General Optimal Trajectory Planning:Enabling Autonomous Vehicles with the Principle of Least Action

This study presents a general optimal trajectory planning(GOTP)framework for autonomous vehicles(AVs)that can effectively avoid obstacles and guide AVs to complete driving tasks safely and efficiently.Firstly,we employ the fifth-order Bezier curve to generate and smooth the reference path along the road centerline.Cartesian coordinates are then transformed to achieve the curvature continuity of the generated curve.Considering the road constraints and vehicle dynamics,limited polynomial candidate trajectories are generated and smoothed in a curvilinear coordinate system.Furthermore,in selecting the optimal trajectory,we develop a unified and auto-tune objective function based on the principle of least action by employing AVs to simulate drivers’behavior and summarizing their manipulation characteristics of“seeking benefits and avoiding losses.”Finally,by integrating the idea of receding-horizon optimization,the proposed framework is achieved by considering dynamic multi-performance objectives and selecting trajectories that satisfy feasibility,optimality,and adaptability.Extensive simulations and experiments are performed,and the results demonstrate the framework’s feasibility and effectiveness,which avoids both dynamic and static obstacles and applies to various scenarios with multi-source interactive traffic participants.Moreover,we prove that the proposed method can guarantee real-time planning and safety requirements compared to drivers’manipulation.

Research on Anthropomorphic Obstacle Avoidance Trajectory Planning for Adaptive Driving Scenarios Based on Inverse Reinforcement Learning Theory

The forward design of trajectory planning strategies requires preset trajectory optimization functions,resulting in poor adaptability of the strategy and an inability to accurately generate obstacle avoidance trajectories that conform to real driver behavior habits.In addition,owing to the strong time-varying dynamic characteristics of obstacle avoidance scenarios,it is necessary to design numerous trajectory optimization functions and adjust the corresponding parameters.Therefore,an anthropomorphic obstacle-avoidance trajectory planning strategy for adaptive driving scenarios is proposed.First,numerous expert-demonstrated trajectories are extracted from the HighD natural driving dataset.Subsequently,a trajectory expectation feature-matching algorithm is proposed that uses maximum entropy inverse reinforcement learning theory to learn the extracted expert-demonstrated trajectories and achieve automatic acquisition of the optimization function of the expert-demonstrated trajectory.Furthermore,a mapping model is constructed by combining the key driving scenario information that affects vehicle obstacle avoidance with the weight of the optimization function,and an anthropomorphic obstacle avoidance trajectory planning strategy for adaptive driving scenarios is proposed.Finally,the proposed strategy is verified based on real driving scenarios.The results show that the strategy can adjust the weight distribution of the trajectory optimization function in real time according to the“emergency degree”of obstacle avoidance and the state of the vehicle.Moreover,this strategy can generate anthropomorphic trajectories that are similar to expert-demonstrated trajectories,effectively improving the adaptability and acceptability of trajectories in driving scenarios.

Trajectory planning for multi-robot coordinated towing system based on stability

Given the unconstrained characteristics of the multi-robot coordinated towing system,the rope can only provide a unidirectional constraint force to the suspended object,which leads to the weak ability of the system to resist external disturbances and makes it difficult to control the trajectory of the suspended object.Based on the kinematics and statics of the multi-robot coordinated towing system with fixed base,the dynamic model of the system is established by using the Newton-Euler equations and the Udwadia-Kalaba equations.To plan the trajectories with high stability and strong control,trajectory planning is performed by combining the dynamics and stability of the towing system.Based on the dynamic stability of the motion trajectory of the suspended object,the stability of the suspended object is effectively improved through online real-time planning and offline manual adjustment.The effectiveness of the proposed method is verified by comparing the motion stability of the suspended object before and after planning.The results provide a foundation for the motion planning and coordinated control of the towing system.

Trajectory Planning for OTFS-Based UAV Communications

Unmanned aerial vehicles(UAVs)have attracted growing research interests in recent years,which can be used as cost-effective aerial platforms to transmit collected data packets to ground access points(APs).Thus,it is crucial to investigate robust airto-ground(A2G)wireless links for high-speed UAVs.However,the A2G wireless link is unstable as it suffers from large path-loss and severe Doppler effect due to the high mobility of UAVs.In order to meet these challenges,we propose an orthogonal time frequency space(OTFS)-based UAV communication system to relief the Doppler effect.Besides,considering that the energy of UAV is limited,we optimize the trajectory planning of UAV to minimize the energy consumption under the constraints of bit error rate(BER)and transmission rate,where the Doppler compensation is taken into account.Simulation results show that the performance of OTFS-based UAV system is superior to orthogonal frequency division multiplexing(OFDM)-based UAV systems,which can accomplish transmission tasks over shorter distances with lower energy consumption.

