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.

4D ConflictFree Trajectory Planning for Fixed-Wing UAV

Four-dimensional trajectory based operation(4D-TBO)is believed to enhance the planning and execution of efficient flights,reduce potential conflicts and resolve upcoming tremendous flight demand.Most of the 4D trajectory planning related studies have focused on manned aircraft instead of unmanned aerial vehicles(UAVs).This paper focuses on planning conflict-free 4D trajectories for fixed-wing UAVs before the departure or during the flight planning.A 4D trajectory generation technique based on Tau theory is developed,which can incorporate the time constraints over the waypoint sequence in the flight plan.Then the 4D trajectory is optimized by the particle swarm optimization(PSO)algorithm.Further simulations are performed to demonstrate the effectiveness of the proposed method,which would offer a good chance for integrating UAV into civil airspace in the future.

Minimum-time trajectory planning based on the shortest path for the wheeled mobile robot

The time-optimal trajectory planning is proposed under kinematic and dynamic constraints for a 2-DOF wheeled robot. In order to make full use of the motor’s capacity, we calculate the maximum torque and the minimum torque by considering the maximum heat-converted power generated by the DC motor. The shortest path is planned by using the geometric method under kinematic constraints. Under the bound torques, the velocity limits and the maximum acceleration (deceleration) are obtained by combining with the dynamics. We utilize the phase-plane analysis technique to generate the time optimal trajectory based on the shortest path. At last, the computer simulations for our laboratory mobile robot were performed. The simulation results prove the proposed method is simple and effective for practical use.

Trajectory Planning of High Precision Collaborative Robots

In order to satisfy the high efficiency and high precision of collaborative robots,this work presents a novel trajectory planning method.First,in Cartesian space,a novel velocity look-ahead control algorithm and a cubic polynomial are combined to construct the end-effector trajectory of robots.Then,the joint trajectories can be obtained through the inverse kinematics.In order to improve the smoothness and stability in joint space,the joint trajectories are further adjusted based on the velocity look-ahead control algorithm and quintic B-spline.Finally,the proposed trajectory planning method is tested on a 4-DOF serial collaborative robot.The experimental results indicate that the collaborative robot achieves the high efficiency and high precision,which validates the effectiveness of the proposed method.

A Trajectory Planning-Based Energy-Optimal Method for an EMVT System

In this paper,a trajectory planning-based energy-optimal method is proposed to reduce the energy consumption of novel electromagnetic valve train(EMVT).Firstly,an EMVT optimization model based on state equation was established.Then,the Gauss pseudospectral method(GPM)was used to plan energy-optimal trajectory.And a robust feedforward-feedback tracking controller based on inverse system method is proposed to track the energy-optimal trajectory.In order to verify the effectiveness of the energyoptimal trajectory,a test bench was established.Finally,co-simulations based on MATLAB Simulink and AVL Boost were carried out to illustrate the effect of energyoptimal trajectories on engine performance.Experimental results show that the robust tracking controller can achieve good position tracking performance.And these energyoptimal trajectories can save up to 40%of the energy consumption compared with the conventional camshaft valve trajectories.

Self-adapting control parameters modifieddifferential evolution for trajectoryplanning of manipulators

Control parameters of original differential evolution （DE） are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optiinization problems. According to the relative position of two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the scale factor F of the difference vector is proposed. In terms of the convergence status of the target vector in the current population, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have a lower CFI while worse target vectors have a large CFI. At the same time, the mutation operator is modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark problems and applied to the trajectory planning of a three-joint redundant manipulator. Finally, the experiment results show that the proposed approaches can greatly improve robustness and convergence speed.

Real-time trajectory planning for UCAV air-to-surface attack using inverse dynamics optimization method and receding horizon control

This paper presents a computationally efficient real-time trajectory planning framework for typical unmanned combat aerial vehicle （UCAV） performing autonomous air-to-surface （A/S） attack. It combines the benefits of inverse dynamics optimization method and receding horizon optimal control technique. Firstly, the ground attack trajectory planning problem is mathematically formulated as a receding horizon optimal control problem （RHC-OCP）. In particular, an approximate elliptic launch acceptable region （LAR） model is proposed to model the critical weapon delivery constraints. Secondly, a planning algorithm based on inverse dynamics optimization, which has high computational efficiency and good convergence properties, is developed to solve the RHCOCP in real-time. Thirdly, in order to improve robustness and adaptivity in a dynamic and uncer- tain environment, a two-degree-of-freedom （2-DOF） receding horizon control architecture is introduced and a regular real-time update strategy is proposed as well, and the real-time feedback can be achieved and the not-converged situations can be handled. Finally, numerical simulations demon- strate the efficiency of this framework, and the results also show that the presented technique is well suited for real-time implementation in dynamic and uncertain environment.

