Problem Of Trajectories Research Articles

The problem of personal trajectories of additional education of teachers

Introduction. The possibilities of implementing additional education in the context of modern trends in the development of education in Russia and the world can be identified by the following prospects: 1) the formation and improvement of a multilevel/continuous education system; 2) improvement of educational distance technologies, including and especially information/online technologies, platforms, infrastructures that increase access to educational resources; 3) “peer education”, group or mutual education; 4) networking and the formation of a unified system of educational services institutions within the complex “school – college – university – enterprise”; 5) activation of cooperation with educational institutions and systems of Russia and abroad, harmonization of world and national education standards and their variations; 6) a combination of inclusive and special education; 7) a combination of specialized training and general cultural training of a person as a subject of culture; 8) development of the asynchronous education system, including global/additional and alternative education; 9) reorientation to teaching and upbringing as a process of formation and development of metacompetencies, that is, metaknowledge and metaskills that make it possible to successfully study and teach others; 10) the formation and development of additional education as a global one. Research methodology . The work contains a theoretical understanding of the problem of personal trajectories of education of teachers in additional education. Our study is an attempt to implement a systematic approach to the study of problems in the practice of training modern teachers. Results of the study. We can define the concept of an individual educational trajectory in the context of the problems of high-quality training of a modern teacher in general and additional education as an individualized (individually-specific) way of a person’s search and implementation of his personal, interpersonal and professional potential in educational and professional activities, his creative and reproductive, pedagogical and other abilities, realized with the support and participation of a tutor, supervisor or other mentor, or completely independently (in the context of self-education). Conclusion . Even the created and implemented trajectory, being presented in the didactic and mentoring interaction of the teacher (subject teacher, class teacher/curator, other mentor-tutor) and the student, requires work on its verification, reflection, correction, etc. The activation of educational and professional activity of students can take different forms, however, in general, it is associated with the formation and implementation of an individual educational trajectory of personal, interpersonal and professional formation and development of a person. An educational trajectory that activates and creates conditions for the all-round development of a person is formed and implemented under the condition of synchronizing the lines of personal, interpersonal and educational-professional improvement in general and additional education, harmonizing the space-time of education and the space-time of being of each person as a student. Such synchronicity and harmony is the result of the conscious, multilateral and constant efforts of all subjects of education at all stages of development and implementation of the educational trajectory of the future teacher, up to reflection and correction of the educational route and its different stages.

Geometric approach to the solution of the Dubins car problem in the formation of program trajectories

The paper considers an approach to the formation of control program trajectories of moving objects (UAVs, ships) as a solution to the optimal problem in terms of Dubins path search. Instead of directly solving the Pontryagin’s maximum principle, it is proposed to use a simple analysis of possible control strategies in order to determine among them the optimal one in terms of time spent on a trajectory. The problem of finding the shortest trajectory of movement of an object from one point to another is solved, and for both points their coordinates and heading angles at these points are given, as well as three absolute values of the circulation radii corresponding to the given control signals on each of the three sections of the trajectory. The problem of finding the Dubins curves is reduced to determining the parameters of two intermediate points at which the control changes. All possible directions of control change options are considered, taking into account the existing constraints, also the lengths of the corresponding motion trajectories are calculated, and the optimal one is selected. The problem of constructing a trajectory is solved as well, which ensures a smooth conjugation of two linear fragments of trajectories and passes through the point of their intersection. The solution of the optimal trajectory problem using the Dubins car gives a single trajectory. In contrast to this, the proposed method considers several trajectories admissible by the constraints, from which the optimal one is selected by exhaustive search. The presence of several feasible strategies gives advantages for each specific situation of choosing a trajectory depending on the environment. Instead of directly solving the Pontryagin’s maximum principle and constructing a three-dimensional optimal trajectory, the authors used a simple analysis of possible control strategies in order to determine among them the optimal one in terms of elapsed time. The approach was motivated by the limited number of possible control strategies for Dubins paths, as well as the simplicity of analytical calculations for each of them, which allows performing these calculations in real time. The high speed of calculations for the problem of determining the optimal trajectory is due to the fact that the proposed method does not require complex calculations to solve the problem of nonlinear optimization, which follows from the Pontryagin’s principle.

