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The establishment and solution of the inverse kinematic model is the key to improve the efficiency of trajectory optimization. To improve the trajectory smoothness and reduce energy consumption of multi-degree-of-freedom (MDOF) robots, this article presents the time-, jitter-, and energy-optimal trajectory optimization method based on pseudo-attractor and radial basis function neural network. Based on the geometric method, the forward kinematic model of MDOF robots is firstly established. The diversity of inverse kinematic solutions is reduced by determining redundant joints. Combined with the attractor theory, the time-adaptive allocation strategy can automatically endow time information with path points. On this basis, the 7-time polynomial interpolation method is used to fit discrete trajectory points and generate the initial trajectory without singularity points. Affected by the pseudo-attractor, radial basis function neural network is transformed into the improved radial basis function neural network (I-RBFNN) to optimize the initial trajectory. The 2-redundancy planar feeding manipulator (2-RPFM) is introduced to verify the effectiveness of the proposed method. Experiment and simulation results show that the proposed method is available in generating high-performance trajectories, which is beneficial to improve the production efficiency of the auto-body-out-panel stamping line. [ABSTRACT FROM AUTHOR]

The distribution of internal defects in large-diameter steel pipes can be complicated. Due to the harsh working environments involved, the manual grinding method for correcting such defects is inaccurate, inefficient, and risky. Therefore, in this study, we designed a new internal pipe grinding robot with five degrees of freedom. The grinding trajectory was optimized, and dynamic and kinematic models of the robot were established for the internal space of a pipe with a diameter between 800 and 1,200 mm. The feasibility of the robot was verified by simulation. A trajectory optimization method that focuses on the time, energy, and impact of the trajectory of the grinding robot is proposed. The method uses modified multiobjective particle swarm optimization (MMOPSO) in the robot's trajectory planning module to obtain a Pareto solution set. The analytic hierarchy process is used with the minimum fuzzy entropy (AHP-MFE) method in the decision-making module to select the most appropriate trajectory according to the relevant working conditions. The experimental results validated the space accessibility and trajectory optimization performance. Compared with the original trajectory, operation time was shortened by 15.4%, energy consumption was reduced by 17.5%, and impact was reduced by 12.4%. The experimental error was less than 2.8%. The experimental results showed that the pipe grinding robot is safe and efficient. [ABSTRACT FROM AUTHOR]

Lower-limb exoskeletons (LLEs) can provide rehabilitation training and walking assistance for individuals with lower-limb dysfunction or those in need of functionality enhancement. Adapting and personalizing the LLEs is crucial for them to form an intelligent human–machine system (HMS). However, numerous LLEs lack thorough consideration of individual differences in motion planning, leading to subpar human performance. Prioritizing human physiological response is a critical objective of trajectory optimization for the HMS. This paper proposes a human-in-the-loop (HITL) motion planning method that utilizes surface electromyography signals as biofeedback for the HITL optimization. The proposed method combines offline trajectory optimization with HITL trajectory selection. Based on the derived hybrid dynamical model of the HMS, the offline trajectory is optimized using a direct collocation method, while HITL trajectory selection is based on Thompson sampling. The direct collocation method optimizes various gait trajectories and constructs a gait library according to the energy optimality law, taking into consideration dynamics and walking constraints. Subsequently, an optimal gait trajectory is selected for the wearer using Thompson sampling. The selected gait trajectory is then implemented on the LLE under a hybrid zero dynamics control strategy. Through the HITL optimization and control experiments, the effectiveness and superiority of the proposed method are verified. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative approach for constrained rendezvous trajectory optimization (CRTO) using stochastic optimal feedback control and unscented transform (UT) uncertainty quantification. The method overcomes limitations of traditional deterministic CRTO solutions that suffer from uncontrolled terminal state error growth and severely deteriorated path constraint satisfaction when initial state uncertainty, dynamics uncertainty, and navigation uncertainty are considered. The approach involves constructing a stochastic optimal feedback control (SOFC) problem with chance constraints and introducing linear feedback control to regulate both the mean and variance of terminal state errors. UT is employed to approximately quantify the state errors and their propagation, transforming the SOFC problem into an unconstrained deterministic optimization (UDO) problem. Differential dynamic programming (DDP) is then used to solve the UDO problem. The obtained stochastic optimal solution provides a robust rendezvous trajectory and a corresponding explicit closed-loop guidance law, improving terminal accuracy and path constraint satisfaction in the presence of various considered uncertainties. The influence of different term weights in the objective function on terminal accuracy and path constraint satisfaction is also studied. The effectiveness of the proposed approach is verified through Monte Carlo simulation, demonstrating the robustness of the closed-loop control strategy. The results highlight the potential of the method in enhancing terminal accuracy and path constraint satisfaction in uncertain rendezvous scenarios. • The uncertainty-resilient rendezvous trajectory optimization algorithm provides not only a nominal trajectory but an explicit optimal state-feedback control policy. • Rendezvous trajectory uncertainty caused by initial state errors, dynamics errors, and navigation errors is propagated using an unscented transformation method. • The proposed method considers common input constraints and path constraints in space rendezvous missions. [ABSTRACT FROM AUTHOR]

In this article, a mission planning and trajectory optimization scheme in unmanned aerial vehicle (UAV) swarm for track deception against radar networks is proposed. The core of this scheme is to formulate the track deception problem as a model with the objective of simultaneously maximizing the number of phantom tracks while minimizing the total flight distance of the UAV swarm, subject to the constraints of UAV kinematic performance, phantom track rotation angles, and a homology test. It is shown that the formulated track deception problem is a mixed-integer programming, multivariable, and non-linear optimization model. By incorporating mission planning based on platform reuse and a particle swarm optimization (PSO) algorithm, a three-stage solution methodology is proposed to tackle the above problem. Through joint optimization for mission planning and flight trajectories of the UAV swarm, a low-speed UAV swarm is capable of generating a number of high-speed phantom tracks. Numerical results demonstrate that the proposed scheme enables a low-speed UAV swarm to generate as many high-speed phantom tracks as possible, effectively achieving track deception against radar network. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) are considered as a promising method to provide service for Internet of Remote Things (IoRT). The incorporation of non-orthogonal multiple access (NOMA) into UAV-assisted networks provides a possibility for massive IoRT devices access. In this paper, we investigate the downlink transmission UAV-assisted wireless communication system based on NOMA in IoRT networks, where UAVs fly vertically to provide services for IoRT devices. In order to transmit as much data as possible, we aim to maximize the energy efficiency (EE) of the UAV by jointly optimizing NOMA user scheduling, UAV trajectory and power allocation. Due to the coupling between variables, the derived problem is mixed integer optimization and non-convex. To solve this challenging problem, we first decouple the variables and split the original problem into three subproblems, i.e., user scheduling, trajectory planning, and power allocation. Then, a double-loop iterative algorithm is proposed to solve the corresponding subproblems based on the Dinkelbach method and successive convex approximation (SCA) techniques. Finally, simulation results give some insights e.g., NOMA outperforms OMA in both spectral efficiency and energy efficiency and the proposed NOMA-based EE-oriented scheme is approximate three times energy efficient than benchmark schemes. [ABSTRACT FROM AUTHOR]