Two-layer autonomous intelligence dynamic trajectory planning method based on shield-tunnel ring-geology interactions

To solve the problem that current attitude planning methods do not fully consider the interaction and constraints among the shield,segmental tunnel ring,and geology,and cannot adapt to the changes in the actual engineering environment,or provide feasible long-term and short-term attitude planning,this paper proposes autonomous intelligent dynamic trajectory planning(AI-DTP)to provide tunnel ring and centimeter-layer planning targets for a self-driving shield to meet long-term accuracy and short-term rapidity.AI-DTP introduces the Frenet coordinate system to solve the problem of inconsistent spatial representation of tunnel data,segmental tunnel ring location,and surrounding geological conditions,designs the long short-term memory attitude prediction model to accurately predict shield attitude change trend based on shield,tunnel,and geology,and uses a heuristic algorithm for trajectory optimization.AI-DTP provides ring-layer and centimeter-layer planning objectives that meet the needs of long-term accuracy and short-term correction of shield attitude control.In the Hangzhou-Shaoxing Intercity Railroad Tunnel Project in China,the “Zhiyu”shield equipped with the AI-DTP system was faster and more accurate than the manually controlled shield,with a smoother process and better quality of the completed tunnel.

DDQNC-P:A framework for civil aircraft tactical synergetic trajectory planning under adverse weather conditions

Adverse weather during aircraft operation generates more complex scenarios for tactical trajectory planning,which requires superior real-time performance and conflict-free reliability of solving methods.Multi-aircraft real-time 4D trajectory planning under adverse weather is an essential problem in Air Traffic Control(ATC)and it is challenging for the existing methods to be applied effectively.A framework of Double Deep Q-value Network under the Critic guidance with heuristic Pairing(DDQNC-P)is proposed to solve this problem.An Agent for two aircraft synergetic trajectory planning is trained by the Deep Reinforcement Learning(DRL)model of DDQNC,which completes two aircraft 4D trajectory planning tasks preliminarily under dynamic weather conditions.Then a heuristic pairing algorithm is designed to convert the multi-aircraft synergetic trajectory planning into multi-time pairwise synergetic trajectory planning,making the multiaircraft trajectory planning problem processable for the trained Agent.This framework compresses the input dimensions of the DRL model while improving its generalization ability significantly.Substantial simulations with various aircraft numbers,weather conditions,and airspace structures were conducted for performance verification and comparison.The success rate of conflict-free trajectory resolution reached 96.56% with an average calculation time of 0.41 s for 3504D trajectory points per aircraft,finally confirming its applicability to make real-time decision-making support for controllers in real-world ATC systems.

Trajectory planning and motion control of full-row seedling pick-up arm

Frequent start-stops of automatic seedling transplanters would lengthen the seedling picking time due to alternating movement of the motor,and cause positioning errors and frequent motor vibrations when starting the machine.To solve these problems and ensure the pick-up continuity of automatic transplanters,in this study the smooth circular arc interpolation algorithm and the least square method for multinomial curve fitting were used to conduct the trajectory planning of automatic transplanter based on the movement of the pick-up arm of the transplanter.Velocity and time curves were fitted in segments to acquire motion control parameters and further tracking control was conducted.The mathematical model of the control system was established using Simulink,and simulation analysis and system debugging test were performed.Experiments show that the trajectory curves obtained by MATLAB’s data processing can realize the continual and smooth motion trajectory of the pick-up arm;stepper motor velocity control can effectively track the planning curve and improve the seedling pick-up efficiency.The pick-up and pushing time of each motion of the planned plug seedling transplanter reduced by 1.0678 s and the start-stop times reduced from 6 to 1,which solved the frequent motor vibrations when starting the machine and improved the stability of the system.In addition,overstep and out-of-step of the motor at the start-stop moment were avoided and displacement error was reduced.

A double-layered nonlinear model predictive control based control algorithm for local trajectory planning for automated trucks under uncertain road adhesion coefficient conditions

We present a double-layered control algorithm to plan the local trajectory for automated trucks equipped with four hub motors. The main layer of the proposed control algorithm consists of a main layer nonlinear model predictive control(MLN-MPC) controller and a secondary layer nonlinear MPC(SLN-MPC) controller. The MLN-MPC controller is applied to plan a dynamically feasible trajectory, and the SLN-MPC controller is designed to limit the longitudinal slip of wheels within a stable zone to avoid the tire excessively slipping during traction. Overall, this is a closed-loop control system. Under the off-line co-simulation environments of AMESim, Simulink, dSPACE, and TruckSim, a dynamically feasible trajectory with collision avoidance operation can be generated using the proposed method, and the longitudinal wheel slip can be constrained within a stable zone so that the driving safety of the truck can be ensured under uncertain road surface conditions. In addition, the stability and robustness of the method are verified by adding a driver model to evaluate the application in the real world. Furthermore, simulation results show that there is lower computational cost compared with the conventional PID-based control method.

