Trajectory Optimization Approach Research Articles

Online Trajectory Optimization of an ASV Based on an Improved RBFNN

Optimization based on conventional neural networks can only guarantee calculation speed. However, the accuracy of network prediction is also a key index in online trajectory optimization. This paper proposes a novel online trajectory optimization approach based on an Improved Radial Basis Function Neural Network (IRBFNN). First, multiple optimal trajectories for different variations of Air-Breathing Supersonic Vehicles (ASVs) are generated, considering attitude, and collected as the dataset. Then, an IRBFNN is trained to predict trajectories online with the above dataset, in which an enhanced loss function is introduced to improve prediction accuracy. Finally, numerical simulations are presented to demonstrate the feasibility and superiority of the proposed online trajectory optimization method. The open-source code of the proposed method is shared in the form of a link to showcase its implementation.

Refined mode classification and performance analysis method of dual-mode scramjet vehicles for flight trajectory optimization

Hypersonic air-breathing vehicles, utilizing ramjet and scramjet propulsion systems, are emerging as a promising option for future hypersonic transportation due to high specific impulse. The performance of hypersonic aircraft is significantly influenced by their flight trajectory, as combustion efficiency and aerodynamic forces vary markedly with altitude. Although numerous studies have focused on optimizing these trajectories, they have not adequately considered the potential for operational failures in the propulsion system, such as unstart and blowout. This study introduces a trajectory optimization approach for hypersonic aircraft that proactively addresses and mitigates these operational failures. This is achieved by establishing an operational classification process for a dual-mode scramjet engine and proposing a failure mode avoidance strategy using a Gaussian process classifier. Optimized ascent trajectories are achieved through the development of a two-stage robust sequential convex programming approach. The results of trajectory optimization indicate that the failure mode avoidance strategy proposed is crucial in obtaining minimal time trajectories, and that the optimal trajectories include drop motion in the initial stage flight in order to increase combustion efficiency.

Input Design for Active Fault Detection: Reconciling System Control Objectives.

Active fault detection (AFD) is the newest frontier in the field of fault detection and has drawn increasing amounts of research attention. AFD technology can enhance fault detection performance by injecting a predesigned auxiliary input signal for a specific fault. In most existing studies, system control objectives are not fully considered in the auxiliary input design of AFD. This article investigates a new reconciliatory input design problem for both achieving control objectives and improving fault detection performance. An exemplary algorithm for the reconciliatory input design is proposed, by using a trajectory optimization approach. The proposed algorithm consists of three parts: 1) residual generation; 2) trajectory optimization; and 3) input design. A state observer is designed to obtain residual signals used as fault indicators. Considering the optimization index composed of the fault indicators, a trajectory optimization technique is carried out to find an optimal system trajectory which can improve the fault detection ability to the greatest extent. The control input is designed to track this optimal trajectory while complying with system physical constraints. In order to demonstrate the effectiveness of the proposed methodology, simulation cases on an underwater manipulator are conducted.

Efficient Motion Primitives-Based Trajectory Planning for UAVs in the Presence of Obstacles

The achievement of full autonomy in Unmanned Aerial Vehicles (UAVs) is significantly dependent on effective motion planning. Specifically, it is crucial to plan collision-free trajectories for smooth transitions from initial to final configurations. However, finding a solution executable by the actual system adds complexity: the planned motion must be dynamically feasible. This involves meeting rigorous criteria, including vehicle dynamics, input constraints, and state constraints. This work addresses optimal kinodynamic motion planning for UAVs in the presence of obstacles by employing a hybrid technique instead of conventional search-based or direct trajectory optimization approaches. This technique involves precomputing a library of motion primitives by solving several Two-Point-Boundary-Value Problems (TPBVP) offline. This library is then repeatedly used online within a graph-search framework. Moreover, to make the method computationally tractable, continuity between consecutive motion primitives is enforced only on a subset of the state variables. This approach is compared with a state-of-the-art quadrotor-tailored search-based approach, which generates motion primitives online through control input discretization and forward propagation of the dynamic equations of a simplified model. The effectiveness of both methods is assessed through simulations and real-world experiments, demonstrating their ability to generate resolution-complete, resolution-optimal, collision-free, and dynamically feasible trajectories. Finally, a comparative analysis highlights the advantages, disadvantages, and optimal usage scenarios for each approach.

