is adopted to improve the ability to escape local optima. The optimized solution obtained by NSL-GWO is then used as the initial guess for hpRPM to achieve high-precision local refinement. Simulation results show that the proposed NSL-GWO-hpRPM achieves a feasible range of 71,211.514 m, improving the range by 4.53% over hpRPM and 1.48% over GWO-hpRPM. Statistical results from 35 independent runs further demonstrate that the proposed method obtains the best mean range, Friedman mean rank, and significant Wilcoxon test results with $p<0.001$. The optimized trajectory reaches a maximum range of approximately 71.2 km with an optimal launch angle of ${62.4}^{\circ }$ while satisfying all flight constraints, indicating that the proposed framework is effective for complex constrained glide trajectory optimization. Full article

Trajectory planning for morphing gliding reentry vehicles is a nonconvex optimization problem driven by nonlinearity, parameter uncertainty, and multiple constraints. No-fly zones (NFZs) are a critical constraint because their rapid movement and expansion hinder the real-time generation of optimal flight trajectories and wing morphing strategies. Therefore, this study proposes an innovative online trajectory optimization method based on sequential convex optimization integrated with a deep neural network (DNN). The proposed method first uses the Radau pseudospectral method to discretize continuous dynamics and convert the non-convex trajectory planning problem into a relaxed convex subproblem. The subproblem is reformulated as an augmented Lagrangian function through linearization and is iteratively solved using the interior-point method. Finally, the DNN learns the mapping between flight states and optimal control variables (angle of attack rate, bank angle rate, and wing sweep angle rate) to rapidly generate control variables. Different from the time-consuming offline optimization method, the proposed model only requires 0.4 ms to predict three groups of control variables, with the predicted control errors remaining below 2.25%. This method efficiently provides high-precision and stable reentry trajectories and morphing strategies for gliding reentry vehicles. Thus, the proposed method achieves synchronous flight path and wing deformation optimization and demonstrates strong robustness under time-varying mission conditions. Full article

Prediction of the reachable domain for high-threat unmanned aerial vehicles (UAVs) is critical for enabling cross-domain flight vehicles to perform proactive avoidance maneuvers. To address this challenge, this paper proposes a novel generic framework that integrates a Radau pseudospectral method (RPM) with a BP neural network, supported by information acquired from satellites. The framework begins by estimating a preliminary state vector of the non-cooperative target, including its coarse position and velocity, via a Newton iterative algorithm. To refine this initial estimate and enable continuous tracking, an Extended Kalman Filter (EKF) is fused with a flight vehicle dynamics model. Subsequently, the RPM is employed to solve the trajectory planning problem, generating a comprehensive database for offline training. This database is then used to train a multilayer feedforward neural network within an offline training and online application framework, which drastically reduces computational complexity and time. Finally, numerical simulations demonstrate the method’s high prediction accuracy and strong robustness against tracking uncertainties. Crucially, the neural network predicts the reachable domain in just 0.01 s, making it highly viable for real-time online applications. Full article

Addressing prevalent challenges in current cooperative task assignment methods for cross-domain unmanned swarm, such as the disconnection between decision-making and execution processes, and the inadequate incorporation of platform kinematic constraints, this study introduces an integrated decision-control cooperative task assignment approach based on a bi-level optimization framework. The proposed framework formulates a bi-level programming model that tightly couples upper-level task assignment with lower-level optimal control. The upper-level model aims to minimize the maximum task completion time by optimizing the assignment and visitation sequences of diverse target types across heterogeneous unmanned platforms. The lower-level model, given the task sequences from the upper level, addresses a minimum-time optimal control problem based on a comprehensive nonlinear kinematic model. This approach enables precise computation of task execution times, which are subsequently fed back to the decision-making layer, thereby establishing a closed-loop optimization mechanism. To solve this complex model efficiently, the lower-level employs differential flatness transformation to eliminate trigonometric functions in the kinematic equations and discretizes the continuous-time optimal control problem into a nonlinear programming problem via the Radau pseudospectral method. For the upper-level combinatorial optimization, an improved genetic algorithm is developed, integrating hybrid encoding, dual-archive elitism preservation, adaptive crossover and mutation strategies, and periodic local search. Simulation results demonstrate that, compared with traditional Euclidean-distance-based assignment methods, the proposed approach generates kinematically feasible and smooth trajectories while thoroughly accounting for the kinematic constraints of heterogeneous platforms, thereby demonstrating its effectiveness and superiority in improving the comprehensive mission performance of cross-domain unmanned swarms. Full article

