Trajectory Optimization Model Research Articles

A time-fuel hybrid optimal guidance for micro/nano satellite’s glideslope approach

Aimed at the trajectory planning problem of micro/nano satellites’ approaching missions under multiple constraints, this paper proposes a V-bar glideslope maneuver optimization method considering both time and fuel consumption. A dual-objective trajectory optimization model is established based on the CW motion equation, considering the constraints of trajectory and impulse. The optimal solution set of the glideslope point position and maneuvering time is obtained by employing the NSGA2 algorithm. In order to reduce computational complexity, a method for simplifying trajectory optimization is proposed. By solving a constrained dual-impulse optimization problem, the feasible range of distance and transfer time between adjacent glideslope points are obtained, which transforms the constraint equations of the glideslope maneuver optimization into the search space of optimization variables. The problem is simplified to an unconstrained optimization problem. Finally, a simulation is conducted with the approaching mission of a typical micro/nano satellite. The results demonstrate that the proposed method can provide an optimal solution set considering both fuel and time consumption, offering a flexible maneuver planning strategy for on-orbit application.

Pedestrian shuttle service optimization for autonomous intersection management

Autonomous intersection management (AIM) has been widely investigated over the past two decades as a solution for signal-free intersections in a fully connected and autonomous environment. However, existing AIM approaches lack consideration for crossing pedestrians, especially in a way that enables pedestrians to cross streets safely while optimizing upcoming vehicles at the intersection to maintain traffic continuity. To address this issue, this paper proposes an Automated Pedestrian Shuttle (APS) service system to transport pedestrians across the street. Using a coupled space–time network modeling method, an optimization model, which incorporates pedestrian ride strategies and aims to minimize the total crossing time, is first established for the APS operation scheme. A Shuttle-by-Shuttle-Planning (SBSP) algorithm is developed for model solving to determine the APS operation route and the departure time from each station along the route. Then, a timing schedule optimization model is proposed to adjust the departure time of APS at each station and the time of main-lane vehicles entering an intersection to avoid vehicle conflicts. To ensure that the main-lane vehicles can enter the intersection on time, a trajectory optimization model is proposed to provide a specific driving strategy for each main-lane vehicle. A rolling horizon strategy is adopted to bridge the different optimization time windows. Finally, the effectiveness of the proposed APS service system is demonstrated through numerical simulation experiments. The results show that (1) the APS service can effectively help pedestrians cross the street with minor delays to main-lane vehicles; (2) The dynamic-route scheme is adaptable to the needs of randomly arriving pedestrians due to its demand-responsive nature; (3) The service efficiency of the system is related to the number of APSs, and the more APSs, the higher the service efficiency under the premise of unsaturation; (4) The designed SBSP algorithm significantly reduces the model-solving time compared to the commercial solver, making the APS service system potentially applicable for field implementation.

Improved Immune Moth-Flame Optimization Based on Gene Correction for Automatic Reverse Parking.

During the process of reverse parking, it is difficult to achieve the ideal reference trajectory while avoiding collision. In this study, with the aim of establishing reference trajectory optimization for automatic reverse parking that smooths and shortens the trajectory length and ensures the berthing inclination angle is small enough, an improved immune moth-flame optimization method based on gene correction is proposed. Specifically, based on the standard automatic parking plane system, a reasonable high-quality reference trajectory optimization model for automatic parking is constructed by combining the cubic spline-fitting method and a boundary-crossing solution based on gene correction integrated into moth-flame optimization. To enhance the model's global optimization performance, nonlinear decline strategies, including crossover and variation probability and weight coefficient, and a high-quality solution-set maintenance mechanism based on fusion distance are also designed. Taking garage No.160 of the Dalian Shell Museum located in Dalian, Xinghai Square, as the experimental site, experiments on automatic parking reference trajectory optimization and tracking control were carried out. The results show that the proposed optimization algorithm provides higher accuracy for reference trajectory optimization and can achieve better tracking control of the reference trajectory.