A three-stage sequential convex programming approach for trajectory optimization

Recently, sequential convex programming (SCP) has become a potential approach in trajectory optimization because of its high efficiency. To improve stability and discretization accuracy, a three-stage SCP approach based on the hp-adaptive Radau pseudospectral discretization is proposed in this paper. In most instances, the initial subproblem may risk infeasibility due to the undesignated initial guess. Therefore, we design a constraint relaxation stage for the SCP to enhance the feasibility of the subproblem as much as possible. Once the subproblem can be directly solved, the iteration enters the second stage, during which a mesh refinement algorithm based on discretization error analysis is utilized to decrease the discretization error to the tolerance. In the final stage, the damping term is introduced into the objective of the subproblem to suppress the oscillation of the solution and accelerate the convergence. A dual-channel control reentry trajectory optimization and an ascent trajectory optimization are taken as examples, and the simulation results show that the proposed approach outperforms conventional SCP approaches in terms of accuracy and efficiency.

Multi-Objective Robust Trajectory Design for Powered Descent and Landing

A robust trajectory optimization approach for guidance algorithm gain and target vector selection for powered descent and landing is developed. A genetic algorithm is used to determine optimized guidance algorithm parameters to minimize the impact of initial condition, environment, navigation, and vehicle property uncertainty on flight performance for a given sensor suite. Vehicle state uncertainties are computed efficiently using linear covariance analysis techniques. When implemented in the guidance algorithm, the optimized gains and target vectors shape a trajectory that has more favorable conditions for a given navigation sensor suite, resulting in improved flight performance. As a demonstration of this method, the optimized guidance parameters are found for a multiphase trajectory from powered descent initiation to touchdown for a robotic lunar landing mission. Single-objective optimization results demonstrate a reduction in uncertainty and an improvement in nominal performance. Multi-objective optimization results showing the tradeoff between terminal position uncertainty and total propellant usage are presented for multiple sensor suite compositions. Further, guidance parameters selected using the developed robust trajectory design approach may enable acceptable flight performance with fewer and/or lower-quality sensors. The resulting Pareto fronts present the optimal trade space early in the mission design process to enable informed decision-making.

Comparative Analysis of Metaheuristic Optimization Methods for Trajectory Generation of Automated Guided Vehicles

This paper presents a comparative analysis of several metaheuristic optimization methods for generating trajectories of automated guided vehicles, which commonly operate in industrial environments. The goal is to address the challenge of efficient path planning for mobile robots, taking into account the specific capabilities and mobility limitations inherent to automated guided vehicles. To do this, three optimization techniques are compared: genetic algorithms, particle swarm optimization and pattern search. The findings of this study reveal the different efficiency of these trajectory optimization approaches. This comprehensive research shows the strengths and weaknesses of various optimization methods and offers valuable information for optimizing the trajectories of industrial vehicles using geometric occupancy maps.

A Hybrid Secure Resource Allocation and Trajectory Optimization Approach for Mobile Edge Computing Using Federated Learning Based on WEB 3.0

A Hybrid Secure Resource Allocation and Trajectory Optimization Approach for Mobile Edge Computing Using Federated Learning Based on WEB 3.0

Mitigating oscillations of mixed traffic flows at a signalized intersection: A multiagent trajectory optimization approach based on oscillation prediction

To mitigate the traffic oscillations generated when traffic flow encounters a red light at a signalized intersection, many studies have used reinforcement learning to control connected and automated vehicles (CAVs) trajectories to avoid oscillations. These methods, which are effective in mitigating oscillations in a pure CAV environment, perform poorly when applied to mixed traffic streams, due to the fact that most of the methods ignore that human vehicles (HVs) in mixed traffic flows stop at red lights and trigger oscillations, resulting in significant “trajectory fluctuation” phenomena in some CAVs, which will lead to poor effectiveness in mitigating oscillations.To address this problem, We propose a method that combines oscillation prediction and multiagent trajectory optimization to mitigate the oscillations generated by HVs. First, we predict the oscillation caused by HVs stopping during a red light, and after that, we use the Newell model to predict the propagation range of the oscillation. According to whether the HV ahead produces oscillation or not, we classify CAVs into two types of agents and design the control scheme separately. The first type of CAVs are immediately adjacent to the oscillation, and we use a jam-absorption driving (JAD) strategy to treat them as absorbing vehicles to absorb the oscillation. While the second type of CAVs are vehicles other than the first type of CAVs, we use the deep reinforcement learning (DRL) method to control them to arrive at the intersection within the predicted green light time. We tested the method in a mixed traffic flow simulation environment. Experimental results show that this method can effectively suppress the phenomenon of “trajectory fluctuations” under different CAV penetration rates, achieving the goal of effectively mitigating oscillations thus significantly improving traffic efficiency and reducing vehicle fuel consumption. Meanwhile, the method also has the advantages of fast convergence during training and high stability during testing compared with traditional reinforcement learning methods.