Fuel-Optimal Ascent Trajectory Problem for Launch Vehicle via Theory of Functional Connections

In this study, we develop a method based on the Theory of Functional Connections (TFC) to solve the fuel-optimal problem in the ascending phase of the launch vehicle. The problem is first transformed into a nonlinear two-point boundary value problem (TPBVP) using the indirect method. Then, using the function interpolation technique called the TFC, the problem’s constraints are analytically embedded into a functional, and the TPBVP is transformed into an unconstrained optimization problem that includes orthogonal polynomials with unknown coefficients. This process effectively reduces the search space of the solution because the original constrained problem transformed into an unconstrained problem, and thus, the unknown coefficients of the unconstrained expression can be solved using simple numerical methods. Finally, the proposed algorithm is validated by comparing to a general nonlinear optimal control software GPOPS-II and the traditional indirect numerical method. The results demonstrated that the proposed algorithm is robust to poor initial values, and solutions can be solved in less than 300 ms within the MATLAB implementation. Consequently, the proposed method has the potential to generate optimal trajectories on-board in real time.

Hypersonic Vehicle Trajectory Prediction Algorithm Based on Hough Transform

Trajectory prediction is a prerequisite for missile and high-speed vehicle guidance interception. To address the trajectory problem for the near space hypersonic unpowered gliding vehicle. Firstly, the trajectory prediction mechanism is analyzed. Based on the existing NSHV trajectory prediction method, the key techniques of trajectory prediction are discussed from the perspectives of prediction parameter selection and prediction parameter description. Then, a trajectory prediction method based on Hough transform is proposed. The core of the method is to select the longitude latitude, and high direction positions as prediction parameters, and use the Hough transform to fit the prior basis functions. In the latitude and longitude direction, the rationality of predicting parameters is discussed from two aspects: position extreme point and lateral maneuverability. In the height direction, for the NSHV oscillation drop characteristic, two Hough transforms are used to separate the periodic term from the linear term. In addition, we give the approximate interval of the parameter values of the method, and design a parameter adaptive scheme. Finally, trajectory prediction is performed on two different control patterns. The error of the prediction time of 100s is within 25km, and the results show the effectiveness of the proposed method.

Trajectory Design for Throughput Maximization in UAV-Assisted Communication System

In this paper, we study an unmanned aerial vehicle (UAV) assisted communication system to provide service to the ground users. We address the problem of UAV deployment in three-dimensional (3D) space to provide on-demand coverage to the users such that their sum rate is maximized. First, we find the optimal UAV location in 3D space where the sum rate is maximized for all ground users. Thereafter an optimal trajectory is designed for the UAV to travel from the initial to the optimal location, such that the overall average sum rate during the flight is maximized while meeting the on-board energy availability and flight duration constraints. The problem formulated is non-convex. To obtain the optimal location, we approximate the rate expression to obtain the concave regions and apply alternating optimization. An iterative scheme is proposed to obtain the optimal UAV trajectory, which computes the optimal location in each time slot sequentially, followed by a greedy approach to reach the final location. Simulation results provide useful insights into the optimal location and the UAV trajectory problem and show on an average 16.5% improvement over the benchmark schemes.

Robust adaptive dual layer sliding mode controller: Methodology and application of uncertain robot manipulator

This paper presents a novel robust adaptive dual layer sliding mode control (ADLSMC) for the problem of high accuracy tracking trajectory of robot manipulator in the presence of uncertainties and external disturbances. This new control scheme has a dual layer structure. The first layer drives the robot manipulator system reaches the global nonlinear sliding surface in finite time, and the second layer tackles the values of the two control gains overestimation problem. Moreover, compared with the traditional super-twisting with time delay estimation algorithm, the proposed controller can realize not only set-point tracking but also dynamic tracking, which is very widely used in practice. The stability of the closed–loop system and the finite time convergence are analyzed using Lyapunov techniques. The effectiveness of the proposed method is demonstrated by simulations and experimental studies.

Mesh Manifold Based Riemannian Motion Planning for Omnidirectional Micro Aerial Vehicles

This letter presents a novel on-line path planning method that enables aerial robots to interact with surfaces. We present a solution to the problem of finding trajectories that drive a robot towards a surface and move along it. Triangular meshes are used as a surface map representation that is free of fixed discretization and allows for very large workspaces. We propose to leverage planar parametrization methods to obtain a lower-dimensional topologically equivalent representation of the original surface. Furthermore, we interpret the original surface and its lower-dimensional representation as manifold approximations that allow the use of Riemannian Motion Policies (RMPs), resulting in an efficient, versatile, and elegant motion generation framework. We compare against several Rapidly-exploring Random Tree (RRT) planners, a customized CHOMP variant, and the discrete geodesic algorithm. Using extensive simulations on real-world data we show that the proposed planner can reliably plan high-quality near-optimal trajectories at minimal computational cost. The accompanying multimedia attachment demonstrates feasibility on a real OMAV. The obtained paths show less than 10% deviation from the theoretical optimum while facilitating reactive re-planning at kHz refresh rates, enabling flying robots to perform motion planning for interaction with complex surfaces.