Stable trajectory planning and energyefficience control allocation of lane change maneuver for autonomous electric vehicle

Purpose–The purpose of this paper is to investigate problems in performing stable lane changes and tofind a solution to reduce energy consumption of autonomous electric vehicles.Design/methodology/approach–An optimization algorithm,model predictive control(MPC)and Karush–Kuhn–Tucker(KKT)conditions are adopted to resolve the problems of obtaining optimal lane time,tracking dynamic reference and energy-efficient allocation.In this paper,the dynamic constraints of vehicles during lane change arefirst established based on the longitudinal and lateral force coupling characteristics and the nominal reference trajectory.Then,by optimizing the lane change time,the yaw rate and lateral acceleration that connect with the lane change time are limed.Furthermore,to assure the dynamic properties of autonomous vehicles,the real system inputs under the restraints are obtained by using the MPC method.Based on the gained inputs and the efficient map of brushless direct-current in-wheel motors(BLDC IWMs),the nonlinear cost function which combines vehicle dynamic and energy consumption is given and the KKT-based method is adopted.Findings–The effectiveness of the proposed control system is verified by numerical simulations.Consequently,the proposed control system can successfully achieve stable trajectory planning,which means that the yaw rate and longitudinal and lateral acceleration of vehicle are within stability boundaries,which accomplishes accurate tracking control and decreases obvious energy consumption.Originality/value–This paper proposes a solution to simultaneously satisfy stable lane change maneuvering and reduction of energy consumption for autonomous electric vehicles.Different from previous path planning researches in which only the geometric constraints are involved,this paper considers vehicle dynamics,and stability boundaries are established in path planning to ensure the feasibility of the generated reference path.

Real‑Time Optimal Trajectory Planning for Autonomous Driving with Collision Avoidance Using Convex Optimization

An online trajectory planning method for collision avoidance is proposed to improve vehicle driving safety and comfort simultaneously.The collision-free trajectory for autonomous driving is formulated as a nonlinear optimization problem.A novel approximate convex optimization approach is developed for the online optimal trajectory in both longitudinal and lateral directions.First,a dual variable is used to model the non-convex collision-free constraint for driving safety and is calculated by solving a dual problem of the relative distance between vehicles.Second,the trajectory is further optimized in a model predictive control framework considering the safety.It realizes continuous-time and dynamic feasible motion with collision avoidance.The geometry of object vehicles is described by polygons instead of circles or ellipses in traditional methods.In order to avoid aggressive maneuver in the longitudinal and lateral directions for driving comfort,rates of the acceleration and the steering angle are restricted.The final formulated optimization problem is convex,which can be solved by using quadratic programming solvers and is computationally efficient for online application.Simulation results show that this approach can obtain similar driving performance compared to a state-of-the-art nonlinear optimization method.Furthermore,various driving scenarios are tested to evaluate the robustness and the ability for handling complex driving tasks.

Energy-efficient receding horizon trajectory planning of high-speed trains using real-time traffic information

Optimal trajectory planning of high-speed trains(HSTs)aims to obtain such speed curves that guarantee safety,punctuality,comfort and energy-saving of the train.In this paper,a new shrinking horizon model predictive control(MPC)algorithm is proposed to plan the optimal trajectories of HSTs using real-time traffic information.The nonlinear longitudinal dynamics of HSTs are used to predict the future behaviors of the train and describe variable slopes and variable speed limitations based on real-time traffic information.Then optimal trajectory planning of HSTs is formulated as the shrinking horizon optimal control problem with the consideration of safety,punctuality,comfort and energy consumption.According to the real-time position and running time of the train,the shrinking horizon is updated to ensure the recursive feasibility of the optimization problem.The optimal speed curve of the train is computed by online solving the optimization problem with the Radau Pseudo-spectral method(RPM).Simulation results demonstrate that the proposed method can satisfy the requirements of energy efficiency and punctuality of the train.

Task Space Division and Trajectory Planning for a Flexible Macro-Micro Manipulator System

This paper deals with a flexible macro-micro manipulator system, which includes a long flexible manipulator and a relatively short rigid manipulator attached to the tip of the macro manipulator. A flexible macro manipulator possesses the advantages of wide operating range, high speed, and low energy consumption, but the disadvantage of a low tracking precision. The macro-micro manipulator system improves tracking performance by compensating for the endpoint tracking error while maintaining the advantages of the flexible macro manipulator. A trajectory planning scheme was built utilizing the task space division method. The division point is chosen to optimize the error compensation and energy consumption for the whole system. Then movements of the macro-micro manipulator can be determined using separate inverse kinematic models. Simulation results for a planar 4-DOF macro-micro manipulator system are presented to show the effectiveness of the control system.