Optimization of isolated intersection signal timing and trajectory planning under mixed traffic environment: The flexible catalysis of connected and automated vehicles

With the development of connected and automated vehicles (CAVs) enables real-time interaction between intersection signals and vehicle trajectories. The full use of this technological breakthrough will help traffic managers improve the performance of intersections. Most previous research focuses on the 100% CAV environment and the single lateral or longitudinal optimization of CAVs. Based on the flexible characteristics of CAVs, this paper proposes that CAV is regarded as the catalyst of vehicle platoon in mixed traffic environment and considers the uncertainty of CAVs and CHVs’ interaction in the real-world, which can promote the generation of controllable platoon through the “catalytic” mode of cooperative, accelerated, or direct lane-changing, and cooperative or direct overtaking. Simultaneously, a two-stage optimization model of mixed traffic trajectory and signal timing is proposed. Stage I: Based on the predicted vehicle platoon information, a dynamic NEMA signal timing scheme without duplicate structures is generated to minimize vehicle delays. Stage II: Based on the timing scheme, the generation of controllable and stable platoon and vehicle trajectory optimization model are established to minimize vehicle emissions. Dynamic programming with NEMA signal groups as sub-states is designed to solve the proposed model. The performance of the proposed model under different scenarios is investigated through numerical experiments and compared with benchmark models. Results show that the proposed model will outperform the benchmark models regarding average vehicle delay and emission under more realistic traffic demands. The average vehicle delay can be reduced by 54.32% and 7.33%, and the average vehicle emissions can be reduced by 19.1% and 0.8%, respectively. Meanwhile, the sensitivity analysis of CAV market penetration shows that the proposed model can perform satisfactorily at 20% CAV market penetration. Notedly, with increased market penetration, the proposed model will obtain better performance.

3D Path Planning of the Solar Powered UAV in the Urban-Mountainous Environment with Multi-Objective and Multi-Constraint Based on the Enhanced Sparrow Search Algorithm Incorporating the Levy Flight Strategy

In response to practical application challenges in utilizing solar-powered unmanned aerial vehicle (UAV) for remote sensing, this study presents a three-dimensional path planning method tailored for urban-mountainous environment. Taking into account constraints related to the solar-powered UAV, terrain, and mission objectives, a multi-objective trajectory optimization model is transferred into a single-objective optimization problem with weight factors and multi-constraint and is developed with a focus on three key indicators: minimizing trajectory length, maximizing energy flow efficiency, and minimizing regional risk levels. Additionally, an enhanced sparrow search algorithm incorporating the Levy flight strategy (SSA-Levy) is introduced to address trajectory planning challenges in such complex environments. Through simulation, the proposed algorithm is compared with particle swarm optimization (PSO) and the regular sparrow search algorithm (SSA) across 17 standard test functions and a simplified simulation of urban-mountainous environments. The results of the simulation demonstrate the superior effectiveness of the designed improved SSA based on the Levy flight strategy for solving the established single-objective trajectory optimization model.

A reduced-order lie group-based race car model for systematic trajectory optimization on 3D tracks

AbstractThis paper derives the dynamic equations of a reduced-order race-car model using Lie-group methods. While these methods are familiar to computational dynamicists and roboticists, their adoption in the vehicle dynamics community is limited. We address this gap by demonstrating how this framework integrates smoothly with the Articulated-Body Algorithm (ABA) and provides a fresh and systematic formulation of vehicle dynamics. For the first time, we model the car body as the end effector of a serial robot with a floating base connected to the track via virtual revolute and prismatic joints. Our formulation also accounts for the effects of 3D track geometry, providing a natural embedding of the car into the 3D track. We rigorously reconcile the ABA steps with key aspects of vehicle dynamics, including road-tire interactions, aerodynamic forces, and load transfers. The resulting model, simple yet accurate, is a powerful tool to efficiently solve Minimum-Lap-Time Planning problems. To demonstrate the effectiveness of our approach, we show numerical results obtained on the Nürburgring circuit. Our optimization problem is formulated via a direct collocation method and solved using the CasADi optimization suite. To validate the results, we test our reduced-order model against a full-fledged multi-body model recently developed by the same authors. The comparison confirms the validity of our reduced-order model, proving both the accuracy of the solution and the computational efficiency achieved.