Ground Station Visible Region Determination Method in Chang’E-5 Reentry

A method based on the reentry trajectory is proposed for analysis the region for ground-based Telemetry, Tracking and Command（TT&C）station, aiming at the problem of multi-day trajectory TT&C station layout optimization and resource allocation in emergency TT&C in the process of the TT&C general analysis and design in reentry. Firstly, the model between the position of the station, the reentry module and the elevation angle of the station is propagated, the detail method of the calculation of the station distribution area, in where reentry module is visible, is put forward, and finally the results of the visible region of the ground station are calculated according to the theoretical reentry trajectory. The method proposed in this paper can quickly obtain the station area visible to the reentry module, which is of great significance for the overall design and of emergency control in reentry.

Security Efficiency Maximization for Multi-UAV–Aided Network With Mobile Edge Computing

In this study, we consider a security efficiency maximization problem in a multiple unmanned aerial vehicle (UAV)-aided system with mobile edge computing (MEC). Two kinds of UAVs, including multiple computing UAVs (CUAVs) and multiple jamming UAVs (JUAVs), are considered in this system. CUAVs would receive partial computation bits and send the computation results to ground users. JUAVs do not undertake computing tasks and only send interference signals to counter potential ground eavesdroppers. We jointly optimize the ground user scheduling, UAV power, and UAV trajectory to maximize the security efficiency. The original problem is non-convex and difficult to solve. We first use the Dinkelbach method combined with continuous convex approximation technology, and then propose three corresponding subproblems, including user scheduling subproblem, UAV power subproblem, and UAV trajectory problem. Further, we apply the branch and bound method to solve the user scheduling subproblem, and optimize the two remaining subproblems by introducing auxiliary variables and Taylor expansion. The simulation results show that the proposed scheme can obtain better secure off-loading efficiency with respect to the existing schemes.

Low-Thrust Gravity-Assist Trajectory Design Using Optimal Multimode Propulsion Models

The complexities in using indirect optimization methods get compounded for practical co-optimization problems in the presence of continuous and discrete design variables. In this paper, realistic multimode electric propulsion systems are incorporated within the formulation of gravity-assist, low-thrust trajectory design problems. Electric thrusters operate over a large set of discrete operation modes, and each mode is characterized by specific values for power, thrust, specific impulse, and mass flow rate. Unlike the traditional methods that approximate the aggregate behavior of electric thrusters’ performance (using polynomials fits), a novel construct is proposed to incorporate optimal discrete operating modes within indirect optimization. The capability of the tool and the efficacy of the proposed methodology are demonstrated by solving a multiyear, fuel-optimal trajectory problem from Earth to asteroid Psyche via a Mars gravity-assist maneuver and using a Hall-effect SPT-140 thruster with 21 operating modes. Comparisons with the traditional polynomial-based thruster modeling are presented.

Human Trajectory Forecasting in Crowds: A Deep Learning Perspective

Since the past few decades, human trajectory forecasting has been a field of active research owing to its numerous real-world applications: evacuation situation analysis, deployment of intelligent transport systems, traffic operations, to name a few. In this work, we cast the problem of human trajectory forecasting as learning a representation of human social interactions. Early works handcrafted this representation based on domain knowledge. However, social interactions in crowded environments are not only diverse but often subtle. Recently, deep learning methods have outperformed their handcrafted counterparts, as they learn about human-human interactions in a more generic data-driven fashion. In this work, we present an in-depth analysis of existing deep learning-based methods for modelling social interactions. We propose two domain-knowledge inspired data-driven methods to effectively capture these social interactions. To objectively compare the performance of these interaction-based forecasting models, we develop a large scale interaction-centric benchmark <i>TrajNet</i>&#x002B;&#x002B;, a significant yet missing component in the field of human trajectory forecasting. We propose novel performance metrics that evaluate the ability of a model to output socially acceptable trajectories. Experiments on TrajNet&#x002B;&#x002B; validate the need for our proposed metrics, and our method outperforms competitive baselines on both real-world and synthetic datasets.