With the development of science and technology and economy, UAV is used more and more widely. However, the existing UAV trajectory planning methods have the limitations of high cost and low intelligence. In view of this, grey Wolf algorithm is being used to achieve collaborative trajectory optimization of UAV groups. However, it is found that the Grey Wolf optimization algorithm (GWO) has the problem of weak cooperation. In this study, based on the traditional GWO pheromone factor is introduced to improve it.. Aiming at the problem of unstable performance of swarm intelligence optimization algorithm under dynamic threat, deep reinforcement learning is used to optimize the model. An unmanned aerial vehicle swarm trajectory planning model was constructed based on the improved grey wolf algorithm. Through experimental analysis, the optimal fitness value of the improved grey wolf algorithm was lower than 0.43 of the grey wolf algorithm. Compared with other algorithms, the fitness value of this algorithm is significantly reduced and the stability is higher. In complex scenarios, the improved grey wolf algorithm had a trajectory length of 70.51 km and a planning time of 5.92 s, which was clearly superior to other algorithms. The path length planned by the research and design model was 58.476 km, which was significantly smaller than the other three models. The planning time was 5.33 s and the number of path extension points was 46. The indicator values of the Unmanned Aerial Vehicle swarm trajectory planning model designed by this research were all smaller than the other three models. By analyzing the results, the model can achieve low-cost trajectory optimization, providing more reasonable technical support for unmanned aerial vehicle mission execution. [ABSTRACT FROM AUTHOR]

The infiltration of heterogenous fleets of autonomous Unmanned Aerial Vehicles (UAVs) in smart cities is leading to the consumerization of city air space which includes infrastructure creation of roads, traffic design, capacity estimation, and trajectory optimization. This study proposes a novel autonomous Advanced Aerial Mobility (AAM) logistical system for high density city centers. First, we propose a real-time 3D geospatial mining framework for LiDAR data to create a dynamically updated digital twin model. This enables the identification of viable airspace volumes in densely populated 3D environments based on the airspace policy/regulations. Second, we propose a robust city airspace dynamic 4D discretization method (Skyroutes) for autonomous UAVs to incorporate the underlying real-time constraints coupled with externalities, legal, and optimal UAV operation based on kinematics. An hourly trip generation model was applied to create 1138 trips in two scenarios comparing the cartesian discretization to our proposed algorithm. The results show that the AAM enables a precise airspace capacity/cost estimation, due to its detailed 3D generation capabilities. The AAM increased the airspace capacity by up to 10%, the generated UAV trajectories are 50% more energy efficient, and significantly safer. [ABSTRACT FROM AUTHOR]

During terminal guidance, the attack platform is provided with a high‐resolution image of the target area through the application of synthetic aperture radar. Additionally, the stealth trajectory with low observability can significantly impact mission success. This paper considers both the performance of missile‐borne synthetic aperture radar imaging and stealth performance as influencing factors for terminal trajectory optimization, which is modelled as a constrained multi‐objective optimization problem. The application of the pseudospectral method in the solution of optimal control problems has led to the proposal of the hybrid genetic algorithm pseudospectral optimization framework. The problem is decomposed into several single‐objective optimal control problems, which can generate a specific initial population for the genetic algorithm to obtain a set of Pareto‐optimal solutions. Finally, the numerical simulations demonstrate the effectiveness of the proposed optimization approach compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a cell-free massive multiple-input multiple-output (CF-mMIMO) system with a reconfigurable intelligent surface (RIS) carried by an unmanned aerial vehicle (UAV), called the UAV-RIS. Compared with the RIS located on the ground, the UAV-RIS has a wider coverage that can reflect all signals from access points (APs) and user equipment (UE). By correlating the UAV location with the Rician K-factor, we derive a closed-form approximation of the UE achievable downlink rate. Based on this, we obtain the optimal UAV location and RIS phase shift that can maximize the UE sum rate through an alternating optimization method. Simulation results have verified the accuracy of the derived approximation and shown that the UE sum rate can be significantly improved with the obtained optimal UAV location and RIS phase shift. Moreover, we find that with a uniform UE distribution, the UAV-RIS should fly to the center of the system, while with an uneven UE distribution, the UAV-RIS should fly above the area where UEs are gathered. In addition, we also design the best trajectory for the UAV-RIS to fly from its initial location to the optimal destination while maintaining the maximum UE sum rate per time slot during the flight. [ABSTRACT FROM AUTHOR]

This study presents a novel framework that integrates the universal jamming gripper (UG) with unmanned aerial vehicles (UAVs) to enable automated grasping with no human operator in the loop. Grounded in the principles of granular jamming, the UG exhibits remarkable adaptability and proficiency, navigating the complexities of soft aerial grasping with enhanced robustness and versatility. Central to this integration is a uniquely formulated constrained trajectory optimization using model predictive control, coupled with a robust force control strategy, increasing the level of automation and operational reliability in aerial grasping. This control structure, while simple, is a powerful tool for various applications, ranging from material handling to disaster response, and marks an advancement toward genuine autonomy in aerial manipulation tasks. The key contribution of this research is the combination of a UG with a suitable control strategy, that can be kept relatively straightforward thanks to the mechanical intelligence built into the UG. The algorithm is validated through numerical simulations and virtual experiments. [ABSTRACT FROM AUTHOR]

Video stabilization plays a pivotal role in enhancing video quality by eliminating unwanted jitter in shaky videos. This paper introduces a novel video stabilization algorithm that leverages low‐rank constraint and trajectory optimization to effectively eliminate undesirable motion and generate stabilized videos. In the proposed algorithm, a low‐rank constraint regularization term is incorporated to enhance the smoothness of motion trajectories. Additionally, a predictive path smoothness term is integrated to ensure the consistency of motion across neighbouring frames. To address the problem of excessive cropping resulting from aggressive smoothing, a flexible local window strategy that emphasizes local motion relationships within the trajectories is introduced. The experimental results show that, compared to other excellent video stabilization algorithms, the proposed algorithm improves the stability metric by approximately 2.3%. Furthermore, in the stabilized videos generated by the algorithm, an approximate improvement of 2.18 dB in average image temporal fidelity and a 5.7% increase in average structural similarity between adjacent frames are achieved. The code that implements the proposed method is publicly accessible at https://github.com/CZS0319/VS_Low‐Rank_Constraint_Trajectory_Optimization. [ABSTRACT FROM AUTHOR]