Robust convex optimization for reentry glide trajectory using polynomial chaos

Aiming at the reentry glide trajectory design of hypersonic vehicles with uncertain parameters, a robust trajectory optimization method is proposed to enhance the anti-interference ability and process reliability. Firstly, a robust trajectory optimization model for re-entry gliding under uncertain conditions is constructed, which is transformed into a deterministic trajectory optimization problem with dimension expansion by using an uncertainty propagation algorithm based on the Gaussian quadrature and non-intrusive polynomial chaos. Then, the convex optimization technology is used to convexity and discretize the problem, and a deterministic trajectory optimization strategy based on the sequential convex optimization algorithm is designed to achieve a fast solution for the high-dimensional deterministic problem. Finally, the hypersonic glide reentry of the American X-33 is chosen as an example for the numerical simulation. The results show that comparing with the traditional deterministic trajectory optimization algorithm, the present method can effectively reduce the impact of random interference on the reentry glide trajectory and improve the reliability and robustness of the trajectory.

Design and motion planning of a 7-DOF assembly robot with heavy load in spacecraft module

Currently, there is great demand for automated assembly of equipment inside spacecraft module, which would require an assembly robot with small size, large workspace, high load capacity, and high flexibility. To meet this demand, a redundant seven-degree-of-freedom (7-DOF) assembly robot with three prismatic joints and four rotating joints is proposed in this study. First, a kinematic model of the assembly robot is established, and the positional forward kinematics are derived. Then, the positional inverse kinematic equations are derived by using the fixed joint method and the coordinate inverse transformation method for the characteristics of the robot with redundant degrees of freedom. The inverse solution optimization model of the assembly robot is designed based on genetic algorithm, and B-spline interpolation algorithm is used for joint trajectory planning. Next, NSGA-2 algorithm is used to construct the trajectory optimization model, and the time-pulsation multi-objective Pareto optimal frontier is obtained. Finally, the joint simulation model of mechatronics and the prototype experiment are established to verify the effectiveness of the optimization results. Analysis shows that the proposed assembly robot has better load-bearing capacity and dynamic characteristics than similar existing assembly robots. Furthermore, the segmented trajectory optimization strategy for the assembly robot using inverse solution optimization, interpolation algorithm, and NSGA-2 based multi-objective optimization gets each motion joint to realize the trajectory tracking function quickly and stably, and the trajectory tracking error is small enough to meet the requirements of end positioning accuracy.

A train timetable rescheduling approach based on multi-train tracking optimization of high-speed railways

PurposeThis paper aims to propose a train timetable rescheduling (TTR) approach from the perspective of multi-train tracking optimization based on the mutual spatiotemporal information in the high-speed railway signaling system.Design/methodology/approachFirstly, a single-train trajectory optimization (STTO) model is constructed based on train dynamics and operating conditions. The train kinematics parameters, including acceleration, speed and time at each position, are calculated to predict the arrival times in the train timetable. A STTO algorithm is developed to optimize a single-train time-efficient driving strategy. Then, a TTR approach based on multi-train tracking optimization (TTR-MTTO) is proposed with mutual information. The constraints of temporary speed restriction (TSR) and end of authority are decoupled to calculate the tracking trajectory of the backward tracking train. The multi-train trajectories at each position are optimized to generate a time-efficient train timetable.FindingsThe numerical experiment is performed on the Beijing-Tianjin high-speed railway line and CR400AF. The STTO algorithm predicts the train’s planned arrival time to calculate the total train delay (TTD). As for the TSR scenario, the proposed TTR-MTTO can reduce TTD by 60.60% compared with the traditional TTR approach with dispatchers’ experience. Moreover, TTR-MTTO can optimize a time-efficient train timetable to help dispatchers reschedule trains more reasonably.Originality/valueWith the cooperative relationship and mutual information between train rescheduling and control, the proposed TTR-MTTO approach can automatically generate a time-efficient train timetable to reduce the total train delay and the work intensity of dispatchers.

