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Spacecraft need to be able to reliably slew quickly and rather than simply commanding a final angle, a trajectory calculated and known throughout a maneuver is preferred. A fully solved trajectory allows for control based off comparing current attitude to a time varying desired attitude, allowing for much better use of control effort and command over slew orientation. This manuscript introduces slew trajectories using sinusoidal functions compared to optimal trajectories using Pontryagin’s method. Use of Pontryagin’s method yields approximately 1.5% lower control effort compared to sinusoidal trajectories. Analysis of the simulated system response demonstrates that correct understanding of the effect of cross-coupling is necessary to avoid unwarranted control costs. Additionally, a combination of feedforward with proportional derivative control generates a system response with 3% reduction in control cost compared to a Feedforward with proportional integral derivative control architecture. Use of a calculated trajectory is shown to reduce control cost by five orders of magnitude and allows for raising of gains by an order of magnitude. When control gains are raised, an eight orders of magnitude lower error is achieved in the slew direction, and rather than an increase in control cost, a decrease by 11.7% is observed. This manuscript concludes that Pontryagin’s method for generating slew trajectories outperforms the use of sinusoidal trajectories and trajectory generation schemes are essential for efficient spacecraft maneuvering.

The vibration suppression directly affects the dynamic performance and working accuracy of flexible manipulators, which is one of the important issues in the robotics field. However, most of the relevant literature only studies the vibration suppression of planar flexible manipulators, which is difficult to adapt to more general space motion. This paper proposes a strategy for vibration suppression of a spatial rigid-flexible link manipulator based on transfer matrix method of multibody system and RBF interpolation method. Firstly, the dynamics model of the system is constructed using the acceleration transfer matrix strategy, which provides support for vibration control. Secondly, the basic trajectories of the manipulator joints satisfying the boundary conditions are constructed and interpolated using an RBF with infinite smoothness. Based on this, an optimization objective based on the system dynamics model is proposed, which is to minimum the residual vibration of the flexible link. Meanwhile, an optimized hybrid particle swarm optimization algorithm is presented to solve the optimal problem of joint trajectories under minimum residual vibration. Finally, the effectiveness of the proposed dynamics model and trajectory optimization method is verified by numerical simulations. The dynamics modeling method proposed in this paper does not need to derive the global model of the system, which greatly improves the computational efficiency under the premise of ensuring accuracy, while the proposed trajectory optimization method based on RBF interpolation can be effective in reducing the system residual vibration on the basis of ensuring the infinite continuous smoothness of the optimized trajectory; meanwhile, the method does not need to measure the vibration with additional sensors, which effectively reduces the economic cost and has high practical value.

The effective training of large-scale distributed deep learning models has become an active and emerging research area in recent years. Federated learning (FL) can address those challenges by training global models through parameter exchange of client models rather than raw data sharing, thereby preserving security and communication efficiency. However, conventional linear aggregation approaches in FL neglect heterogeneous client models and non-IID data. This often results in inter-layer information imbalance and feature-space misalignment, leading to low overall accuracy and unstable training. To overcome these limitations, we propose HyFLM, a personalized federated learning framework that maximizes performance with Multidimensional Trajectory Optimization theory (MTO) on diffusion paths. HyFLM extends a diffusion-based FL framework by encoding client–parameter dependencies with a diffusion model and precisely controlling dimension-specific paths, thereby generating personalized weights that reflect both the data complexity and the resource constraints of each client. In addition, a lightweight hypernetwork generates client-specific adapters or weights to further enhance personalization. Extensive experiments on multiple benchmarks demonstrate that HyFLM consistently outperforms major baselines in terms of both accuracy and communication efficiency, achieving faster convergence and higher accuracy. Furthermore, ablation studies verify the contribution of MAC to convergence acceleration, confirming that HyFLM is an effective and practical personalized FL paradigm for heterogeneous client models.

The strong growth rate of the aviation industry in recent years has created significant challenges in terms of environmental impact. Air traffic contributes to climate change through the emission of carbon dioxide (CO2) and other non-CO2 effects, and the associated climate impact is expected to soar further. The mitigation of CO2 contributions to the net climate impact can be achieved using novel propulsion, jet fuels, and continuous improvements of aircraft efficiency, whose solutions lack in immediacy. On the other hand, the climate impact associated with non-CO2 emissions, being responsible for two-thirds of aviation radiative forcing, varies highly with geographic location, altitude, and time of the emission. Consequently, these effects can be reduced by planning proper climate-aware trajectories. To investigate these possibilities, this paper presents a survey on operational strategies proposed in the literature to mitigate aviation’s climate impact. These approaches are classified based on their methodology, climate metrics, reliability, and applicability. Drawing upon this analysis, future lines of research on this topic are delineated.

In this paper, an improved retractable body model (IRBM) is established, which has an advantage in simulating the flexion-and-extension motion of skier’s legs during carved turning and straight gliding. The trajectory optimization problem for the nonlinear alpine skiing system is transformed into a multi-phase optimal control (MPOC) problem. Subsequently, a constrained multi-phase trajectory optimization model is developed based on the optimal control theory, where the optimization target is to minimize the total skiing time. The optimization model is discretized by using the Radau pseudospectral method (RPM), which transcribes the MPOC problem into a nonlinear programming (NLP) problem that is then solved by SNOPT solver. Through numerical simulations, the optimization results under different constraints are obtained using MATLAB. The variation characteristics of the variables and trajectories are analyzed, and four influencing factors related to the skiing time are investigated by comparative experiments. It turns out that the small turning radius can reduce the total skiing time, the flexion-and-extension motion of legs is beneficial to skier’s performance, and the large inclination angle can shorten skier’s turning time, while the control force has a slight effect on the skiing time. The effectiveness and feasibility of the proposed models and trajectory optimization strategies are validated by simulation and experiment results.