Mitigation of signalized intersection collision risks with trajectory based dynamic dilemma zone protection

Dilemma zone is one of the major factors causing red-light violations, right-angled and rear-end crashes at signalized intersections. In this paper, a dilemma zone protection system is introduced, which employs a dynamic vehicular trajectory optimization approach to guide vehicles approaching a signalized intersection. Unlike conventional methods that aim to eliminate dilemma zones, this system adjusts the speed profiles of individual vehicles to shift the distribution of dilemma zones and prevent vehicles from becoming trapped. Extensive simulated experiments were conducted to test and validate the proposed system for both individual vehicles and platoons. Results demonstrate that the system offers superior protection for individual vehicles, with full coverage across various settings of initial speeds and distances to the stop line. In the traffic environment with realistic platooning settings, the proposed system significantly reduces the number of vehicles in the dilemma zone, resulting in improved operational and safety benefits such as reduced risks of hazardous maneuvers and savings in vehicular delay.

Stochastic Optimal Control for Multivariable Dynamical Systems Using Expectation Maximization.

Trajectory optimization is a fundamental stochastic optimal control (SOC) problem. This article deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic models. Exact/complete solutions to these kind of control problems have been deemed analytically intractable in literature because they come under the category of partially observable Markov decision processes (MDPs). Therefore, effective solutions with reasonable approximations are widely sought for. We propose a reformulation of stochastic control in a reinforcement learning setting. This type of formulation assimilates the benefits of conventional optimal control procedure, with the advantages of maximum likelihood approaches. Finally, an iterative trajectory optimization paradigm called as SOC-expectation maximization (SOC-EM) is put forth. This trajectory optimization procedure exhibits better performance in terms of reduction in cumulative cost-to-go which is proven both theoretically and empirically. Furthermore, we also provide novel theoretical work which is related to uniqueness of control parameter estimates. Analysis of the control covariance matrix is presented, which handles stochasticity through efficiently balancing exploration and exploitation.

Observability-Enhancement Boresight Calibration of Camera-IMU System: Theory and Experiments

Airborne target tracking with vision sensors is one of the indispensable and critical components in unmanned aerial vehicles (UAVs). It is critical to calibrate the misalignment angles between the onboard camera and Inertial Measurement Unit (IMU) to improve the accuracy of target tracking. In this paper, the observability of boresight misalignment angle estimation using a cooperative target is first analyzed. Based on the observability Gramian, an optimization criterion for maximizing the degree of observability is determined, and the optimal geometries between the UAV and the target are derived. Taking the physical constraints of the UAV into consideration, an online trajectory optimization approach for a UAV with a vision sensor is proposed to achieve in-flight calibration of the misalignment angles. Both numerical simulations and experiments are conducted to validate the proposed method.

Polytopal approximation for thrust magnitude constraints in rocket trajectory optimization

This paper proposes a linear programming approach for onboard optimization of rocket trajectories, motivated by the need for reliable and computationally efficient trajectory optimization methods in real-time applications. To reformulate rocket trajectory optimization problems within a linear programming framework, a polytopal approximation method is developed. The polytopal approximation method approximates the thrust magnitude constraint using a set of artificial variables and linear constraints. Compared with a state-of-the-art approximation method, the polytopal approximation method demonstrates a higher accuracy-to-size ratio, enabling rocket trajectory optimization problems to be cast into linear subproblems without significantly increasing problem sizes. As linear subproblems can be readily solved by linear programming solvers, the proposed trajectory optimization approach inherits the solver’s reliability and computational efficiency, making it potentially useful for critical onboard applications. An ascent trajectory optimization problem is provided as an illustrative example to demonstrate the effectiveness of the proposed linear programming approach.

Trajectory Optimization for Multi-Sensor Multi-Target Search and Tracking with Bearing-Only Measurements

This paper proposes a trajectory optimization approach for multi-sensor multi-target search and tracking using bearing-only sensors. Based on the framework of the joint integrated probabilistic data association (JIPDA) filter, the intensity of potential unknown targets is updated according to the trajectories of the UAVs. The performance indices for target search and tracking are constructed based on, respectively, the intensity of unknown targets in the search area and the tracking error covariance. A dimensionless criterion, evaluating the search and tracking performance, is formulated and leveraged as the objective function of the UAV trajectory optimization problem. Simulations were carried out in different search and tracking scenarios to demonstrate the effectiveness of the proposed approach.