Trajectory optimization of wall-building robots using response surface and non-dominated sorting genetic algorithm III

Traditional wall-building robots regard brick masonry as a simple assembly process, ignoring the viscoelastic effect of cement mortar, which leads to poor masonry quality. Therefore, this paper proposes a many-objective trajectory optimization method based on response surface methodology (RSM) and non-dominated sorting genetic algorithm III (NSGA-III). Firstly, a substitution model between the objective functions and the design variables is established using RSM, which solves the problem of difficult construction of cement mortar viscoelastic model. Then, a trajectory optimization model is constructed based on seven times non-uniform B-spline, and it is solved using NSGA-III. Finally, the optimal solution is obtained from the Pareto solution set, and it is compared and analyzed with the standard gate-type masonry solution. The results show that after the trajectory optimization, the masonry error is reduced from 2.62 mm to 0.11 mm, which significantly improves the masonry quality, and other performance indicators are also improved. These results contribute to the construction of walls and promote the development of the smart construction industry.

A speed-maximization trajectory optimization model on a reservation-based intersection control system

Cooperative CAV crossing a reservation-based intersection is an integrated control problem that consists of the trajectory modeling and scheduling optimization. In order to achieve the best system performance in the intersection, a final speed is traditionally modeled as large as possible when reaching the intersection in the trajectory modeling level, coupled with a delay-minimization problem. However, the delay optimization problem may not find the best solution in terms of the system efficiency. This paper aims to theoretically justify the best objective function and propose an optimal integrated control model. A speed-maximization trajectory optimization model is proposed based on the queue theory. The optimization model is formulated as a discrete-time mixed integer programming model based on the trajectory analysis. Through extensive numerical simulations with platooning and turning movements, the optimization model achieves better system performance than state-of-the-art methods. The results validate the advantages of maximizing the average speed using the discrete-time trajectory modeling method.

Search task oriented path planning method of airborne radar network

Reasonable planning the trajectory of the airborne radar network can decrease its repeated surveillance region, and improve the search efficiency. To complete a wider range of reconnaissance searches within a certain time, a search task oriented path optimization method of airborne radar network is proposed. Firstly, the single-platform search range by combing the radar equation is characterized, and the multi-radar area coverage function based on the rasterization idea is calculated. A trajectory optimization model with the goal of maximizing the search coverage function is constructed, by combining with the motion constraints of each node and adopting an intelligent method. Simulation results show that the present method can obtain higher search coverage within specified time.

Multi-objective Optimal Motion Planning of Heavy-duty Assembly Robot for Large Spacecraft Entering Cabin

The space inside the space capsule such as the space station sky and the core module is narrow, the size of the depth is large, and the bearing points are scattered and weak, there are some difficulties in loading, large size, different shape, complicated interface, scattered position, difficult position and pose adjustment, high assembly risk, etc.. To solve these problems, a six-DOF heavy-duty assembly robot is proposed in this paper. The robot adopts the combination of linear drive and rotating joint to increase the working space and bearing capacity of the robot. The kinematics and dynamics analysis model of the robot is established, and the path planning is carried out by means of quintic non-uniform B-spline interpolation method, considering fully the space constraints of the assembled equipment, a multi-objective trajectory optimization model based on NSGA2 algorithm is established to obtain the Pareto optimal solution set with time, impact and energy consumption as optimization objectives, prove that the equipment can be efficient and smooth. Reliable installation, with less impact and less power consumption under multi-objective optimization analysis.

