Guidance Problem Research Articles

Three six-degree-of-freedom dynamic descent convex optimization guidance methods

A key technology for soft landing of powered descent of aircraft is to solve the six-degree-of-freedom powered descent guidance problem in real time, which can be described as the fuel-saving trajectory optimization problem under multiple constraints. Three optimization models are established by selecting three independent variables: flight time, time substitution variable, and trajectory height. The original trajectory optimization problem is transformed into a solvable form of sequential convex optimization for iterative solution, forming three online guidance methods. The three guidance methods are compared in terms of convergence, real-time performance, optimality, and solution accuracy. The results show that all three guidance methods can solve the six-degree-of-freedom powered descent problem. The guidance method with flight time as the independent variable has the shortest calculation time and the least fuel consumption, but the powered descent flight time needs to be determined in advance. The guidance methods based on the other two types of independent variables can optimize the powered descent flight time, but they are all suboptimal solutions, and the calculation time is significantly increased. The solution accuracy of the three methods is similar under the same number of discrete points. If sequential convex optimization is used as the online guidance scheme for powered descent, how to determine the optimal flight time, approach the optimal solution for fuel, and further shorten the calculation time still needs to be further studied.

Distributed cooperative guidance strategy based on virtual negotiation and rolling optimization

The problem of multi-UAV cooperative guidance under target maneuvering conditions is studied, and a distributed cooperative guidance strategy based on virtual negotiation mechanism and rolling horizon optimization is proposed. Firstly, in order to improve the time coordination and guidance control effect at the same time, local coordination variables and objective functions are designed under the rolling horizon optimization framework, and a multi-constrained cooperative guidance optimization model in a limited time domain is constructed; secondly, in order to enhance the robustness of the guidance system to maneuvering targets, a disturbance observer based on nonlinear autoregressive neural network is designed; thirdly, for the control input coupling between UAVs, a virtual negotiation mechanism is proposed to achieve synchronous decision-making and eliminate internal "differences", and the root mean square propagation algorithm of Nesterov momentum is used to design the guidance command generation strategy; finally, digital simulation and semi-physical simulation experiments are carried out respectively. The results show that the proposed guidance strategy can cope with various interferences and improve the cooperative guidance effect through online prediction and optimization, and is expected to be further applied and tested in actual tasks.

Olfactory-based powered descent guidance for Mars methane plume exploration in long-time-average wind environment

This paper investigates an olfactory-based powered descent guidance method that enable a lander to autonomously locate and target the vent source of any methane plume in long-time-average wind environment on Mars. The episodic methane plumes emanating from the Martian surface invite the possibility of direct access to the subsurface methane reservoir to acquire pristine organic materials. Constrained by the insufficient knowledge of the accurate plume vent location, Mars landers must infer the target location — the plume source — autonomously during the powered descent. However, existing powered descent guidance methods require the target location as a terminal constraint, rendering them ineffective in plume exploration missions. We propose an olfactory-based powered descent guidance method that could steer a lander to target the methane vent source by tracking the gradient of methane concentration in long-time-average wind environment, imposing sub-optimal fuel consumption. A novel olfactory navigation method based on tracking the negative logarithmic concentration gradient, and the corresponding gradient measurement method, is proposed. By implementing the negative logarithmic gradient field, gradient-dependent dynamic equations for the powered descending lander are proposed. The gradient-dependent equations provide a way to transform the original optimal guidance problem, which is non-convex and terminal-free, into a convex and terminal-fixed problem. A suboptimal guidance law, similar to E-guidance, is then derived by solving this problem. The proposed guidance could target the vent source of any methane plume in long-time-average wind environment, imposing modest fuel consumption by feeding back the concentration gradient. Numerical simulations illustrate that, in comparison to the terminal-fixed E-guidance and the open-loop fuel-optimal guidance, the lander imposes additional fuel consumption of 2.57% and 12.15% respectively, using the proposed guidance law.