Leader trajectory planning method considering constraints of formation controller

To ensure safe flight of multiple fixed-wing unmanned aerial vehicles(UAVs)formation,considering trajectory planning and formation control together,a leader trajectory planning method based on the sparse A*algorithm is introduced.Firstly,a formation controller based on prescribed performance theory is designed to control the transient and steady formation configuration,as well as the formation forming time,which not only can form the designated formation configuration but also can guarantee collision avoidance and terrain avoidance theoretically.Next,considering the constraints caused by formation controller on trajectory planning such as the safe distance,turn angle and step length,as well as the constraint of formation shape,a leader trajectory planning method based on sparse A^(*)algorithm is proposed.Simulation results show that the UAV formation can arrive at the destination safely with a short trajectory no matter keeping the formation or encountering formation transformation.

Smooth Trajectory Planning for a Cable Driven Parallel Waist Rehabilitation Robot Based on Rehabilitation Evaluation Factors

Rehabilitation robots can help physiatrists to assist patients in improving their movement ability.Due to the interaction between rehabilitation robots and patients,the robots need to complete rehabilitation training on a safe basis.This paper presents an approach for smooth trajectory planning for a cable-driven parallel waist rehabilitation robot(CDPWRR)based on the rehabilitation evaluation factors.First,motion capture technology is used to collect the motion data of several volunteers in waist twisting.Considering the impact of motion variability,the feature points at the center of the human pelvis are obtained after eliminating unreasonable data through rationality judgments.Then,point-to-point waist training trajectory planning based on quintic polynomial and cycloid functions,and multipoint waist training trajectory planning based on quintic B-spline functions are carried out.The corresponding planned curves and kinematics characteristics using three methods are compared and analyzed.Subsequently,the rehabilitation evaluation factors are introduced to conduct smooth trajectory planning for waist training,and the waist trajectory with better compliance is obtained based on the safety and feasibility of waist motion.Finally,the physical prototype of the CDPWRR is built,and the feasibility and effectiveness of the proposed smooth trajectory planning method are proved by numerical analysis and experiments.

DQN-Based Proactive Trajectory Planning of UAVs in Multi-Access Edge Computing

The main aim of future mobile networks is to provide secure,reliable,intelligent,and seamless connectivity.It also enables mobile network operators to ensure their customer’s a better quality of service(QoS).Nowadays,Unmanned Aerial Vehicles(UAVs)are a significant part of the mobile network due to their continuously growing use in various applications.For better coverage,cost-effective,and seamless service connectivity and provisioning,UAVs have emerged as the best choice for telco operators.UAVs can be used as flying base stations,edge servers,and relay nodes in mobile networks.On the other side,Multi-access EdgeComputing(MEC)technology also emerged in the 5G network to provide a better quality of experience(QoE)to users with different QoS requirements.However,UAVs in a mobile network for coverage enhancement and better QoS face several challenges such as trajectory designing,path planning,optimization,QoS assurance,mobilitymanagement,etc.The efficient and proactive path planning and optimization in a highly dynamic environment containing buildings and obstacles are challenging.So,an automated Artificial Intelligence(AI)enabled QoSaware solution is needed for trajectory planning and optimization.Therefore,this work introduces a well-designed AI and MEC-enabled architecture for a UAVs-assisted future network.It has an efficient Deep Reinforcement Learning(DRL)algorithm for real-time and proactive trajectory planning and optimization.It also fulfills QoS-aware service provisioning.A greedypolicy approach is used to maximize the long-term reward for serving more users withQoS.Simulation results reveal the superiority of the proposed DRL mechanism for energy-efficient and QoS-aware trajectory planning over the existing models.