A Two-Stage Optimization Method for Schedule and Trajectory of CAVs at an Isolated Autonomous Intersection

Autonomous intersection management has become a state-of-the-art control strategy customized for connected and autonomous vehicles. Combining the advantages of tile-based and conflict point-based approaches, this paper proposes a two-stage optimization method based on a developed intersection modeling approach. The first stage is a timing schedule optimization model, assigning vehicle arrival times at an intersection. Based on the output of the first stage, the second stage is a trajectory optimization model, which gives the eco-driving strategies. Moreover, a rolling optimization with a variable cycle length is adopted to run the method continuously. Simulation results show that the proposed method outperforms the genetic algorithm-based method in terms of computation time, and can reduce vehicle delay and fuel consumption by 89.48% and 46.84%, respectively, under different traffic demands compared to the first-come-first-serve method. Furthermore, the performance of the proposed method under asymmetric traffic demand is discussed. Sensitivity analyses suggest that (1) a long cycle length benefits the proposed method within certain limits and (2) a proper deceleration within the intersection can balance traffic delay with fuel consumption. In addition, an additional model with a heuristic rule is compared with the original timing schedule optimization model. It is found that reducing binaries in the first stage can make a tradeoff between the quality of the solution and efficiency, which can be used in conjunction with long cycles.

Refined MagSail thrust model for preliminary mission design and trajectory optimization

A magnetic sail is an advanced propellantless propulsion system concept for deep space missions, proposed by Dana Andrews and Robert Zubrin about 30 years ago. The thrust is generated by the electromagnetic interaction between the solar wind charged particles and an artificial magnetic field obtained through a large current-carrying coil made of superconducting material. This paper discusses an up-to-date single-loop magnetic sail thrust model based on the numerical and experimental results obtained in the last decade. In particular, a particle model is initially used to evaluate the performance of a reference configuration in terms of thrust components in a body reference frame. Then, some scaling relationships are used to estimate the magnetic sail performance as a function of the design parameters. The proposed thrust model is used to analyze the minimum-time transfer problem between two circular and coplanar heliocentric orbits. Minimum flight times necessary to complete ephemeris-free Earth-Venus and Earth-Mars transfers are calculated as a function of the magnetic sail characteristic size in a parametric way.

Application of adaptive grid-based multi-objective particle swarm optimization algorithm for directional drilling trajectory design

The parameters optimization is the key issue for directional drilling trajectory design in oil and gas fields development, and there are three main challenges in multi-objective and multi-constraint optimization: (1) how to establish a multi-objective optimization model based on geological constraints; (2) how to design an appropriate optimization algorithm and solve the optimization model effectively; (3) how to select the desired result from the obtained Pareto solution and meet the engineering requirements. To build a safe and cost-efficient directional drilling trajectory, a new multi-objective optimization model is established in this paper. The effective objective functions to evaluate the drilling trajectory are summarized as the minimum trajectory length, torque, and strain energy. Moreover, the new model takes the wellbore stability based on Mohr–Coulomb criterion as constraint to prevent the borehole from collapsing. A novel adaptive grid-based multi-objective particle swarm optimization(AGMOPSO) is presented to achieve a set of Pareto optimal solutions of the established optimization model. In this algorithm, a new particle flight mode based on arcsine function of inertia weight and Gaussian mutation strategy are introduced to further improve the global searching ability and obtain more non-inferior solutions. To ensure the uniformity of non-inferior solutions, the adaptive grid based on density control factor is designed to map the space of objective functions to the grid space and adaptively adjust the density of non-inferior solutions in the external archive. Besides, a linear weighted summation function is developed to realize leader selection and archive maintenance of non-inferior solutions. The optimization results on the Pareto front indicate that AGMOPSO has better convergence and uniformity than the unmodified algorithm and reported results. To be concluded, AGMOPSO achieves a better optimization performance and obtain a better trajectory for drilling trajectory optimization model with geological constraints, which has good practical and theoretical significance for directional drilling trajectory optimization.