Path tracking control is a key technology in the research of intelligent vehicles. In the path tracking process of intelligent vehicles, there are multiple constraints and time-varying nonlinear system states. To address the problems of low tracking accuracy and poor robustness, a method based on Radau pseudospectral method(RPM) is designed. Firstly, a 4-DOF vehicle model was established. Secondly, the multiple phase Radau pseudospectral method(MPRPM) was used to discretize the control and state variables. Then, the path tracking problem was transformed into a nonlinear programming problem. Finally, the method was compared with other control methods such as Gaussian pseudospectral method(GPM) and linear quadratic regulator (LQR). The simulation results show that the tracking error of the proposed method is 0.075 m while those of the GPM and LQR are 0.029 m and 0.05 m, respectively. The simulation and virtual as well as the real vehicle test results indicate that the method can control the vehicle track the given path while meeting various constraint requirements achieving ideal results and good tracking accuracy. Full article

Aiming at the problem of multiple constraints and low solving efficiency in the process of vehicle path tracking, an improved hp-adaptive Radau pseudospectral method (I-hp-ARPM) which uses a double-layer optimization iteration strategy and the residual of differential algebraic constraints at sampling points with a Gaussian distribution as the error evaluation criterion is proposed. Firstly, a four-DOF vehicle motion model is established. Secondly, on the basis of establishing algebraic differential constraints and path constraints and satisfying the optimization objective function, the I-hp-ARPM is used to transform the optimal control problem (OCP) into a general nonlinear programming problem for solution. Finally, the effectiveness of the proposed method is verified compared with the traditional hp-adaptive pseudospectral method. The simulation results and the virtual test show that there are peak values at 3.5 s and 4.8 s, as well as 6 s, for both the steering wheel angle and the sideslip angle with the condition of $\mu$ = 0.8. And also, there are peak values at the times of 3.5 s and 5.5 s, as well as 7.5 s, with the condition of $\mu$ = 0.4. This indicates the vehicle can track the reference path well with the control of the proposed algorithm. Both the initial and final constraints, as well as the path constraint, meet the requirements. The proposed method can generate the optimal trajectory that meets various constraint requirements. This method provides a design basis for path tracking of autonomous vehicles and has significance in engineering. Full article

In cruise ship manufacturing, it is common practice for prefabricated modular cabin units (PMCU) to be assembled in the workshop and transported to a designated installation location on board the ship. This paper proposed a Radau pseudospectral method based on a probabilistic roadmap (PRM) for PMCU path planning in complex deck environments. Firstly, a kinematic model is constructed, and the continuous-time optimal control path planning problem is established. Among them, an area-based obstacle avoidance constraint is applied to the approach. Then, the continuous-time optimal control problem is discretized into a nonlinear programming (NLP) problem using the orthogonal collocation method. For the initial value-sensitive NLP problem solving, a strategy using PRM combined with a heuristic rule is used to obtain a high-quality initial guess. Finally, experiments under two operating scenarios of PMCU pushing demonstrate that the method is capable of generating a better path while ensuring that the whole process is collision-free. The results show that the algorithm proposed in this paper can effectively solve the PMCU pushing path planning problem in the complex deck environment, and the path considering kinematic characteristics can be used for cabin installation, which has strong operability and applicability. Full article

This research introduces an innovative strategy to impede and lessen lateral and rear-end vehicular collisions by consolidating braking systems with active emergency steering controls. This study puts forward a T-type active emergency steering method, designed to circumvent both lateral and rear-end collisions at vehicular intersections. To secure vehicular stability and condense the time required for steering during the T-type active emergency process, this research formulates a nonlinear dynamic model for the vehicle, in addition to a nonlinear tire model. This study also engages in a thorough analysis of the constraints linked to the initial and terminal states of the steering process. The issue at hand is articulated as an optimization control problem with boundary value restrictions, which is subsequently resolved using the Radau pseudospectral method. Simulation results corroborate that the prompt commencement of the anti-collision strategy can effectively deter potential collisions. This pioneering approach shows considerable promise in augmenting the active safety of intelligent vehicles and bears meaningful implications for high-precision automotive collision evasion systems. Full article

A high-precision online trajectory optimization method combining convex optimization and Radau pseudospectral method is presented for the large attitude flip vertical landing problem of a starship-like vehicle. During the landing process, the aerodynamic influence on the starship-like vehicle is significant and non-negligible. A planar landing dynamics model with pitching motion is developed considering that there is no extensive lateral motion modulation during the whole flight. Combining the constraints of its powered descent landing process, a model of the fuel optimal trajectory optimization problem in the landing point coordinate system is given. The nonconvex properties of the trajectory optimization problem model are analyzed and discussed, and the advantages of fast solution and convergence certainty of convex optimization, and high discretization precision of the pseudospectral method, are fully utilized to transform the strongly nonconvex optimization problem into a series of finite-dimensional convex subproblems, which are solved quickly by the interior point method solver. Hardware-in-the-loop simulation experiments verify the effectiveness of the online trajectory optimization method. This method has the potential to be an online guidance method for the powered descent landing problem of starship-like vehicles. Full article