Aircraft crew are aware of the delay they have experienced at departure. However, uncertainties ahead, and in particular holdings at arrival, can have an impact on the final performance of their operations. When optimizing a trajectory, the expected cost at the arrival gate should be considered. Consequently, taking into account potential congestion and extra delay at the arrival airspace is paramount to avoid making sub-optimal decisions during the early stages of a flight. This paper presents a framework to optimize trajectories in the execution phase of the flight considering expected delays at arrival. A flight from Athens (LGAV) to London Heathrow (EGLL) is used as an illustrative example, systematically exploring a range of departure delays and expected holdings at arrival. [ABSTRACT FROM AUTHOR]

There is a strong dynamic coupling between the base of free-floating space robot and the space manipulator. In order to reduce the interference of the movement of the space manipulator on the robot's base, the trajectory of the space manipulator needs to be optimized. In this paper, the joint path of space manipulators is optimized by using the pseudo-spectral method to reduce the impact of the arm movement on the base. For space robots, parameters identification is the premise of trajectory planning. A parameters identification method is proposed, which only needs to measure the base's angular speed. Numerical simulation results verify the validity of the proposed method. The attitude angle of floating base returns to the initial state after maneuvers of space manipulators. [ABSTRACT FROM AUTHOR]

• A dynamic model for space multi-fingered system with uncertainties and disturbances is formulated. • The dynamic capture domain is designed to envelop space tumbling target for multi-fingered mechanism. • Composite controller based on model predictive control and disturbance observer is proposed. • Proposed method can handle constraints while having better interference rejection. Space debris are usually with diverse geometric shapes and no grappling points. Current capture methods lack the capability to adjust to the target shape dynamically. The capture of space debris remains a significant challenge for operational space missions. This paper presents a multi-finger envelope control strategy based on dynamic capture region in the pre-grasping phase. In the method, the proximal joints of each finger are first determined according to the target shapes. Then, an appropriate joint threshold is selected to generate a set of candidate configurations for the rest of the finger joints, and the effective multi-fingered envelope configuration that resembles the target contour is chosen from candidate finger configurations based on the Hausdorff Distance. Further, the optimal joint trajectories are obtained by minimizing the impact of multi-finger movements on the palm. Considering the model uncertainties, external disturbances and actuator saturation, a composite controller combining disturbance observer and nonlinear model predictive control (NMPC) is proposed for trajectory tracking control of multi-fingered mechanism. The simulation results show that the proposed method can rapidly find an effective envelope capture configuration and has a higher trajectory tracking performance in the presence of uncertainty compared to the Proportional Integral Differential and NMPC controllers. [ABSTRACT FROM AUTHOR]

This work investigates a downlink nonorthogonal multiple access (NOMA) scheme with unmanned aerial vehicle (UAV) aided wireless communication, where a single UAV was regarded as an air base station (ABS) to communicate with multiple ground users. Considering the constraints of velocity and maneuverability, a UAV energy efficiency (EE) model was proposed via collaborative design resource allocation and trajectory optimization. Based on this, an EE maximization problem was formulated to jointly optimize the transmit power of ground users and the trajectory of the UAV. To obtain the optimal solutions, this nonconvex problem was transformed into an equivalent convex optimization problem on the basis of three user clustering algorithms. After several alternating iterations, our proposed algorithms converged quickly. The simulation results show an enhancement in EE with NOMA because our proposed algorithm is nearly 99.6% superior to other OMA schemes. [ABSTRACT FROM AUTHOR]

Nowadays, the digital development of marine ranching requires a communication system with wide coverage, high transmission rate and stable communication links. It is known that fixed‐wing unmanned aerial vehicles (UAVs) have great advantages in long‐range applications. They have the potential to serve as low‐altitude communication platforms for maritime communication. In this study, with a developmental perspective, considering the intense growth of marine terminals in the future, a new clustering algorithm applied to cluster nonorthogonal multiple access (C‐NOMA) is proposed and its advantages are investigated. In addition, considering the limited energy of marine terminals, combining the wireless power communication (WPC) technology for the UAV to charge terminals, the charging and communication time are optimized with the Lagrange multiplier method and the bisection search method. After completing the above optimization content of charging and communication, combined with the optimization results, it is found the trajectory that maximizes the energy efficiency of the UAV with the convex optimization technique. Experimental results show that the proposed clustering algorithm has good throughput performance, better fairness and lower algorithm complexity, and the proposed trajectory optimization scheme has better energy efficiency. [ABSTRACT FROM AUTHOR]

Due to the complex aerodynamic effects, the reentry trajectory optimization problem is highly nonlinear. When using sequential convex programming (SCP) methods to solve it, the iteration solution is difficult to converge. To improve this, we propose a hybrid-order soft trust region-based SCP method. We analyze the penalty effect of typical trust regions. Based on the analysis, we develop a hybrid-order soft trust region combining a small-weight first-order component and a higher-order components. To solve the subproblem reliably and effectively, we equivalently reformulate it as a second-order cone programming (SOCP) form through the relaxation technique. Combined with the line search method, we further design an SCP algorithm with guaranteed convergence under some assumptions. In the numerical simulations, the effectiveness and robustness of the proposed method have been verified using a nominal case and 200 Monte Carlo cases. [ABSTRACT FROM AUTHOR]

The deformation of the compliant part is the key factor that affects the production efficiency of the automobile press line. Considering multi-manipulator trajectories and part contours, this paper quantitatively analyzes the deformation of compliant parts when the manipulator transfers sheet metal parts. A multi-objective co-optimization method is proposed to generate smooth motion curves with smaller velocity, acceleration, and jerk. Based on the built-in module of rigid to flex in ADAMS software, some rigid parts such as the end effector and sheet metal part are transformed into compliant ones. And the redundant manipulator in the press line is taken as the representative case to check whether the trajectory performance is conducive to deformation suppression. Simulation result shows that the jerk curve without cusp points is more conducive to suppressing the part deformation than that with cusp points. [ABSTRACT FROM AUTHOR]