Conventional, Heuristic and Learning-Based Robot Motion Planning: Reviewing Frameworks of Current Practical Significance

Motion planning algorithms have seen considerable progress and expansion across various domains of science and technology during the last few decades, where rapid advancements in path planning and trajectory optimization approaches have been made possible by the conspicuous enhancements brought, among others, by sampling-based methods and convex optimization strategies. Although they have been investigated from various perspectives in the existing literature, recent developments aimed at integrating robots into social, healthcare, industrial, and educational contexts have attributed greater importance to additional concepts that would allow them to communicate, cooperate, and collaborate with each other, as well as with human beings, in a meaningful and efficient manner. Therefore, in this survey, in addition to a brief overview of some of the essential aspects of motion planning algorithms, a few vital considerations required for assimilating robots into real-world applications, including certain instances of social, urban, and industrial environments, are introduced, followed by a critical discussion of a set of outstanding issues worthy of further investigation and development in future scientific studies.

Multistage approach for trajectory optimization for a wheeled inverted pendulum passing under an obstacle

AbstractA 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.

Analytical Uncertainty Propagation and Robust Trajectory Optimization for Continuous-Thrust Relative Motion

Analytical continuous-thrust uncertainty propagation is derived under the control error and the initial navigation error for the linear relative motion near elliptic orbits. Two continuous-thrust control error models are considered: control-linear error model and thrust-magnitude-direction error model. The analytical uncertainty propagation expression is obtained by using the thrust series expansion with respect to eccentric anomaly. Based on the derived analytical uncertainty propagation, the robust energy-optimum and fuel-optimum orbital rendezvous problems are formulated as nonlinear programming ones. In particular, the robust energy-optimum rendezvous problem under the control-linear error model is converted into solving a one-dimensional equation. Several numerical examples indicate that the derived analytical uncertainty propagation is accurate and that the developed robust trajectory optimization approach is computationally efficient.

Capacity Maximization in RIS-UAV Networks: A DDQN-Based Trajectory and Phase Shift Optimization Approach

Reconfigurable Intelligent Surface (RIS) has grown rapidly due to its performance improvement for wireless networks, and the integration of unmanned aerial vehicle (UAV) and RIS has obtained widespread attention. In this paper, the downlink of non-orthogonal multiple access (NOMA) UAV networks equipped with RIS is considered. The objective is to optimize the UAV trajectory with RIS phase shift to maximize the system capacity under the UAV energy consumption constraint. By deep reinforcement learning, a capacity maximization scheme under energy consumption constraints based on double deep Q-Network (DDQN) is proposed. The joint optimization of UAV trajectory with RIS phase shift design is achieved by DDQN algorithm. From the numerical results, the proposed optimization scheme can increase the system capacity of the RIS-UAV-assisted NOMA networks.

A Unified Trajectory Optimization Approach for Long-Term and Reactive Motion Planning of Legged Locomotion

A Unified Trajectory Optimization Approach for Long-Term and Reactive Motion Planning of Legged Locomotion

Optimizing training trajectories in variational autoencoders via latent Bayesian optimization approach *

Unsupervised and semi-supervised ML methods such as variational autoencoders (VAE) have become widely adopted across multiple areas of physics, chemistry, and materials sciences due to their capability in disentangling representations and ability to find latent manifolds for classification and/or regression of complex experimental data. Like other ML problems, VAEs require hyperparameter tuning, e.g. balancing the Kullback–Leibler and reconstruction terms. However, the training process and resulting manifold topology and connectivity depend not only on hyperparameters, but also their evolution during training. Because of the inefficiency of exhaustive search in a high-dimensional hyperparameter space for the expensive-to-train models, here we have explored a latent Bayesian optimization (zBO) approach for the hyperparameter trajectory optimization for the unsupervised and semi-supervised ML and demonstrated for joint-VAE with rotational invariances. We have demonstrated an application of this method for finding joint discrete and continuous rotationally invariant representations for modified national institute of standards and technology database (MNIST) and experimental data of a plasmonic nanoparticles material system. The performance of the proposed approach has been discussed extensively, where it allows for any high dimensional hyperparameter trajectory optimization of other ML models.