The design and optimization of re-entry spacecraft or its subsystems is a multidisciplinary or multiobjective optimization problem by nature. Multidisciplinary design optimization (MDO) focuses on using numerical optimization in designing systems with several subsystems or disciplines that have interactions and independent actions. In the present paper, the system-level optimizer, trajectory, geometry and shape, aerodynamics, and aerothermodynamics differential equations, are converted to algebraic equations using the Radau pseudospectral method (RPM) since a spacecraft is a nonlinear, extensive, and sparse system. The solution to the problem with the help of MDO is reached by iterating all the disciplines together; one can simultaneously enhance the design, decrease the time and cost of the entire design cycle, and minimize the structural mass of a re-entry spacecraft. Considering various methods presented in earlier research works, a combined and innovative all-at-once (AAO), RPM-based MDO method, including the key subsystems in the design process of a re-entry capsule-shape spacecraft with a low lift-to-drag ratio (L/D), is presented. Considering the applicable state and control variables, various constraints, and parameters applied to several geometric shapes of a blunt capsule and using Apollo’s aerodynamic and aerothermodynamic coefficients, the optimized dimensions for a re-entry spacecraft are presented. The introduced optimization scheme led to a 17% mass reduction compared to the original mass of the Apollo vehicle. Fast computing and simplified models are used together in this method to analyze a wide range of vehicle shapes and entry types during conceptual design. Full article

Parafoil trajectory directly affects the power generation of a high-altitude wind power generation (HAWPG) device. Therefore, it is particularly important to optimize the parafoil trajectory and then to track it effectively. In this paper, the trajectory of the parafoil at high altitudes is optimized and tracked in a comprehensively parameterized manner. Both the complex dynamic characteristics of the parafoil and the dexterous demand of the high-altitude controller are considered. Firstly, the trajectory variables and control signals are parameterized as Lagrange polynomials in terms of the corresponding values at the selected nodes. Then, the Radau pseudospectral method (PSM) is employed to reformulate the original dynamic trajectory optimization problem into a static nonlinear programming (NLP) problem. By doing so, the parameterized optimal trajectory, which has the maximum net power generation, can be obtained. To attenuate the strong nonlinear, multivariable and coupling characteristics of the flexible parafoil, a bandwidth parameterized linear extended state observer (ESO) is used to estimate and reject these dynamics explicitly in a unified way. Finally, the simulation results demonstrate the effectiveness of the proposed parameterized trajectory optimization and control strategies. The main contribution of this study is that complicated nonlinear parafoil dynamics with a complex trajectory can be well regulated by a PID-type linear time-invariant controller, which is appealing for practitioners. Full article

For the battery pack’s limited remaining power, two energy-aware ecological driving problems are discussed. A real-time energy-aware ecological driving control strategy is proposed to optimize energy consumption and meet the ECO driving demand. First, the vehicle longitudinal driving dynamics model and energy consumption model are established. Then, the optimal control problem is constructed with the maximum driving distance and the shortest driving time as the objective functions, respectively. With the multinomial Radau pseudo-spectral method, the optimization results of residual power, vehicle speed, and acceleration are obtained. The results show that in the case of in-vehicle driving the remaining power of the battery pack can be sensed in real-time, and the driving of intelligent electric vehicles can be planned in real-time to realize the most ecological driving with the largest driving distance and shortest driving time. The energy consumptions of vehicles, traveling at the same distance, are compared. The consumption obtained through optimization, is 26% less than the consumption of the vehicle that has not been optimized. The results show that the optimization process has certain advantages. In the future, as one of intelligent vehicles’ autonomous driving control strategies, the results have guiding and practical significance. Full article

The powertrain model of the series-parallel plug-in hybrid electric vehicles (PHEVs) is more complicated, compared with series PHEVs and parallel PHEVs. Using the traditional dynamic programming (DP) algorithm or Pontryagin minimum principle (PMP) algorithm to solve the global-optimization-based energy management strategies of the series-parallel PHEVs is not ideal, as the solution time is too long or even impossible to solve. Chief engineers of hybrid system urgently require a handy tool to quickly solve global-optimization-based energy management strategies. Therefore, this paper proposed to use the Radau pseudospectral knotting method (RPKM) to solve the global-optimization-based energy management strategy of the series-parallel PHEVs to improve computational efficiency. Simulation results showed that compared with the DP algorithm, the global-optimization-based energy management strategy based on the RPKM improves the computational efficiency by 1806 times with a relative error of only 0.12%. On this basis, a bi-level nested component-sizing method combining the genetic algorithm and RPKM was developed. By applying the global-optimization-based energy management strategy based on RPKM to the actual development, the feasibility and superiority of RPKM applied to the global-optimization-based energy management strategy of the series-parallel PHEVs were further verified. Full article