Shape-based methods are commonly used in solving the low-thrust trajectory optimization problem. Designing a shape trajectory by maximizing a given performance index has been widely researched in recent years. The main contribution of this paper is to present a new pseudoequinoctial shaping method with parameter optimization to solve general low-thrust spacecraft rendezvous problems. The shaping method can solve the rendezvous problem with a large inclination difference between the initial and target orbits and greatly improve the performance index of the trajectory while meeting the thrust constraints. At the same time, the shape can provide a better feasible solution for solving the low-thrust trajectory optimization problem by direct methods. Another contribution is to introduce a general adjoint estimation for indirect methods. By linearizing the equation of motion near the proposed shape-based trajectory and constructing the Hamiltonian function, the initial guess of the adjoint variables can be obtained in a closed form. The general linearization formulations applicable to all coordinate systems are presented, and three numerical examples are given, in which the first example verifies the superiority of the proposed shape-based method, the second example tests the feasibility of the shape as the initial value for a direct method, and the last example compares the convergence rates of the initial adjoint variables generated by the proposed method under different coordinate systems for an indirect method. [ABSTRACT FROM AUTHOR]

In this paper, Particle Swarm Optimization with energy-to-fuel continuation is proposed for initializing the co-state variables for low-thrust minimum-fuel trajectory optimization problems in the circular restricted three-body problem. Particle Swarm Optimization performs a search of the solution space by minimizing the weighted sum of squares of the two-point boundary-value problem final boundary condition residuals for the minimum-energy problem. Next, an energy-to-fuel homotopy is employed to transition the minimum-energy trajectory to a minimum-fuel trajectory, starting from the generated guess. The proposed methodology is applied to two low-thrust transfer problems in the Earth–Moon system: a transfer from a geostationary transfer orbit to an L1 halo orbit, and a transfer from an L2 halo orbit to an L1 halo orbit. The resulting minimum-fuel trajectories are validated with the literature. It is demonstrated that the methodology can successfully generate guesses for the initial co-state variables which converge to a solution for both scenarios. A strategically chosen particle swarm size is shown to improve the efficiency of the methodology. The proposed approach is of simple implementation, can be easily extended to other trajectory optimization problems, facilitates the discovery of multiple candidate trajectories, and does not require a user-provided guess, all of which are advantageous features for the preliminary phase of mission design. • Particle Swarm Optimization is proposed to guess the Lagrange co-states variables. • PSO initialization is paired with homotopy continuation for trajectory optimization. • The proposed algorithm facilitates discovery of multiple unique optimal trajectories. • Two minimum-fuel trajectory optimization problems are solved. • The effect of the particle swarm size on successful convergence is analyzed. [ABSTRACT FROM AUTHOR]

High vertical jumping motion, which enables a humanoid robot to leap over obstacles, is a direct reflection of its extreme motion capabilities. This article proposes a single sequential kino-dynamic trajectory optimization method to solve the whole-body motion trajectory for high vertical jumping motion. The trajectory optimization process is decomposed into two sequential optimization parts: optimization computation of centroidal dynamics and coherent whole-body kinematics. Both optimization problems converge on the common variables (the center of mass, momentum, and foot position) using cost functions while allowing for some tolerance in the consistency of the foot position. Additionally, complementarity conditions and a pre-defined contact sequence are implemented to constrain the contact force and foot position during the launching and flight phases. The whole-body trajectory, including the launching and flight phases, can be efficiently solved by a single sequential optimization, which is an efficient solution for the vertical jumping motion. Finally, the whole-body trajectory generated by the proposed optimized method is demonstrated on a real humanoid robot platform, and a vertical jumping motion of 0.5 m in height (foot lifting distance) is achieved. [ABSTRACT FROM AUTHOR]

The irregular satellites within the Jupiter system hold high scientific value due to their potential to contain clues about the early evolution of the solar system. This paper proposes an optimization algorithm for multiple irregular satellites flyby trajectories, which includes the powered gravity assist from Galilean moons. The algorithm is based on beam search and uses virtual trajectories to determine potential flyby targets, solving for trajectories that satisfy constraints on velocity increment, mission duration, and perijove radius. By changing the initial orbital period and optimizing the number of branches with Galilean moon gravity assist during branching, and comparing with the case without Galilean moon gravity assist, the effects of these factors on the number of irregular satellite flybys are summarized. The simulation results show that the algorithm can effectively solve for orbits that flyby multiple irregular satellites for initial orbits of different periods. The three trajectories obtained can serve as references for future missions. [ABSTRACT FROM AUTHOR]

There are complex coupling relationships between flight motion and energy management for hybrid electric fixed wing UAVs with photovoltaic/fuel cell/battery. Aiming at realizing high-energy-efficiency long endurance autonomous flight, this paper proposes a coordinated optimization method of trajectory optimization and energy management for hybrid electric UAVs. Numerical simulation and experiment are carried out. Separated by surplus demand energy except that produced by PV, this method includes an optimal energy flight trajectory optimization layer and an energy management layer. For the former, fuzzy neural network sequential convex optimization (FNNSCP) is proposed to handle the flight trajectory optimization problem for maximizing utilization solar energy. For the latter, an online energy management strategy based on convex quadratic programming MPC (CQPMPC) is proposed to realize the power allocation. Numerical simulation results show that FNNSCP reduced 2% energy requirement compared with Radau pseudo-spectral method (RPM) from flight trajectory optimization level. From energy management level, CQPMPC saves hydrogen consumption by 3.1% and 16.3% compared with nonlinear model predictive control (NMPC) and fuzzy logic state machine (FLSM), respectively. In the experiment, less hydrogen fuel is consumed by proposed method by 5.2% and 15.6% compared with NMPC and FLSM, respectively. Experimental results show that the proposed method has better energy-saving performance and excellent real time performance. It indicates that optimizing flight trajectory and improving energy management efficiency can realize the high-energy-efficiency flight of hybrid electric UAVs. This method is conducive to promoting the application of hydrogen energy in the field of UAVs. [Display omitted] • A coordinated optimization method is proposed for the high-energy-efficiency flight. • Fuzzy neural network adaptive sequential convex optimization method is proposed. • Online energy management strategy with convex quadratic programming MPC is proposed. • The proposed method is verified by simulation and energy management experiment. [ABSTRACT FROM AUTHOR]

This paper presents a distributed trajectory optimization algorithm for the reconfiguration of large-scale spacecraft formation, which uses a low thrust propulsion system to safely guide the spacecraft formation to a desired formation. Formation reconfiguration is formulated as a trajectory optimization problem with complex constraints, and the relative motion is accurately described by a nonlinear relative dynamics considering J 2 perturbation. The collision avoidance constraint is convexified into a tangent plane to ensure the accuracy of the solution. The resulting nonlinear trajectory optimization problem is solved by applying the h p -adaptive pseudospectral method to convert it into a nonlinear programming problem. In order to overcome the disadvantage of huge computation of centralized algorithm considering collision avoidance, "predicted trajectory" is introduced to transmit information between spacecraft, and the parallel computing is implemented. Finally, a numerical simulation is given to verify the computational efficiency and collision avoidance effectiveness of the proposed distributed algorithm. • Distributed trajectory optimization algorithm for massive formation reconfiguration. • The J 2 nonlinear relative dynamics is used to obtain accurate optimal trajectory. • Parallel computation is achieved by information interaction of neighbors. • Neighbor updating is proposed to reduce communication traffic. • Significantly decrease computation and achieve collision avoidance. [ABSTRACT FROM AUTHOR]