Three-dimensional cooperative guidance with impact angle constraints via value-policy decomposed multi-agent reinforcement learning

For a three-dimensional impact angle-constrained time-coordination guidance problem, a value-policy decomposed multi-agent twin delayed deep deterministic (VPD-MATD3) policy gradient algorithm is proposed in this paper, and a temporal-spatial cooperative guidance law is designed consequently. The derived cooperative engagement kinematics is formulated as a value-policy decomposed partially observable Markov decision process. Value decomposition and policy decomposition are correspondingly proposed to address the two bottlenecks of reward coupling and policy coupling in 3D guidance, thus improving the training process. The training environment with multiple uncertainties, such as observation noise, maneuverability perturbation, autopilot time lag, switching communication topology, and random initialization, is subsequently constructed. Time-energy type reward functions are designed, incorporating energy consumption as a direct optimization indicator via a penalty term. A long short-term memory network layer is inserted inside the policy networks to suppress the negative effect of observation noise. The policy training curves verify the significant effect of the proposed algorithm in improving training convergence. The policy testing results illustrate the robustness and generalization of the VPD-MATD3 cooperative guidance law and its ability to cope with randomly switched communication topologies. Moreover, the comparative testing further reveals its time-energy suboptimal property.

Task-driven geometric synthesis method of a bistable compliant mechanism for the rigid guidance problem

Abstract. Compliant bistable mechanisms are specialized mechanisms that have specific self-locking characteristics in two positions. They are widely used in aerospace, micro-electromechanical systems, and high-precision manufacturing. The coupling of kinematic with elastomechanical behaviors of compliant mechanisms, known as kinetostatics, increases the difficulty of synthesizing compliant mechanisms. Currently, most research relies on optimization approaches to find compliant mechanisms that meet motion requirements. To address this challenge, this paper proposes a geometric synthesis method for compliant bistable mechanisms to solve the rigid guidance problem. The pole similarity transformation characteristics of planar beams and the static equilibrium characteristic of bistable mechanisms at stable positions are utilized to decouple the kinematic synthesis and static analysis. The proposed method introduces a task-driven synthesis process, where the critical structural parameters in compliant mechanisms are determined based on the desired guidance positions of motion tasks. This approach eliminates the need for a tedious and time-consuming iterative optimization process. The resulting bistable mechanisms have two stable positions that correspond to the desired guidance positions of the motion task. To illustrate the effectiveness of the geometric synthesis method, a two-position problem of a compliant bistable mechanism is provided as an example.

Meta-Reinforcement Learning for Spacecraft Proximity Operations Guidance and Control in Cislunar Space

Innovative lightweight and model-free guidance algorithms are essential to achieve full autonomy of spacecraft and address future space exploration challenges. In the near future, this type of technology will be essential for cislunar space proximity operations, such as NASA’s Artemis program and its Lunar Gateway project. In this scenario, a meta-reinforcement learning algorithm is employed to address the real-time optimal guidance problem of a spacecraft in the cislunar environment. Non-Keplerian orbits pose complex dynamics, where classic control theory may be less adaptable and more computationally expensive compared to machine learning approaches. Meta-RL stands out for its ability to learn how to learn through experience, training on various tasks to enhance efficiency, and effectiveness in tackling new ones. By modeling a stochastic optimal control problem within the circular restricted three-body problem framework as a Markov decision process, an LSTM-based network agent is trained using proximal policy optimization, considering operational constraints and stochastic effects for safety and robustness evaluation. Additionally, an MLP-based agent and an optimal control pseudo-spectral solution are assessed for comparison. The resulting tool autonomously guides spacecraft in cislunar proximity operations, approximating the optimal control solution with a versatile algorithmic framework. This ensures both robustness and computational efficiency.

Analytical time-coordinated entry guidance for multi-hypersonic vehicles within three-dimensional corridor

A coordinated entry mission requires multiple hypersonic vehicles to arrive at the designated area simultaneously from different times and locations. To satisfy the coordinated entry mission, this paper investigates the coordinated entry guidance problem for multi-hypersonic vehicles. An analytical time-coordinated entry guidance method is proposed based on the algorithms of analytical prediction, profile correction, and coordination time determination. Firstly, considering the altitude variations of the trajectory, high-precision analytical solutions for the remaining flight time and range are derived based on quasi-equilibrium glide conditions. Compared to the traditional numerical integration prediction methods, this analytical prediction method achieves superior computational efficiency while ensuring high-precision prediction. Subsequently, a flight corridor based on longitudinal lift-to-drag ratio is constructed, extending from the traditional two-dimensional corridor to a three-dimensional one. Within the corridor, the analytical lift-to-drag ratio profile is corrected by minimizing the prediction errors, and the guidance commands for both angle of attack and bank angle can be generated directly without tracking law. With the above analytical solutions and algorithms, the coordinated entry guidance method enables rapid generation of guidance commands for each hypersonic vehicle. Finally, numerical simulations under dispersed launching time and launching location conditions are performed, and the simulation results verify the effectiveness and robustness of the proposed time-coordination entry guidance algorithm.