Applicability Evaluation of Several Spatial Clustering Methods in Spatiotemporal Data Mining of Floating Car Trajectory

Spatial analysis is an important means of mining floating car trajectory information, and clustering method and density analysis are common methods among them. The choice of the clustering method affects the accuracy and time efficiency of the analysis results. Therefore, clarifying the principles and characteristics of each method is the primary prerequisite for problem solving. Taking four representative spatial analysis methods—KMeans, Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Clustering by Fast Search and Find of Density Peaks (CFSFDP), and Kernel Density Estimation (KDE)—as examples, combined with the hotspot spatiotemporal mining problem of taxi trajectory, through quantitative analysis and experimental verification, it is found that DBSCAN and KDE algorithms have strong hotspot discovery capabilities, but the heat regions’ shape of DBSCAN is found to be relatively more robust. DBSCAN and CFSFDP can achieve high spatial accuracy in calculating the entrance and exit position of a Point of Interest (POI). KDE and DBSCAN are more suitable for the classification of heat index. When the dataset scale is similar, KMeans has the highest operating efficiency, while CFSFDP and KDE are inferior. This paper resolves to a certain extent the lack of scientific basis for selecting spatial analysis methods in current research. The conclusions drawn in this paper can provide technical support and act as a reference for the selection of methods to solve the taxi trajectory mining problem.

Определение траекторий наибыстрейшего движения материальной точки в горизонтальном векторном поле

Предложено решение известной навигационной задачи Цермело классическими вариационными методами. Классическая задача Цермело в рамках теории оптимального управления формулируется следующим образом. Корабль должен пройти через область сильных течений, величина и направление скорости течения задаются как функции фазовых переменных. При этом задается относительная скорость корабля, модуль которой во время движения остается постоянным. Нужно найти такое оптимальное управление, которое обеспечивает прибытие корабля в заданную точку за минимальное время, то есть следует определить управление кораблем по быстродействию. Рассмотрено брахистохронное движение материальной точки в плоском векторном поле подвижной жидкости, для которого сформулирована классическая вариационная задача поиска экстремальных траекторий. Целью исследования является получение уравнений экстремальных траекторий движения, вдоль которых материальная точка перемещается от заданной стартовой точки к заданной финишной за кратчайшее время. Решение поставленной задачи осуществлялось с помощью классических методов теории вариационного числа. Для заданного варианта граничных условий установлены алгебраические уравнения экстремалей движения материальной точки в виде отрезков степеневого ряда. Проведен сравнительный анализ быстродействия как по экстремальным траекториям, так и альтернативным путем — по прямой линии, соединяющей две заданные точки старта и финиша. Анализ результатов показал, что рассматриваемая вариационная задача имеет две решения, которые отличаются лишь знаком. Однако только одно решение обеспечивает минимальное время перемещения материальной точки между двумя заданными. Также установлено, что экстремальная траектория брахистохронного движения точки не прямой, а имеет колебательный характер.&#x0D; Запропоновано розвʼязання відомої навігаційної задачі Цермело класичними варіаційними методами. Класична задача Цермело в рамках теорії оптимального керування формулюється таким чином. Корабель повинен пройти через область сильних течій, величина і напрямок швидкості течії задаються як функції фазових змінних. При цьому задається відносна швидкість корабля, модуль якої під час руху залишається сталим. Потрібно знайти таке оптимальне керування, яке забезпечує прибуття корабля в задану точку за мінімальний час, тобто слід визначити керування кораблем за швидкодією. Розглянуто брахістохронний рух матеріальної точки в плоскому векторному полі рухомої рідини, для якого сформульовано класичну варіаційну задачу пошуку екстремальних траєкторій. Метою дослідження є отримання рівнянь екстремальних траєкторій руху, уздовж яких матеріальна точка переміщується від заданої стартової точки до заданої фінішної за найкоротший час. Розвʼязання поставленої задачі здійснювалося за допомогою класичних методів теорії варіаційного числення. Для заданого варіанту граничних умов встановлені алгебраїчні рівняння екстремалей руху матеріальної точки у вигляді відрізків степеневого ряду. Проведено порівняльний аналіз швидкодії як за екстремальними траєкторіями, так і альтернативним шляхом — за прямою лінією, яка зʼєднує дві задані точки старту і фінішу. Аналіз результатів показав, що розглянута варіаційна задача має два розвʼязки, які відрізняються лише знаком. Однак тільки одне рішення забезпечує мінімальний час переміщення матеріальної точки між двома заданими. Також встановлено, що екстремальна траєкторія брахістохронного руху точки не є прямою, а має коливальний характер.