• A tailored optimal control computational framework is developed by exploiting the sparsity pattern of the sampling-based approach. • Trajectory optimization of a benchmark re-entry problem with complex path and boundary constraints under high-dimensional uncertainties is conducted. • Robustness-optimality tradeoff is studied for different combinations of uncertainties. • A boundary arc consisting of a continuous line formed by the boundary contact points of each sampled trajectory is observed in the ensemble case. • Results are promising in terms of computational efficiency, accuracy and optimality for use in actual multi-phase mission design studies. This paper introduces a sampling-based computational framework with a pseudospectral transcription, designed to investigate performance-robustness tradeoffs for constrained re-entry flights with a non-Gaussian uncertainty propagation. Ensemble of trajectories which are generated with sparse grids with Conjugate Unscented Transformation have been integrated into the nonlinear programming via a vectorized and parallelized formulation. A cross-range maximization problem is formulated to assess the influences of uncertainties in entry interface conditions and model parametric uncertainties. A comprehensive analysis, facilitated by rapid gradient-based optimization convergence and warm-starting, highlights the significant effects of initial speed uncertainties and drag coefficient on problem feasibility, offering insights into optimal control behavior under different degrees and combinations of uncertainties. Proper scaling of controls and the objective function proves pivotal for achieving convergence. Furthermore, a novel phenomenon called "contact arcs" is discovered, composed of contact points that form an arc at the edge of the path constraint in the constrained ensemble optimal control as a counterpart to the boundary arcs in deterministic optimal control problems. Simulation results show excellent agreement with the derived optimality conditions. [ABSTRACT FROM AUTHOR]

This study proposes a Gaussian-discretization control vector parametrization (CVP) algorithm to improve the reentry trajectory optimization accuracy of a hypersonic vehicle (HV) with a complex path and terminal state constraints. First, the reentry trajectory optimization problem (TOP) of the HV is established by analyzing the equations of motion and constraints. Second, a Gaussian distribution strategy is derived to obtain a suitable control parametrization time grid for improving control quality. By combining the handling strategies for path and terminal constraints, an efficient, non-uniform control parametrization trajectory optimization method is established, and the HV trajectory optimization algorithm framework is provided in detail. Lastly, the proposed algorithms are implemented on a widely studied common aero vehicle model. Numerical simulation tests are conducted on terminal-time-free and terminal-time-fixed TOPs to optimize the reentry downrange. Test results show that the proposed method has a stable solving ability with high satisfaction of terminal constraints. Simulation results reveal that the proposed method efficiently increases the downrange compared with other CVP methods under the tested scenario, thus showing the effectiveness of the proposed distribution strategy. [ABSTRACT FROM AUTHOR]

To overcome the time-consuming training caused by the sparse reward function in reinforcement learning, an efficient dense reward framework for robust low-thrust trajectory optimization is proposed. The dense reward functions are designed separately for the deterministic and considered uncertain scenarios, including state uncertainties, observation uncertainties and execution uncertainties. For the uncertainties, the dense reward function is designed to diminish the deviation with respect to the isochronous nominal state along the corresponding deterministic optimal trajectory at each step, rendering the reward function no longer sparse and suitable for complex multirevolution problems. In addition, a multistage reward function of the terminal constraints for the rendezvous missions is designed by incorporating some exponential acceleration terms, enabling significant improvement in training efficiency as the terminal errors become low. In addition, a dense reward function for the deterministic scenario is also proposed via the introduction of empirical forbidden zones and an exponential term. The effectiveness and efficiency of the proposed method is demonstrated in a simple Earth-Mars mission and a complex Earth-Venus multirevolution mission. The promising results verify the significant effect of the proposed method in speeding up the process of training an initial incapable agent to an 'expert' while guaranteeing or even improving the performance. [ABSTRACT FROM AUTHOR]

In space mission design, an important operational constraint is planned periodic coast arcs during which various mission-critical tasks such as navigation or ground communications are performed. These constraints, typically implemented as thruster duty cycles, can be characterized as discrete coast arcs enforced periodically during intervals of deterministic thrusting. A typical approach to incorporate duty cycles is by enforcing maximum thrust levels that are less than a nominal value. This work presents an embedded homotopy indirect optimization method for a smooth enforcement of discrete duty-cycle constraints for low-thrust trajectory optimization. The complexity of enforcing such discrete constraints is two-fold: (1) a precise event-detection strategy is needed to determine the beginning of deterministic thrust arcs, which must be successively updated along the trajectory and (2) a smooth modeling of the discrete coast events occurring on the order of 10s or even 100s depending on the duration of deterministic thrust arcs. Duty cycle constraints are enforced at the level of the Hamiltonian using a Composite Smooth Control (CSC) method, producing high-resolution optimal control solutions conscious of planned duty cycle coast arcs. Numerical solutions are presented for the heliocentric transfer phases of three space missions. The results are then validated against the Evolutionary Mission Trajectory Generator (EMTG), one of NASA's global trajectory optimization tools used for interplanetary mission design and capable of the explicit enforcement of periodic duty cycle coasting. The proposed indirect method is suitable for obtaining high-resolution trajectory solutions with realistically enforced thruster duty cycle, which could then be used as high-quality initial guesses in flight-fidelity mission planning tools. The proposed smooth modeling of discrete coast arcs can also be customized to enforce periodic and non-periodic thrust shutdown constraints. • Duty-cycle aware, multi-revolution, low-thrust, minimum-fuel trajectories. • A novel smooth switching function for embedding forced coast arcs. • Composite Smooth Control (CSC) is used to embed the discrete duty-cycle constraints. • Comparison with NASA's Evolutionary Mission Trajectory Generator (EMTG). • Julia programming language is used for solution of the boundary-value problems. [ABSTRACT FROM AUTHOR]