Enhanced Computational Biased Proportional Navigation with Neural Networks for Impact Time Control

Advanced computational methods are being applied to address traditional guidance problems, yet research is still ongoing regarding how to utilize them effectively and scientifically. A numerical root-finding method was proposed to determine the bias in biased proportional navigation to achieve the impact time control without time-to-go estimation. However, the root-finding algorithm in the original method might experience efficiency and convergence issues. This paper introduces an enhanced method based on neural networks, where the bias is directly output by the neural networks, significantly improving computational efficiency and addressing convergence issues. The novelty of this method lies in the development of a reasonable structure that appropriately integrates off-the-shelf machine learning techniques to effectively enhance the original iteration-based methods. In addition to demonstrating its effectiveness and performance of its own, two comparative scenarios are presented: (a) Evaluate the time consumption when both the proposed and the original methods operate at the same update frequency. (b) Compare the achievable update frequencies of both methods under the condition of equal real-world time usage.

Guidance-As-Progressive in Human Skill Training Based on Deep Reinforcement Learning

To achieve psychological inclusion and skill development orientation in human skill training, this paper proposes a haptic-guided training strategy generation method with Deep Reinforcement Learning (DRL)-based agent as the core and Zone of Proximal Development (ZPD) tuning as the auxiliary. The information of the expert and trainee is stored first with a designed database that can be accessed in real-time, which establishes the data foundation. Then, under the DRL framework, a strategy generation agent is designed, which consists of an actor-network and two Q-networks. The former network generates the agent’s decision policy, while the other two Q-networks work to approximate the state-action value function, and the parameters of all of them are administrated by the Soft Actor-Critic (SAC) algorithm. In addition, for the first time, the psychological ZPD evaluation method is integrated into the strategy generation of the DRL-based agent, which is utilized to describe the relationship between a trainees intrinsic skills and guidance. With it, the problem of transitional guidance or insufficient guidance can be handled well. Finally, simulation experiments validate the proposed method, demonstrating its efficiency in regulating the trainee under favorable training conditions.

Resilient pursuit evasion guidance with feedback game strategy

This paper proposed a resilient guidance strategy for planar pursuit evasion, in which the homing guidance problem is formulated as a Stackelberg game. As is known, the most salient challenge for pursuit evasion guidance is how to ensure an interception despite both players (i.e., missile and target) actively optimize their own interest with preferably incomplete information. Toward this, we introduce a game-theoretic guidance strategy that effectively integrates incentive feedback strategy into pursuit evasion game. In particular, the proposed resilient guidance law takes the form of Stackelberg game conjecture with missile/interceptor as the designated leader, and rigorously proves that leader's interest can be best served with a properly designed feedback gain, and an interception can be made possible in spite of incomplete knowledge on target's intentions (i.e., performance index). Simulation results verify the performance of the proposed strategy.

Deep Reinforcement Learning-Based Differential Game Guidance Law against Maneuvering Evaders

To achieve the intelligent interception of different types of maneuvering evaders, based on deep reinforcement learning, a novel intelligent differential game guidance law is proposed in the continuous action domain. Different from traditional guidance laws, the proposed guidance law can avoid tedious manual settings and save cost efforts. First, the interception problem is transformed into the pursuit–evasion game problem, which is solved by zero-sum differential game theory. Next, the Nash equilibrium strategy is obtained through the Markov game process. To implement the proposed intelligent differential game guidance law, an actor–critic neural network based on deep deterministic policy gradient is constructed to calculate the saddle point of the differential game guidance problem. Then, a reward function is designed, which includes the tradeoffs among guidance accuracy, energy consumption, and interception time. Finally, compared with traditional methods, the interception accuracy of the proposed intelligent differential game guidance law is 99.2%, energy consumption is reduced by 47%, and simulation time is shortened by 1.58 s. All results reveal that the proposed intelligent differential game guidance law has better intelligent decision-making ability.