Unmanned Aerial Vehicles (UAVs) can be deployed as aerial wireless base stations which dynamically cover the wireless communication networks for Ground Users (GUs). The most challenging problem is how to control multi-UAVs to achieve on-demand coverage of wireless communication networks while maintaining connectivity among them. In this paper, the cooperative trajectory optimization of UAVs is studied to maximize the communication efficiency in the dynamic deployment of UAVs for emergency communication scenarios. We transform the problem into a Markov game problem and propose a distributed trajectory optimization algorithm, Double-Stream Attention multi-agent Actor-Critic (DSAAC), based on Multi-Agent Deep Reinforcement Learning (MADRL). The throughput, safety distance, and power consumption of UAVs are comprehensively taken into account for designing a practical reward function. For complex emergency communication scenarios, we design a double data stream network structure that provides a capacity for the Actor network to process state changes. Thus, UAVs can sense the movement trends of the GUs as well as other UAVs. To establish effective cooperation strategies for UAVs, we develop a hierarchical multi-head attention encoder in the Critic network. This encoder can reduce the redundant information through the attention mechanism, which resolves the problem of the curse of dimensionality as the number of both UAVs and GUs increases. We construct a simulation environment for emergency networks with multi-UAVs and compare the effects of the different numbers of GUs and UAVs on algorithms. The DSAAC algorithm improves communication efficiency by 56.7%, throughput by 71.2%, energy saving by 19.8%, and reduces the number of crashes by 57.7%.

Predictive gait simulations currently do not account for environmental or internal noise. We describe a method to solve predictive simulations of human movements in a stochastic environment using a collocation method. The optimization is performed over multiple noisy episodes of the trajectory, instead of a single episode in a deterministic environment. Each episode used the same control parameters. The method was verified on a torque-driven pendulum swing-up problem. A different optimal trajectory was found in a stochastic environment than in the deterministic environment. Next, it was applied to gait to show its application in predictive simulation of human movement. We show that, unlike in a deterministic model, a nonzero minimum foot clearance during swing is predicted by a minimum-effort criterion in a stochastic environment. The predicted amount of foot clearance increased with the noise amplitude.

The 12th Global Trajectory Optimization Competition challenged teams to design trajectories for mining asteroids and transporting extracted resources back to the Earth. This paper outlines the methods and results of the runner-up team, BIT-CAS-DFH, highlighting an overall analysis of the approach as well as detailed descriptions of the methods used. The approach begins with building databases to reduce computational costs in trajectory design. Then, asteroid sequences are determined. A segmentation-based approach was adopted to efficiently handle the large dataset. Each sequence was divided into four time-based segments. Segments 1 and 4 were generated forward and backward, respectively, using a breadth-first beam search. Candidates for these segments were refined using genetic and greedy algorithms. Segments 2 and 3 were then generated and selected forward and backward based on the results of Segments 1 and 4. Following this, a matching process paired candidates from Segments 2 and 3. With the asteroid sequences established, low-thrust trajectories were optimized using indirect methods. A local optimization strategy was employed to maximize the collected mass by fine-tuning rendezvous timings. The final solution is presented, with comparative analyses against other teams’ approaches.

In high-dynamic battlefield environments, anti-ship missiles must perform intricate attitude adjustments and energy management within time constraints to hit a target accurately. Traditional optimization methods face challenges due to the high speed, flexibility, and varied constraints inherent to anti-ship missiles. To overcome these challenges, this research introduces a three-dimensional (3D) multi-stage trajectory optimization approach based on the hybrid multi-objective particle swarm optimization algorithm (MOPSO-h). A multi-stage optimization model is developed for terminal trajectory, dividing the flight process into three stages: cruising, altitude adjustment, and penetration dive. Dynamic equations are formulated for each stage, incorporating real-time observations and overload constraints and ensuring the trajectory remains smooth, continuous, and compliant with physical limitations. The proposed algorithm integrates an adaptive hybrid mutation strategy, effectively balancing global search with local exploitation, thus preventing premature convergence. The simulation results demonstrate that, in typical scenarios, the mean miss distance optimized by MOPSO-h remains no greater than 2.34 m, while the terminal landing angle is consistently no less than 85.68°. Furthermore, MOPSO-h enables the missile’s cruise altitude and speed, driven by multiple models, to maintain long-term stability, ensuring that the maneuver overload adheres to physical constraints. This research provides a rigorous and practical solution for anti-ship missile trajectory design and engagement with shipborne air defense systems in high-dynamic environments, achieved through a multi-stage collaborative optimization mechanism and error analysis.

In this paper, we introduce a numerical optimal control scheme (NOCS) for generating dynamically feasible robot motions under several constraints while optimizing a given performance criterion. In particular, the NOCS transforms continuous optimal control problems into large-scale sparsity-free nonlinear programs (NLPs) by means of a dedicated strategy called the block indexation procedure (BIP). As a result, the optimized open-loop control law is obtained fast under limited-memory allocation. The robot’s equations of motion, and their partial derivatives with respect to the state of the robot and control inputs, are analytically evaluated. For this, state-of-the-art algorithms available in the Pinocchio and RBDL open-source libraries are used. Otherwise, the NOCS applies the BIP with numerical differentiation techniques. The effectiveness of the NOCS is numerically validated with different robots composed by many degrees of freedom. Also, we provide performance comparisons against CasADi, a popular general purpose optimal control framework that applies automatic differentiation.