Recently, advanced in-vehicle technologies have led to the emergence of connected and automated vehicles (CAVs). CAVs are supposed to improve traffic efficiency and safety by coordinating the vehicles based on the communication among vehicles. This study addresses the trajectory optimization of CAVs in the drop-off area of the departure curbside, which consists of many conflict points. We first propose a centralized control method to optimize the trajectories of CAVs and then propose an implementation procedure to deal with the dynamic features and reduce the problem scales for practical instances. Contrast experiments are conducted to test the performance of the proposed control method. Results under various scenarios (different volumes, safety gaps, and desired speeds) demonstrate that CAVs controlled by the proposed method significantly outperform human-driven vehicles without control concerning mean travel time in the drop-off area. [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on a non-orthogonal multiple access (NOMA)-enabled UAV data collection network for Internet of Things devices (IoTDs), where a unmanned aerial vehicle (UAV) is deployed as an aerial base station. During its flight period, the UAV can collect data from IoTDs and take advantage of the simultaneous wireless information and power transfer technology to charge the batteries of IoTDs. With the aid of NOMA, spectrum efficiency has been improved. We aim to prolong the lifetime of the IoT network, via jointly optimizing the UAV trajectory, the time allocation for information communication and wireless power transfer, the IoTDs' transmit power, as well as the IoTDs' group scheduling for NOMA. Then, we use the block coordinate decent and successive convex approximation techniques to tackle the non-convexity of the formulated problem. Numerical results show that the proposed solution increases the residual energy of the IoTDs, thus prolonging the lifetime of the network. [ABSTRACT FROM AUTHOR]

• Reachable set footprint (RSF) after blackout is predicted by trajectory optimization. • Successive convex programming is used to determine RSF with intermediate states. • RSF shrinks with decreasing altitude of additional state observation during blackout. • A decision altitude exists to determine whether to update RSF with new observation. Blackout emerges in the reentry phase of reusable launch vehicles (RLV). Therein, large uncertainties exist in the telemetry signals of RLV, leading to potential safety problems. To facilitate predicting possible ranges of RLV final position when leaving blackout, this paper proposes a modified approach for computing reachable set footprint (RSF). A multi-phase trajectory optimization method is applied to simplified dynamics of RLV. Specifically, partial final boundary conditions are additionally supplemented to the first phase to exploit the intermediate state information during blackout. On this basis, RSF is predicted via solving a series of trajectory optimization problem by sequential convex programming. RSF with additional state information from different altitude are compared in numerical cases. Simulation results show that there exists a suitable range to update RSF using intermediate information. The decision altitude of updating RSF is determined for the exemplary RLV. [ABSTRACT FROM AUTHOR]

Autonomous mining transportation is an intelligent traffic control system that can provide better economics than traditional transportation systems. The velocity trajectory of a manned vehicle depends on the driver's driving style. Still, it can be optimized utilizing mathematical methods under autonomous driving conditions. This paper takes fuel and electric mining vehicles with a load capacity of 50 tons as the subject. It contributes a multi-objective optimization approach considering time, energy consumption, and battery lifetime. The dynamic programming (DP) algorithm is used to solve the optimal velocity trajectory with different optimization objectives under two types of mining condition simulation. The trajectories optimized by the single objective, energy consumption, usually adopt the pulse-and-gliding (PnG) approach frequently, which causes the battery capacity loss and increases the travel time. Hence, a multi-objective optimization approach is proposed. For electric vehicles, trajectories optimized by the multi-objective approach can decrease the battery capacity loss by 22.01 % and the time consumption by 41.28 %, leading to a 42.12 % increment in energy consumption. For fuel vehicles, it can decrease the time consumption by 32.54 %, leading to a 7.68 % increment in energy consumption. This velocity trajectory is smoother with less fluctuation. It can better meet the requirements of mining transportation and has a particular reference value for optimizing autonomous transportation costs in closed areas. [ABSTRACT FROM AUTHOR]

In Jupiter missions, single-satellite-aided capture employs the gravity assist of one of the Galilean moons, which could decrease the required Δ v to capture a spacecraft into a nominal orbit around Jupiter. Previous studies on single-satellite-aided capture mainly focused on Jovicentric orbits. In this paper, an optimization that focuses on Jovicentric orbits and considers the planetary segment and the nominal orbit around Jupiter was proposed. We use Jupiter arrival excess velocity and arrival time as the link between these two segments, which clearly illustrates single-satellite-aided capturing. VEGA and VEEGA sequences (both planetary gravity assist sequences) are tested in the numerical simulation. The result, with the complete orbits of the mission, indicates the reliability and good convergence of the method. It also turns out that Io and Ganymede are the best options for satellite-aided capture. [ABSTRACT FROM AUTHOR]

The demand for mobile robotics applications has grown considerably in recent years, especially due to the advent of industry 4.0, which has as one of its pillars the autonomous robotics field, the subject of this research. In this context, autonomous mobile robots must interact with the world to achieve their goals. One of the main challenges regarding mobile robots is the navigation problem: a robot can face several problems according to the type of sensor that is chosen in each application. The use of computer vision as a navigation tool in robotics represents an interesting alternative for controlling the movement of a mobile robot, and represent several vision techniques that gained more space in the last few years. Therefore, this work's research proposes the development of a control center to assist navigation and location of mobile robots in closed environments using the global view technique. In addition to computer vision, wireless communication (WiFi) between the exchange and the robots has been investigated to date. The results obtained in the initial steps of the project's development were promising, in which data from an autonomous robot is compared with a human-guided robot. Through the algorithm developed for the project, it was possible to transform the collected data into the robot's kinematics necessary to take the correct path to the destination using multivalued logic as a control algorithm. The optimization of the trajectory between the origin and the destination is performed using the A* and Dijkstra algorithms for calculating the shortest path. [ABSTRACT FROM AUTHOR]

The combination of unmanned aerial vehicles (UAVs) and mobile edge computing (MEC) is considered as a promising approach to tackle soaring computing requirements. The broadcast nature of air‐to‐ground (A2G) links makes UAV communications vulnerable to eavesdroppers, so secure UAV communications remain an open question. This paper proposes a secure communication scheme for reconfigurable intelligent surface (RIS)‐assisted UAV‐MEC systems, in which the RIS assists the user in offloading data to the legitimate UAV, and the legitimate UAV provides computing services to the user. To fully expand the security computing capacity of the system, the communication link is improved by introducing RIS, and the jammer interferes with the eavesdropper. The secure computing capability of the system is maximized by optimizing communication resources and trajectories. Since the proposed problem is non‐convex, successive convex approximation (SCA) technique and block coordinate descent (BCD) technique is combined to solve the problem. The simulation results show that the proposed scheme in this paper can effectively improve the system secure computing bits compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]