Three-dimensional free-will arbitrary time cooperative guidance law against moving target

A novel three-dimensional free-will arbitrary time cooperative guidance law based on biased proportional navigation is proposed for intercepting a high-value moving target. In contrast to existing research, the presented method does not require controlling the interceptors' axial speed or prediction of the interception point. First, the engagement plane is constructed so that a three-dimensional guidance problem can be formulated as a planar problem. Second, a new accurate time-to-go estimation algorithm against the moving target is deduced based on the formulated problem model. Third, a free-will arbitrary time cooperative guidance law is designed utilizing the leader-follower architecture. Multiple missiles can intercept a moving target simultaneously and the intercept time of each missile will converge within a free-will arbitrary time. Fourth, the proposed cooperative guidance law under different communication circumstances is analyzed. When the communication resources are abundant, missiles can reach dynamic average consensus. Meanwhile, the system is robust against the communication imperfection. Finally, numerical simulations are presented to verify the effectiveness of the time-to-go estimation algorithm and proposed cooperative guidance law.

Data-Driven-Method-Based Guidance Law for Impact Time and Angle Constraints

To increase the hit efficiency and lethality of a flight vehicle, it is necessary to consider the vehicle’s guidance law concerning both impact time and angle constraints. In this study, a novel and straightforward impact time and angle control guidance law that is independent of time-to-go and small angle approximations is proposed with two stages using a data-driven method and proportional navigation guidance. First, a proportional navigation guidance-based impact angle control guidance law is designed for the second stage. Second, from various initial conditions on the impact angle control guidance simulation with various initial conditions, the input and output datasets are obtained to build a mapping network. Using the neural network technique, a mapping network model that can output the ideal flight path angle in flight is constructed for impact time control in the first stage. The proposed impact time and angle control guidance law reduces to the proportional navigation guidance law when the flight path angle error converges to zero. The simulation results show that the proposed guidance law delivers excellent performance under various conditions (including cooperative attack) and features better acceleration performance and less control energy than does the comparative impact time and angle control guidance law. The results of this research are expected to supplement those exploring various paradigms to solve the impact time and angle control guidance problem, as concluded in the current literature.

Study on the Construction Path of Master Studios for Vocational Employment and Entrepreneurship Guidance

In the process of cultivating highly skilled technical talents in higher vocational colleges, employment and entrepreneurship guidance plays a crucial role. However, there are still problems such as insufficient resources and unsatisfactory guidance effects in the current vocational colleges’ employment and entrepreneurship guidance. To solve these problems, this study proposes the construction of master studios for employment and entrepreneurship guidance and discusses their construction paths in detail. Through literature analysis, questionnaires, and interviews, this paper analyzes the current status and existing problems of employment and entrepreneurship guidance in vocational colleges, explores the concept, role, and necessity, and feasibility of master studios. The research results show that master studios can significantly improve students’ employment and entrepreneurship abilities and promote the teaching quality of vocational colleges. Based on this, this paper proposes a systematic construction path for master studios, including goal setting, organizational structure design, operation mode, resource allocation and guarantee, and the cultivation and development of the master team. Finally, by analyzing successful cases, the experience and insights of master studio construction are summarized to provide theoretical basis and practical guidance for the construction of master studios for employment and entrepreneurship guidance in vocational colleges.

Intelligent diving guidance with terminal angle and velocity constraints via deep reinforcement learning

An adaptive guidance strategy that integrates optimal guidance and deep reinforcement learning to address a highly dynamic terminal guidance problem that entails meeting terminal position, angle, and velocity constraints. The proposed strategy leverages optimal guidance commands to accomplish position and angle control while introducing a deep reinforcement learning-based bias for the velocity constraint. In the training process, a dual-velocity state space is constructed to enhance the adaptability of the strategy to different guidance tasks, while training is optimized using the prediction-correction and expert knowledge to improve the training efficiency and optimality of the strategy. Simulations demonstrate that the proposed guidance strategy can achieve simultaneous control of terminal position, angle and velocity, and adapt to different guidance tasks.

Dynamic Encircling Cooperative Guidance for Intercepting Superior Target with Overload, Impact Angle and Simultaneous Time Constraints

This paper proposes a dynamic encircling cooperative guidance (DECG) law to enable multiple interceptors to cooperatively intercept a superior target, considering low velocity, limited overload, impact angle and simultaneous arrival constraints. First, the feasible escaping area of the target is analyzed and a dynamic encircling strategy for the target is established. This strategy efficiently provides virtual escaping points, allowing interceptors to dynamically encircle the target without excessive energy consumption, ultimately leading to a successful interception. Second, to enhance the physical feasibility of the kinematic equations governing the interaction between interceptors and target at the virtual escaping points, the independent variable is substituted and the kinematic equations are remodeled. Convex optimization is employed to address the multi-constraint optimal guidance problem for each interceptor, thereby facilitating simultaneous interception. Compared with the existing guidance laws, DECG has a more practical and feasible cooperative strategy, is able to handle more constraints including the interceptor’s own constraints and cooperative constraints, and does not rely on the precise calculation of explicit remaining flight time in the guidance law implementation. Lastly, the effectiveness, superiority and robustness of the DECG law are evaluated through a series of numerical simulations, and its performance is compared with that of the cooperative proportional navigation guidance law (CPNG).