Speed control system in mobile robot based on Bezier curve trajectory

The development of robot technology is currently growing rapidly. Mobile robot is one robot with many applications in everyday life. One of the important things in the field of mobile robots is the problem of trajectories or trajectories, in this case how robots can track approved paths. In this study, the mobile robot control system has been tested to track tracks. The path used in this study is the third-order Bezier Order, with control points and end points of the predetermined pathway. Based on the results of simulation tests on the development of mobile robot trajectories, based on the results of simulation tests on mobile robots, it is found that the performance of the track tracking control system is very dependent on the placement of the Bezier curve control points or in other words the actual path formed by the robot is greatly influenced by the shape of the Bezier trajectory that was designed.

Spatio-temporal parse network-based trajectory modeling on the dynamics of criminal justice system

ABSTRACT We extend the existing group-based trajectory modeling by proposing the network-based trajectory modeling based on judicious design and analysis of a spatio-temporal parse network (STPN) as a representation of neighborhood structure that evolves in time. The STPN offers a principled qualitative specification for an explicit paradigm framework to deal with complex real-world problems. The framework is completed by developing a quantitative specification of latent field representation to merge seamlessly on or alongside the established STPN via hierarchical modeling. The models adopt spatial random effects to characterize the heterogeneity and autocorrelation over the locations where nonlinear trajectories were observed. The trajectories are then investigated in the presence of the operational constraints of the dependence structure induced by the spatial and temporal dimensions. With the framework, complex developmental trajectory problems can be discerned, communicated, diagnosed and modeled in a relatively simple way that interpretation is accessible to nontechnical audiences and quickly comprehensible to technically sophisticated audiences. The proposed modeling is applied to address the challenges of the trajectory modeling of nonlinear dynamics arising from a motivating criminal justice empirical process.

Energy-optimal trajectory problems in relative motion solved via Theory of Functional Connections

In this paper, we present a new approach for solving a broad class of energy-optimal trajectory problems in relative motion using the recently developed Theory of Functional Connections (TFC). A total of four problem cases are considered and solved, i.e. rendezvous and intercept with fixed and free final time. Each problem is constrained and formulated using an indirect approach which casts the optimal trajectory problem as a system of linear or nonlinear two-point boundary value problems for the fixed and free final time cases, respectively. Using TFC, we convert each two-point boundary value problem into an unconstrained problem by analytically embedding the boundary constraints into a “constrained expression.” The latter includes a free-function that is expanded using Chebyshev polynomials with unknown coefficients. Regardless of the values of the unknown coefficients, the boundary constraints are satisfied and simple optimization schemes can be employed to numerically solve the problem (e.g. linear and nonlinear least-square methods). To validate the proposed approach, the TFC solutions are compared with solutions obtained via an analytical based method as well as direct and indirect numerical methods. In general, the proposed technique produces solutions to machine level accuracy. Additionally, for the cases tested, it is reported that computational run-time within the MATLAB implementation is lower than 28 and 300 ms for the fixed and free final time problems respectively. Consequently, the proposed methodology is potentially suitable for on-board generation of optimal trajectories in real-time.