Cooperative capture trajectory optimization of multi-space robots using an improved multi-objective fruit fly algorithm

Abstract Considering that some tasks will require the consistency of the position and attitude of the end-effector, multi-space-robot cooperative capture also needs to consider the synchronization of the two capture arms. Taking the dual-space robots as example, the trajectory planning problem before cooperative capture is focused. First, a drive-transform method based on trapezoidal velocity interpolation is proposed, which combines the advantages of these two methods to obtain the SE(3) motion trajectory, in which the attitude and position are planned synchronously. Then, the trajectory optimization model of cooperative capture is established, which takes the optimal time and the minimum attitude disturbance of the base as the optimization goals, and simultaneously satisfies that the two capture arms reach the capture point synchronously. In order to solve this multi-objective optimization problem, a dual-population multi-objective fruit fly algorithm based on non-dominated sorting was proposed. Finally, the simulation example of dual-space robots shows that the proposed algorithm is effective, and the analysis of the optimal solution set demonstrates that the optimized cooperative capture trajectory is smooth and synchronous.

Space Discretization-Based Optimal Trajectory Planning for Automated Vehicles in Narrow Corridor Scenes

The narrow corridor is a common working scene for automated vehicles, where it is pretty challenging to plan a safe, feasible, and smooth trajectory due to the narrow passable area constraints. This paper presents a space discretization-based optimal trajectory planning method for automated vehicles in a narrow corridor scene with the consideration of travel time minimization and boundary collision avoidance. In this method, we first design a mathematically-described driving corridor model. Then, we build a space discretization-based trajectory optimization model in which the objective function is travel efficiency, and the vehicle-kinematics constraints, collision avoidance constraints, and several other constraints are proposed to ensure the feasibility and comfortability of the planned trajectory. Finally, the proposed method is verified with both simulations and field tests. The experimental results demonstrate the trajectory planned by the proposed method is smoother and more computationally efficient compared with the baseline methods while significantly reducing the tracking error indicating the proposed method has huge application potential in trajectory planning in the narrow corridor scenario for automated vehicles.

Trajectory Planning and Tracking for a Re-Entry Capsule with a Deployable Aero-Brake

In the last decade, the increasing use of NanoSats and CubeSats has made the re-entry capsule an emerging research field needing updates in configuration and technology. In particular, the door to advancements in terms of efficiency and re-usability has been opened by the introduction of inflatable and/or deployable aerodynamic brakes and the use of on-board electronics for active control. Such technologies allow smaller sizes at launch, controlled re-entries, and safe recovery. This paper deals with the design of a guidance and control algorithm for the re-entry of a capsule with a deployable aero-brake. A trajectory optimization model is used both in the mission planning phase to design the reference re-entry path and during the mission to update the trajectory in case of major deviations from the prescribed orbit, thanks to simplifications aimed at reducing the computational burden. Successively, a trajectory tracking controller, based on Nonlinear Model Predictive Control (NMPC), is able to modulate the opening of the aero-brake in order to follow the planned trajectory towards the target. A robustness analysis was carried out, via numerical simulations, to verify the reliability of the proposed controller in the presence of model uncertainties, orbital perturbations, and measurement noise.

Desensitized Optimal Control of Electric Aircraft Subject to Electrical–Thermal Constraints

This article proposes a desensitized optimal control (DOC) methodology to enhance the trajectory robustness of electric aircraft. First, a comprehensive multiphysics model of electric aircraft is built based on the first principle. An emphasis is put on the battery pack characteristics led by the cell unevenness. Thereafter, the optimal control technique is applied to study the influence of thermal effects and battery unevenness on flight performance. Furthermore, to alleviate the impact of cell unevenness, the crude control scheme is augmented by DOC. The proposed method generates a more robust reference trajectory for aircraft against cell unevenness. Processor-in-the-loop tests prove that the trajectory is trackable via a tracking controller. Compared to the standard trajectory optimization and nonlinear model predictive control, the proposed method significantly reduces the sensitivity of battery pack temperature regarding cell unevenness with acceptable computational effort.