Information Freshness-Oriented Trajectory Planning and Resource Allocation for UAV-Assisted Vehicular Networks

In this paper,multi-UAV trajectory planning and resource allocation are jointly investigated to improve the information freshness for vehicular networks,where the vehicles collect time-critical traffic information by on-board sensors and upload to the UAVs through their allocated spectrum resource.We adopt the expected sum age of information(ESAoI)to measure the network-wide information freshness.ESAoI is jointly affected by both the UAVs trajectory and the resource allocation,which are coupled with each other and make the analysis of ESAoI challenging.To tackle this challenge,we introduce a joint trajectory planning and resource allocation procedure,where the UAVs firstly fly to their destinations and then hover to allocate resource blocks(RBs)during a time-slot.Based on this procedure,we formulate a trajectory planning and resource allocation problem for ESAoI minimization.To solve the mixed integer nonlinear programming(MINLP)problem with hybrid decision variables,we propose a TD3 trajectory planning and Round-robin resource allocation(TTPRRA).Specifically,we exploit the exploration and learning ability of the twin delayed deep deterministic policy gradient algorithm(TD3)for UAVs trajectory planning,and utilize Round Robin rule for the optimal resource allocation.With TTP-RRA,the UAVs obtain their flight velocities by sensing the locations and the age of information(AoI)of the vehicles,then allocate the RBs to the vehicles in a descending order of AoI until the remaining RBs are not sufficient to support another successful uploading.Simulation results demonstrate that TTP-RRA outperforms the baseline approaches in terms of ESAoI and average AoI(AAoI).

Progress in reentry trajectory planning for hypersonic vehicle

The reentry trajectory planning for hypersonic vehicles is critical and challenging in the presence of numerous nonlinear equations of motion and path constraints, as well as guaranteed satisfaction of accuracy in meeting all the specified boundary conditions. In the last ten years, many researchers have investigated various strategies to generate a feasible or optimal constrained reentry trajectory for hypersonic vehicles. This paper briefly reviews the new research efforts to promote the capability of reentry trajectory planning. The progress of the onboard reentry trajectory planning, reentry trajectory optimization, and landing footprint is summarized. The main challenges of reentry trajectory planning for hypersonic vehicles are analyzed, focusing on the rapid reentry trajectory optimization, complex geographic constraints, and coop- erative strategies.

Algebraic Method‑Based Point‑to‑Point Trajectory Planning of an Under‑Constrained Cable‑Suspended Parallel Robot with Variable Angle and Height Cable Mast

To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot(UCPR)with variable angle and height cable mast as described in this paper.The end-effector of the UCPR with three cables can achieve three translational degrees of freedom(DOFs).The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed.The motion trajectory of the end-effector comprising six segments is given.The connection points of the trajectory segments(except for point P3 in the X direction)are devised to have zero instantaneous velocities,which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition.The trajectory is respectively planned using three algebraic methods,including fifth degree polynomial,cycloid trajectory,and double-S velocity curve.The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector.Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning.At the points where the velocity suddenly changes,the length and tension variation curves of the planned and unplanned three cables are compared and analyzed.The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment.The effectiveness and feasibility of fifth degree polynomial planning are validated.

Optimal midcourse trajectory planning considering the capture region

An optimal midcourse trajectory planning approach that considers the capture region（CR） of the terminal guidance is proposed in this article based on the Gauss pseudospectral method（GPM）. Firstly, the planar CR of the proportional navigation in terminal guidance is analyzed and innovatively introduced in the midcourse trajectory planning problems, with the collision triangle（CT） serving as the ideal terminal states parameters of the midcourse phase, and the CR area serving as the robustness against target maneuvers. Secondly, the midcourse trajectory planning problem that considers the path, terminal and control constraints is formulated and the well-developed GPM is used to generate the nominal trajectory that meets the CR demands. The interceptor will reshape the trajectory only when the former CR fails to cover the target, which has loosened the critical demand for frequent trajectory modification. Finally, the simulations of four different scenarios are carried out and the results prove the effectiveness and optimality of the proposed method.

Seam-tracking based on dynamic trajectory planning for a mobile welding robot

A new seam-tracking method based on dynamic trajectory planning for a mobile welding robot is proposed in order to improve the response lag of the mobile robot and the high frequency oscillation in seam-tracking.By using a front-placed laser-based vision sensor to dynamically extract the location of the weld seam in front of torch,the trend and direction of the weld line is roughly obtained.The robot system autonomously and dynamically performs trajectory planning based on the isometric approximation model.Arc sensor technology is applied to detect the offset during welding process in real time.The dynamic compensation of the weld path is done in combination with the control of the mobile robot and the executive body installed on it.Simulated and experimental results demonstrate that the method effectively increases the stability of welding speed and smoothness of the weld track,and hence the weld formation in curves and corners is improved.