After the completion of the launch mission, the soft landing recovery and reuse of the carrier rocket's first-stage can effectively control the landing area to ensure safety and significantly reduce the cost of space launch transportation. The trajectory optimization of the whole process from the first section to the landing site is significant to fuel saving. In the entire process, the first-stage needs to go through three startup ignitions of course adjustment, power deceleration, and vertical landing. For this segmented fuel optimization problem, optimizing the thrust size and direction during three sections and the switching time between each section is necessary. Optimizing the vertical landing section is essential to ensure the accuracy of landing position and speed, which greatly complicates the whole process's optimization. Therefore, the optimization process of the vertical landing is substituted by a neural network predictor, which is used to obtain the mapping relationship between the initial state of the vertical landing section and the fuel consumption of the segment. Besides, the thrust profiles of the first two startup sections are reasonably handled based on physical cognition. The combination of convex optimization and neural network successfully converted the multi-stage optimal control problem into a parameter optimization problem and solved it by a genetic algorithm. Optimization results were compared with the conventional method, which indicated its superiority. [ABSTRACT FROM AUTHOR]

When humanoid robots work in human environments, falls are inevitable due to the complexity of such environments. Current research on humanoid robot falls has mainly focused on falls on the ground, with little research on humanoid robots falling from the air. In this paper, we employ an extended state variable formulation that directly maps from the high-level motion strategy space to the full-body joint space to optimize the falling trajectory in order to protect the robot when falling from the air. In order to mitigate the impact force generated by the robot's fall, during the aerial phase, we employ simple proportion differentiation (PD) control. In the landing phase, we optimize the optimal contact force at the contact point using the centroidal dynamics model. Based on the contact force, the changes to the end-effector positions are solved using a dual spring–damper model. In the simulation experiments, we conduct three comparative experiments, and the simulation results demonstrate that the robot can safely fall 1.5 m from the ground at a pitch angle of 45°. Finally, we experimentally validate the methods on an actual robot by performing a side-fall experiment. The experimental results show that the proposed trajectory optimization and motion control methods can provide excellent shock absorption for the impact generated when a robot falls. [ABSTRACT FROM AUTHOR]

• Multi-target Active Debris Removal missions are necessary to reduce the proliferation of debris. • Using of simulated annealing optimization groups debris in an efficient way for removal missions. • Proposed missions have an average delta-V budget of 2.41 km/s and an average duration of 1 years. The proliferation of debris in Low Earth Orbit raises increasing challenges about the sustainability of the space environment. The current international recommendations to deorbit satellites at the end of their life are not sufficient to ensure this sustainability. To accelerate the process, it would be necessary to remove hazardous debris and thus de-congest the high-risk orbits. However, active debris removal missions are very expensive, and still in their early stages. One way to reduce its costs is to remove several pieces of debris per removal mission, which corresponds to a global optimization problem, with the objective of optimizing the number of debris removed while minimizing the cost in mission time and in propellant. In our study, the trajectory optimization is performed using a simulated annealing algorithm. The tool classifies the targets in groups gathered by similarities of orbital parameters, with the objective for each mission not to exceed a total Δ V = 4 km/s for a mission time lower than 3 years. To achieve this, a weighting is made between out-of-plane maneuvers, costly in propellant, and the use of the orbital parameter Ω drift, costly in time, to allow the spacecraft to pass from one debris to another. A criterion is set up to determine from which threshold it is more interesting to carry out a maneuver on Ω rather than to let the gravitational drift act. As a result, applied on the 50 most hazardous debris established by the International Astronautical Federation, we obtain a classification of the 50 pieces of debris into 11 optimal groups, with an average Δ V of 3.05 km/s and an average mission time of 1.5 years, which corresponds to the imposed criteria and validates the feasibility of such ADR missions. [ABSTRACT FROM AUTHOR]

Low–thrust propulsion systems of high specific impulse are advantageous in the fuel efficiency. The fuel expenditure is further reduced together with optimization techniques though fuel–optimal low–thrust trajectories result in a discontinuous bang–bang control structure that can cause numerical difficulties. The present paper introduces regularized formulations into the direct multiple shooting method of minimizing fuel expenditure for low–thrust spacecraft trajectories. Instantaneous velocity changes approximating low–thrust maneuvers are expressed by regularized variables based on the Levi–Civita or Kustaanheimo–Stiefel transformation. The new formulation removes singularities due to null thrust impulses from derivatives of an objective function and constraints. The method automatically and robustly finds fuel–efficient bang–bang control structures for multi–revolutional transfers between periodic orbits in the Earth–Moon circular restricted three–body problem. [ABSTRACT FROM AUTHOR]

This paper investigates an optimization problem corresponding to energy efficiency maximization of an unmanned aerial vehicle (UAV)-enabled relaying system, where a fixed-wing UAV acts as an amplify-and-forward mobile relay to assist data transmission between a source node and a destination node. On the premise of satisfying the speed and acceleration constraints of the UAV, the energy efficiency (EE) of the relaying system is maximized by jointly optimizing the UAV's trajectory and the individual transmit power levels of the source and the UAV relay. The initial joint optimization problem is non-convex and cannot be solved directly. Therefore, the joint optimization problem is decomposed into two sub-problems which are solved by applying the successive convex approximation technique and the Dinkelbach's algorithm. On this basis, an efficient iterative algorithm is proposed to tackle the joint optimization problem through the block coordinate descent technique. Simulation results demonstrated that by conducting the proposed algorithm, the flight trajectory of the UAV and the individual transmit power levels of the nodes can be flexibly adjusted according to the system conditions, and the proposed algorithm contributes to the higher EE compared with the benchmark schemes. [ABSTRACT FROM AUTHOR]

With the integration of unmanned aerial vehicles (UAVs) into fifth generation (5G) networks, UAVs are used in many applications since they enhance coverage and capacity. To increase wireless communication resources, it is crucial to study the trajectory of UAV-assisted relay. In this paper, an energy-efficient UAV trajectory for uplink communication is studied, where a UAV serves as a mobile relay to maintain the communication between ground user equipment (UE) and a macro base station. This paper proposes a UAV Trajectory Optimization (UAV-TO) scheme for load balancing based on Reinforcement Learning (RL). The proposed scheme utilizes load balancing to maximize energy efficiency for multiple UEs in order to increase network resource utilization. To deal with nonconvex optimization, the RL framework is used to optimize the trajectory UAV. Both model-based and model-free approaches of RL are utilized to solve the optimization problem, considering line of sight and non-line of sight channel models. In addition, the network load distribution is calculated. The simulation results demonstrate the effectiveness of the proposed scheme under different path losses and different flight durations. The results show a significant improvement in performance compared to the existing methods. [ABSTRACT FROM AUTHOR]