Minimum-Data-Driven Guidance for Impact Angle Control

This paper investigates the impact-angle-control guidance problem for varying-speed flight vehicles with constrained acceleration. A learning-based bias proportional navigation guidance (L-BPN) law is proposed to achieve impact-angle-constrained impact by constructing a deep neural network (DNN) for nonlinear mapping between the impact angle and the bias term. During the process of dataset establishment, the impact of state variables is evaluated by sensitivity analysis to minimize the quantity of training data. This approach also effectively accelerates sample generation and improves the training efficiency. The simulation results verify the effectiveness of the proposed L-BPN law and demonstrate its advantages over the existing algorithms.

Control of a three-wheeled omnidirectional mobile robot via a mixed FTB/H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal H_\\infty $$\\end{document} approach

In this paper, the problem of guidance and motion control of mobile robots is addressed and solved within the novel framework of the mixed finite-time/H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal H_\\infty $$\\end{document} control theory of nonlinear quadratic systems (NLQSs). Starting from a NLQS describing the dynamics of omnidirectional mobile platforms, the main tasks performed for controlling in closed loop the motion of omnidirectional robots can be conveniently formulated as a mixed finite-time/H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal H_\\infty $$\\end{document} control problem. A robust motion controller, which can effectively rejects disturbances deviating the robot platform from a planned path, can be designed after choosing a linear state-feedback structure for the controller. The synthesis problem is solved through some sufficient conditions contemplating both norm-bounded disturbances and sets constraining initial and terminal conditions, together with a finite-time bound on the output transient. Therefore, for all the allowable uncertainties, in presence of nonzero initial conditions and exogenous disturbance inputs which are possible within an unstructured environment, the motion control tasks can be accomplished through optimal H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal H_\\infty $$\\end{document} performance by simultaneously guaranteeing that the NLQS, which governs in closed loop the robot platform, is finite-time bounded. Finally, the applicability and control performance of the design approach have been evaluated through numerical simulations.

Multiple-stage spatial–temporal cooperative guidance without time-to-go estimation

This paper investigates the spatial–temporal cooperative guidance problem for multiple flight vehicles without relying on time-to-go information. First, a two-stage cooperative guidance strategy, namely the cooperative guidance and the Proportional Navigation Guidance (PNG) stage strategy, is developed to realize the spatial–temporal constraints in two dimensions. At the former stage, two controllers are designed and superimposed to satisfy both impact time consensus and impact angle constraints. Once the convergent conditions are satisfied, the flight vehicles will switch to the PNG stage to ensure zero miss distance. To further extend the results to three dimensions, a planar pursuit guidance stage is additionally imposed at the beginning of guidance. Due to the independence of time-to-go estimation, the proposed guidance strategy possesses great performance in satisfying complex spatial–temporal constraints even under flight speed variation. Finally, several numerical simulations are implemented to verify the effectiveness and advantages of the proposed results under different scenarios.

An Adaptive Route Guidance Model Considering the Effect of Traffic Signals Based on Deep Reinforcement Learning

Navigation or route guidance systems are designed to provide drivers with real-time travel information and the associated recommended routes for their trips. Classical route choice models typically rely on utility theory to represent drivers’ route choice behavior. Such choices, however, may not be optimal from both the individual and the system perspectives. This is simply due to the fact that drivers usually have imperfect knowledge about the time-varying traffic conditions. In this article, we explore and propose a new model-free deep reinforcement learning (DRL) approach to solving the adaptive route guidance problem based on microsimulation. The proposed approach consists of three interconnected algorithms, including a network edge labeling algorithm, a routing plan identification algorithm, and an adaptive route guidance algorithm. Simulation experiments on both a toy network and a real-world network of Suzhou, China, are performed to demonstrate the effectiveness of the proposed approach in terms of guiding a single vehicle as well as multiple vehicles through complex traffic environments. Comparative results confirm that the DRL approach outperforms the traditional shortest path method by further reducing the average travel time in the network.