Evolutionary Trajectory Planning for an Industrial Robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator （AdeptOne XL robot） in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm （NSGA-II） and multi-objective differential evolution （MODE）, have been used for the optimization. Two methods （normalized weighting objective functions and average fitness factor） are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.

Hybrid hierarchical trajectory planning for a fixed-wing UCAV performing air-to-surface multi-target attack

This paper considers the problem of generating a flight trajectory for a single fixed-wing unmanned combat aerial vehicle （UCAV） performing an air-to-surface multi-target attack （A/SMTA） mission using satellite-guided bombs. First, this problem is formulated as a variant of the traveling salesman problem （TSP）, called the dynamic-constrained TSP with neighborhoods （DCT- SPN）. Then, a hierarchical hybrid approach, which partitions the planning algorithm into a roadmap planning layer and an optimal control layer, is proposed to solve the DCTSPN. In the roadmap planning layer, a novel algorithm based on an updatable proba- bilistic roadmap （PRM） is presented, which operates by randomly sampling a finite set of vehicle states from continuous state space in order to reduce the complicated trajectory planning problem to planning on a finite directed graph. In the optimal control layer, a collision-free state-to-state trajectory planner based on the Gauss pseudospectral method is developed, which can generate both dynamically feasible and optimal flight trajectories. The entire process of solving a DCTSPN consists of two phases. First, in the offline preprocessing phase, the algorithm constructs a PRM, and then converts the original problem into a standard asymmet- ric TSP （ATSP）. Second, in the online querying phase, the costs of directed edges in PRM are updated first, and a fast heuristic searching algorithm is then used to solve the ATSP. Numerical experiments indicate that the algorithm proposed in this paper can generate both feasible and near-optimal solutions quickly for online purposes.

An Efficient Trajectory Planning for Cellular-Connected UAV under the Connectivity Constraint

Unmanned Aerial Vehicles(UAVs)acting as aerial users to access the cellular network form a promising solution to guarantee its safe and efficient operations via the high-quality communication.Due to the flexible mobility of UAVs and the coverage range limits of ground base station(GBS),the signalto-noise ratio(SNR)of the communication link between UAVs and GBS will fluctuate.It is an important requirement to maintain the UAV’s cellular connection to meet a certain SNR requirement during the mission for UAV flying from take off to landing.In this paper,we study an efficient trajectory planning method that can minimize a cellular-connected UAV’s mission completion time under the connectivity requirement.The conventional method to tackle this problem adopts graph theory or a dynamic programming method to optimize the trajectory,which generally incurs high computational complexities.Moreover,there is a nonnegligible performance gap compared to the optimal solution.To this end,we propose an iterative trajectory optimizing algorithm based on geometric planning.Firstly,we apply graph theory to obtain all the possible UAV-GBS association sequences and select the candidate association sequences based on the topological relationship among UAV and GBSs.Next,adopting the triangle inequality property,an iterative handover location design is proposed to determine the shortest flight trajectory with fast convergence and low computation complexity.Then,the best flight trajectory can be obtained by comparing all the candidate trajectories.Lastly,we revealed the tradeoff between mission completion time and flight energy consumption.Numerical results validate that our proposed solution can obtain the effectiveness with set accuracy and outperform against the benchmark schemes with affordable computation time.

Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm

Robot manipulators perform a point-point task under kinematic and dynamic constraints.Due to multi-degreeof-freedom coupling characteristics,it is difficult to find a better desired trajectory.In this paper,a multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm(INSGA-II)is proposed.Trajectory function is planned with a new composite polynomial that by combining of quintic polynomials with cubic Bezier curves.Then,an INSGA-II,by introducing three genetic operators:ranking group selection(RGS),direction-based crossover(DBX)and adaptive precision-controllable mutation(APCM),is developed to optimize travelling time and torque fluctuation.Inverted generational distance,hypervolume and optimizer overhead are selected to evaluate the convergence,diversity and computational effort of algorithms.The optimal solution is determined via fuzzy comprehensive evaluation to obtain the optimal trajectory.Taking a serial-parallel hybrid manipulator as instance,the velocity and acceleration profiles obtained using this composite polynomial are compared with those obtained using a quintic B-spline method.The effectiveness and practicability of the proposed method are verified by simulation results.This research proposes a trajectory optimization method which can offer a better solution with efficiency and stability for a point-to-point task of robot manipulators.