Path planning for UAVs formation reconfiguration based on Dubins trajectory

Multiple UAVs are usually deployed to provide robustness through redundancy and to accomplish surveillance,search,attack and rescue missions.Formation reconfiguration was inevitable during the flight when the mission was adjusted or the environment varied.Taking the typical formation reconfiguration from a triangular penetrating formation to a circular tracking formation for example,a path planning method based on Dubins trajectory and particle swarm optimization(PSO)algorithm is presented in this paper.The mathematic model of multiple UAVs formation reconfiguration was built firstly.According to the kinematic model of aerial vehicles,a process of dimensionality reduction was carried out to simplify the model based on Dubins trajectory.The PSO algorithm was adopted to resolve the optimization problem of formation reconfiguration path planning.Finally,the simulation and vehicles flight experiment are executed.Results show that the path planning method based on the Dubins trajectory and the PSO algorithm can generate feasible paths for vehicles on time,to guarantee the rapidity and effectiveness of formation reconfigurations.Furthermore,from the simulation results,the method is universal and could be extended easily to the path planning problem for different kinds of formation reconfigurations.

Optimal control based coordinated taxiing path planning and tracking for multiple carrier aircraft on flight deck

Coordinated taxiing planning for multiple aircraft on flight deck is of vital importance which can dramatically improve the dispatching efficiency.In this paper,first,the coordinated taxiing path planning problem is transformed into a centralized optimal control problem where collision-free conditions and mechanical limits are considered.Since the formulated optimal control problem is of large state space and highly nonlinear,an efficient hierarchical initialization technique based on the Dubins-curve method is proposed.Then,a model predictive controller is designed to track the obtained reference trajectory in the presence of initial state error and external disturbances.Numerical experiments demonstrate that the proposed“offline planningþonline tracking”framework can achieve efficient and robust coordinated taxiing planning and tracking even in the presence of initial state error and continuous external disturbances.

UAV penetration mission path planning based on improved holonic particle swarm optimization

To meet the requirements of safety, concealment, and timeliness of trajectory planning during the unmanned aerial vehicle(UAV) penetration process, a three-dimensional path planning algorithm is proposed based on improved holonic particle swarm optimization(IHPSO). Firstly, the requirements of terrain threat, radar detection, and penetration time in the process of UAV penetration are quantified. Regarding radar threats, a radar echo analysis method based on radar cross section(RCS)and the spatial situation is proposed to quantify the concealment of UAV penetration. Then the structure-particle swarm optimization(PSO) algorithm is improved from three aspects.First, the conversion ability of the search strategy is enhanced by using the system clustering method and the information entropy grouping strategy instead of random grouping and constructing the state switching conditions based on the fitness function.Second, the unclear setting of iteration numbers is addressed by using particle spacing to create the termination condition of the algorithm. Finally, the trajectory is optimized to meet the intended requirements by building a predictive control model and using the IHPSO for simulation verification. Numerical examples show the superiority of the proposed method over the existing PSO methods.

Guidance Control for Parallel Parking Tasks

Parking into small berths remains difficult for unskilled drivers. Researchers had proposed different automatic parking systems to solve this problem. The first kind of strategies(called parking trajectory planning) designs a detailed reference trajectory that links the start and ending points of a special parking task and let the vehicle track this reference trajectory so as to park into the berth. The second kind of strategies(called guidance control) just characterizes several regimes of driving actions as well as the important switching points in certain rule style and let the vehicle follows the pre-selected series of actions so as to park into the berth. Parking guidance control is simpler than parking trajectory planning. However, no studies thoroughly validated parking guidance control before. In this paper, a new automatic parking method is presented, which could characterize the desired control actions directly. Then the feasibility is examined carefully. Tests show that a simple parking guidance control strategy can work in most parallel parking tasks, if the available parking berth is not too small. This finding helps to build more concise automatic parking systems that can efficiently guide human drivers.

Cooperative merging control strategy of connected and automated vehicles on highways

To improve traffic performance when on-ramp vehicles merge into the mainstream,a collaborative merging control strategy is proposed to determine the merging sequence and trajectory control of vehicles.Merging trajectory planning takes the minimization of vehicle acceleration as the optimization objective.Either the variational method or the quadratic programming method is utilized to determine arrival time,optimal time and control variables for each vehicle.As a supplement,the adaptive cruise control(ACC)model is used to calculate each control variable in each time interval on special occasions.Simulation results show that the cooperative merging control strategy outperforms the optimal control strategy.The root mean square(RMS)of acceleration and the root mean square error(RMSE)of time headway are significantly decreased,with the reductions up to 90.1%and 25.2%,respectively.Under the cooperative control strategy,the difference between the average speed and desired speed consistently approaches zero.In addition,few or no collisions occur.To conclude,the proposed strategy favours the improvements in passenger comfort,traffic efficiency,traffic stability and safety around highway on-ramps.