This paper focuses on mixed-integer trajectory optimization of no-fly zones avoidance for a hypersonic vehicle. When there are multiple no-fly zones, the trajectory optimization problem has many local optimal solutions, and the performance of the solution depends on the selection of an initial guess. Essentially, the selection of the initial guess can be abstracted as a discrete path decision. To deal with this issue, this paper first integrates the discrete path decision and continuous trajectory optimization for no-fly zones avoidance and models these as a mixed-integer optimal control problem (MIOCP). As the corner stone, a creative directed graph is established to model the path decision problem, which is then formulated by integer constraints. Combined with the minimum effort optimal control problem (Problem 1), we form the MIOCP (Problem 2), thus integrating the path decision and trajectory optimization to improve global performance. Additionally, to solve the MIOCP, an effective iterative mixed-integer convex programming (IMICP) algorithm is customized by adding two ad-hoc techniques, relaxation and a proximity term, thus remedying the artificial infeasibility. Simulation results show that this approach is practically independent of the initial guess and has better performance than existing methods. • An approach is proposed to improve the global performance of no-fly zones avoidance. • A creative graph is established for path decision and the mixed-integer problem. • Relaxation and proximity terms are used in the IMICP algorithm for stable iteration. • The convergence is not practically dependent on the initial guess. [ABSTRACT FROM AUTHOR]

This paper studies the safe motion of a hopping rover on hazardous terrains of small bodies in the presence of initial state errors and dynamic parameter uncertainties. The collision probability is adopted to optimize the hopping trajectory. Firstly, the hazardous terrain is characterized by the least square median method, and the feasible path point zone is defined for hopping motion. Meanwhile, the hopping trajectory optimization is converted into sequence path point planning and optimal trajectory design problems based on the classical path planning algorithm. Then, considering the effects of errors and uncertainties, a performance index is derived to design a continuous hopping trajectory of sequence path points. Taking the collision probability as an index to indicate safety, local path points are optimized through path point decomposition and replacement strategy. Therefore, a collision-probability-based continuous optimal hopping trajectory can be generated to realize safe and precise motion. Finally, with the simulated hazardous terrain based on the small body 433 Eros, the effectiveness of the proposed method is verified by numerical analysis. [ABSTRACT FROM AUTHOR]

Building upon the recent development of solar sailing primer vector theory and its successful applications, we propose a new formulation for indirect solar-sail trajectory optimization, which minimizes solar angle (cone angle between the sail normal and sunlight vectors) over a trajectory. The minimum solar-angle objective is introduced to address a typical demand in mission design: having the ability to design trajectories with fixed time-of-flight, which is especially crucial when the mission involves time-sensitive events, such as scientific observations with specific lighting conditions, gravity assists at specific epochs, to name a few. We derive an analytical optimal control law for minimum solar-angle sail transfers by applying Pontryagin's optimality principle. Our theoretical results illuminate that a quantity termed solar sailing primer vector characterizes the optimal solar-sail control law for both minimum-time and minimum solar-angle transfers, as is the case in Lawden's primer vector theory for conventional low-thrust transfers. We numerically demonstrate these theoretical results by applying them to asteroid rendezvous transfers for NASA's NEA Scout mission. The numerical examples also reveal the numerical advantage of using the minimum solar-angle objective over the minimum-time one for solar-sail trajectory design because of the smoother optimal control profile. Solar sailing primer vector theory provides a tool to characterize the optimal control law independent of particular state representations or solution methods, enabling mission designers to combine it with a wealth of techniques developed for low-thrust trajectory optimization. • Propose an indirect trajectory optimization formulation based on solar sail primer vector theory. • The formulation minimizes the solar angle over a transfer with fixed time-of-flight. • The formulation derives an analytical optimal control law via Pontryagin's minimum principle. • Numerical examples demonstrate the analytical results in a NASA's NEA Scout exploration scenario. [ABSTRACT FROM AUTHOR]

Passive rehabilitation training in the early poststroke period can promote the reshaping of the nervous system. The trajectory should integrate the physicians' experience and the patient's characteristics. And the training should have high accuracy on the premise of safety. Therefore, trajectory customization, optimization, and tracking control algorithms are conducted based on a new upper limb rehabilitation robot. First, joint friction and initial load were identified and compensated. The admittance algorithm was used to realize the trajectory customization. Second, the improved butterfly optimization algorithm (BOA) was used to optimize the nonuniform rational B-spline fitting curve (NURBS). Then, a variable gain control strategy is designed, which enables the robot to track the trajectory well with small human–robot interaction (HRI) forces and to comply with a large HRI force to ensure safety. Regarding the return motion, an error subdivision method is designed to slow the return movement. The results showed that the customization force is less than 6 N. The trajectory tracking error is within 12 mm without a large HRI force. The control gain starts to decrease in 0.5 s periods while there is a large HRI force, thereby improving safety. With the decrease in HRI force, the real position can return to the desired trajectory slowly, which makes the patient feel comfortable. [ABSTRACT FROM AUTHOR]

Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced by restricting the discrete global optimization to the graph, with corresponding implications on choosing an appropriate graph density. A prime example is flight planning, i.e., the computation of optimal routes in view of flight time and fuel consumption under given weather conditions. Highly efficient discrete shortest path algorithms exist and can be used directly for computing starting points for locally convergent optimal control methods. We derive a priori and localized error bounds for the flight time of discrete paths relative to the optimal continuous trajectory, in terms of the graph density and the given wind field. These bounds allow designing graphs with an optimal local connectivity structure. The properties of the bounds are illustrated on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter error bounds by a posteriori estimators. [ABSTRACT FROM AUTHOR]

A robotic system constructed as a wheeled inverted pendulum (WIP) serves as an impressive demonstrator, since this kind of system is inherently nonlinear, unstable, and nonminimum phase. These properties may pose several difficulties, when it comes to control and trajectory planning. This paper shows a method for deriving a highly dynamic trajectory compliant with the system dynamics by means of solving an optimal control problem (OCP) using multiple shooting. The assumed task includes that the WIP should pass a height-restricting barrier. This can be achieved by leaning back or forth, in order to reduce the overall height of the WIP. The constraints inherent to the definition of this trajectory are nonconvex due to the shape of the robot. The constraint functions have a local minimum in an infeasible region. This can cause problems when the initial guess is within this infeasible region. To overcome this, a multistage approach is proposed for this special OCP to evade the infeasible local minimum. After solving four stages of subsequent optimization problems, the optimal trajectory is obtained and can be used as feedforward for the real system. [ABSTRACT FROM AUTHOR]

This paper presents research on the application of trajectory design, optimization, and control to an orbital transfer from Mars–Phobos Distant Retrograde Orbits to the surface of Phobos. Given a Distant Retrograde Orbit and a landing location on the surface of Phobos, landing trajectories for which total Δ v for a direct 2-burn maneuver is minimized are computed. This is accomplished through the use of Particle Swarm Optimization in which the required Δ v and time of flight are optimization parameters. The non-uniform gravitational environment of Phobos is considered in the computation. Results show how direct transfers can be achieved with Δ v on the order of ∼30 m/s. [ABSTRACT FROM AUTHOR]