Receding-Horizon Trajectory Planning for Under-Actuated Autonomous Vehicles Based on Collaborative Neurodynamic Optimization

This paper addresses a major issue in planning the trajectories of under-actuated autonomous vehicles based on neurodynamic optimization.A receding-horizon vehicle trajectory planning task is formulated as a sequential global optimization problem with weighted quadratic navigation functions and obstacle avoidance constraints based on given vehicle goal configurations.The feasibility of the formulated optimization problem is guaranteed under derived conditions.The optimization problem is sequentially solved via collaborative neurodynamic optimization in a neurodynamics-driven trajectory planning method/procedure.Simulation results with under-actuated unmanned wheeled vehicles and autonomous surface vehicles are elaborated to substantiate the efficacy of the neurodynamics-driven trajectory planning method.

Novel integrated optimization algorithm for trajectory planning of robot manipulators based on integrated evolutionary programming

Optimal trajectory planning for robot manipulators plays an important role in implementing the high productivity for robots. The performance indexes used in optimal trajectory planning are classified into two main categories: optimum traveling time and optimum mechanical energy of the actuators. The current trajectory planning algorithms are designed based on one of the above two performance indexes. So far, there have been few planning algorithms designed to satisfy two performance indexes simultaneously. On the other hand, some deficiencies arise in the existing integrated optimi2ation algorithms of trajectory planning. In order to overcome those deficiencies, the integrated optimization algorithms of trajectory planning are presented based on the complete analysis for trajectory planning of robot manipulators. In the algorithm, two object functions are designed based on the specific weight coefficient method and ' ideal point strategy. Moreover, based on the features of optimization problem, the intensified evolutionary programming is proposed to solve the corresponding optimization model. Especially, for the Stanford Robot,the high-quality solutions are found at a lower cost.

3D Trajectory Planning of Positioning Error Correction Based on PSO-A* Algorithm

Aiming at the yaw problem caused by inertial navigation system errors accumulation during the navigation of an intelligent aircraft,a three-dimensional trajectory planning method based on the particle swarm optimization-A star(PSO-A*)algorithm is designed.Firstly,an environment model for aircraft error correction is established,and the trajectory is discretized to calculate the positioning error.Next,the positioning error is corrected at many preset trajectory points.The shortest trajectory and the fewest correction times are regarded as optimization goals to improve the heuristic function of A star(A*)algorithm.Finally,the index weights are continuously optimized by the particle swarm optimization algorithm.The optimal trajectory is found by the A*algorithm under the current evaluation index,so the ideal trajectory is planned.The experimental results show that the PSO-A*algorithm can quickly search for ideal trajectories in different environment models,indicating that the algorithm has certain feasibility and adaptability,and verifies the rationality of the proposed trajectory planning model.The PSO-A*algorithm has better convergence accuracy than the A*algorithm,and the search efficiency is significantly better than the grid search A star(GS-A*)algorithm.The PSO-A*algorithm proposed in this paper has certain engineering application value.The researchers will study the real-time and systematic nature of the algorithm.

Application of Optimal-Jerk Trajectory Planning in Gait-balance Training Robot

To accommodate the gait and balance disorder of the elderly with age progression and the occurrence of various senile diseases,this paper proposes a novel gait balance training robot(G-Balance)based on a six degree-of-freedom parallel platform.Using the platform movement and IMU wearable sensors,two training modes,i.e.,active and passive,are developed to achieve vestibular stimulation.Virtual reality technology is applied to achieve visual stimulation.In the active training mode,the elderly actively exercises to control the posture change of the platform and the switching of the virtual scene.In the passive training mode,the platform movement is combined with the virtual scene to simulate bumpy environments,such as earthquakes,to enhance the human anti-interference ability.To achieve a smooth switching of the scene,continuous speed and acceleration of the platform motion are required in some scenarios,in which a trajectory planning algorithm is applied.This paper describes the application of the trajectory planning algorithm in the balance training mode and the optimization of jerk(differential of acceleration)based on cubic spline planning,which can reduce impact on the joint and enhance stability.