ІНДИВІДУАЛЬНА ОСВІТНЯ ТРАЄКТОРІЯ УЧНЯ ПРОФІЛЬНОЇ СТАРШОЇ ШКОЛИ ХУДОЖНЬО-ЕСТЕТИЧНОГО НАПРЯМУ НАВЧАННЯ

The formula of the New Ukrainian School consists of nine key components, one of which is a personality-oriented model of education based on the child-centered ideas. This implies the maximum approximation of education and upbringing of a particular child to his essence, abilities and life plans, providing moral and psychological comfort, refusal to focus the educational process on the «average» student. Therefore, today in pedagogy the problem of individual educational trajectory of youth is actively discussed, which makes it possible to create conditions for the harmonious development of the individual, to meet his educational needs. In general, the concept of individualization of the educational trajectory of students is associated with the process of identifying and developing their abilities, the realization of their own educational goals that meet the needs, opportunities, motivation, interests of modern youth. The purpose of the article is to reveal the features of the formation of the individual educational trajectory of the student in the profile senior school of artistic and aesthetic field of training. Artistic and aesthetic field of specialized training is connected with the core of creative industries (literature, music, fine arts, cinema, television, radio, video and computer games, advertising, architecture, design, fashion, etc.), so it is important to personalize educational path of gifted students with a focus on unleashing their creative potential. The formation of individual educational trajectories of students of the artistic and aesthetic field of specialized education begins with the definition of their life plans, hopes for the future and consists of four stages. The first stage is the study of needs, interests, requests, personal characteristics of students. The second stage is associated with the creation of an individual educational program, which involves the definition of long-term goals; conceptual strategies and approaches to creative development, indicators of their achievements, as well as the selection of content and forms of training. Within the third stage there is a correction of pedagogical influences, creation of a positive pedagogical environment around students, elimination of organizational shortcomings, psychological and pedagogical support of senior students’ creative development is carried out. The fourth stage is related to pedagogical monitoring, which is carried out in order to ensure the quality of this process.

Semi-analytical and extremal solutions for design and synthesis of powered descent and landing trajectories

Semi-analytical solutions to the optimal control problem for 3-dimensional fuel-efficient planetary landing trajectories with constant exhaust velocity and limited mass-flow rate in a drag-existing central Newtonian field are presented. The first-order optimality conditions reduce the problem to a Hamiltonian canonical system for the design and synthesis of feasible and extremal planetary entry, descent, and landing trajectories. The proposed solutions allow us to describe the state vector and Lagrange multipliers in terms of time and switching function's characteristics to determine the number and sequence of thrust arcs. These solutions can be adjusted for manoeuvres near other celestial bodies for which a central gravitational acceleration can be dominant. The paper describes new extremal trajectories, which are based on the analysis of first- and second-order optimality conditions. The results of this work can be used to support mission design analysis and synthesis of fuel-efficient trajectories.

Integrated Morphing Strategy and Trajectory Optimization of a Morphing Waverider and Its Online Implementation Based on the Neural Network

In previous studies, a variable-sweep-wing morphing waverider was proposed and its aerodynamic performance and dynamic model were provided. This morphing waverider can change sweep angle according to different flight scenario in order to achieve an optimal flight performance. For the traditional fixed-geometry waverider, the main objective of the trajectory planning problem is to find an optimal trajectory consisting of time-dependent variables including the angle of attack, the velocity, the altitude, the flight path angle and so on. As for this morphing waverider, an optimal morphing wing changing strategy is also required to be calculated together with an optimal trajectory. At first, to alleviate computational cost and improve trajectory-planning efficiency, aerodynamic coefficients of the morphing waverider are approximated and modeled as polynomial functions of multiple variables including the Mach number, the angle of attack and the sweep angle. Thereafter, an offline integrated optimization problem of both wing morphing strategy and trajectory based on the Gauss pseudo-spectral method is investigated, which can fulfill actual task requirements and variable constraints. Compared with four specific fixed-wing waverider configurations, this morphing waverider has a larger downrange distance and a lower angle of attack. However, the real flight trajectory of the morphing waverider may deviate from the nominal condition due to multiple uncertainties and this morphing waverider is required to have an intelligent online optimization ability. Therefore, an online optimization method based on the neural network is proposed for both wing morphing strategy and trajectory optimization. Finally, the overall performance of this method is examined by comparisons and Monte Carlo runs.

A Bio-inspired trajectory planning method for robotic manipulators based on improved bacteria foraging optimization algorithm and tau theory.

In this paper, a novel bio-inspired trajectory planning method is proposed for robotic systems based on an improved bacteria foraging optimization algorithm (IBFOA) and an improved intrinsic Tau jerk (named Tau-J*) guidance strategy. Besides, the adaptive factor and elite-preservation strategy are employed to facilitate the IBFOA, and an improved Tau-J* with higher-order of intrinsic guidance movement is used to avoid the nonzero initial and final jerk, so as to overcome the computational burden and unsmooth trajectory problems existing in the optimization algorithm and traditional interpolation algorithm. The IBFOA is utilized to determine a small set of optimal control points, and Tau-J* is then invoked to generate smooth trajectories between the control points. Finally, the results of simulation tests demonstrate the eminent stability, optimality, and rapidity capability of the proposed bio-inspired trajectory planning method.