Joint Trajectory Optimization Research Articles

A Terminal Residual Vibration Suppression Method of a Robot Based on Joint Trajectory Optimization

Vibration problems have become one of the most important factors affecting robot performance. To this end, a terminal residual vibration suppression method based on joint trajectory optimization is proposed to improve the accuracy and stability of robot motion. Firstly, based on the characteristics of the friction nonlinearity due to joint coupling and physical feasibility of dynamic parameters, a semidefinite programming method is used to identify dynamic parameters with actual physical meaning, thereby obtaining an accurate dynamic model. Then, based on the result of the residual vibration time domain analysis, a joint trajectory optimization model with the goal of minimizing joint tracking error is established. The Chebyshev collocation method is used to discretize the optimization model. The dynamic model is used as the optimization constraint, and barycentric interpolation is used to obtain the optimized joint motion trajectory. Finally, industrial robot experiments prove that the vibration suppression method proposed in this article can reduce the maximum acceleration amplitude of residual vibration by 62% and the vibration duration by 71%. Compared with the input shaping method, the method proposed in this paper can reduce the terminal residual vibration more effectively and ensure the consistency of running time and trajectory.

Joint Vehicle Path Planning for Interruptible 1-D Snake-like Platoons and 2D Flocks in Lane-free Traffic

This article presents a joint trajectory optimization algorithm for connected and automated vehicles forming 1-D snake-like interruptible platoons or 2-D deformable and interruptible flocks in a lane-free traffic environment on highways. A double double-integrator model is employed for the longitudinal and lateral movements of each vehicle. An appropriately defined Euclidian distance to track the front vehicle is utilized to establish and operate a 1-D platoon of vehicles, at selectable distance from each other. The Euclidian distance is used as a soft constraint, which allows for platoons to divide, if required to avoid obstacles, and reunite eventually. Moreover, the distance from a selectable frame (e.g. a triangle) are employed as soft constraints to form and maintain a 2-D deformable and interruptible flock of vehicles. The flock may feature a leader vehicle, e.g. at the front corner of a triangle. A collision avoidance function considering constant time-gaps or space-gaps, is used based on the elliptical distance between each two vehicles or external obstacles. A joint multi-objective function is formulated and minimized using an efficient feasible direction algorithm with respect to constant and state-dependent bounds on control inputs, including road boundary constraints. This leads to creating a flexible platoon or deformable flock accounting for low fuel consumption, passenger convenience, collision avoidance, achievement of desired speed and prevention of infeasible maneuvers. Challenging scenarios are examined on a lane-free straight motorway stretch, producing promising results for further exploration of the proposed concepts within an MPC (model predictive control) framework.

Trajectory planning of a dual-arm space robot for target capturing with minimizing base disturbance

During the on-orbit capture task of the free-floating space robot, its operating space degenerates. The dynamic coupling and dynamic singularity also affect the task operation. In this paper, a general collision-free trajectory planning method to minimize base disturbance is proposed for a free-floating dual-arm space robot. This method can realize smooth joint trajectory planning while avoiding singularity and realizing self-collision avoidance. The singularity can be effectively avoided by transforming the trajectory planning problem into a nonlinear optimization problem. The optimization function is composed of base disturbance penalty function, end effector error function and collision repulsion potential field function, which can be used to solve the optimal joint trajectory parameters. Futhermore, self-collision avoidance is achieved by combining the bacterial foraging optimization algorithm(BFOA) with the geometric vector collision-avoidance method based on artificial potential field to simplify the calculation complexity. Finally, simulations verify the effectiveness of the proposed planning framework.

A trajectory optimization method for UAV cascade relay broadcast communication system

An unmanned aerial vehicle's(UAV) trajectory optimization is an important way to improve the performance of its relay communication system. The trajectory optimization method for the UAV cascade relay broadcast communication system that uses the decoding and forwarding protocols is studied. Firstly, the expressions of the signal-to-noise ratio of the UAV and the user are given. Then, a joint trajectory optimization method and a distributed trajectory optimization method for cascaded UAVs based on the minimized maximum user interruption probability are proposed. The transmission performance of the system link that uses the two trajectory optimization methods is studied; the mathematical expressions of the relay communication system's traverse capacity and the outage probability of a single user are given. Finally, the influence of the relay communication system's characteristic parameters on the optimal trajectory of the cascade relay UAV and its performance are verified with computer simulations. The simulation results show that the performance of the two trajectory optimization methods is basically the same, thus verifying the effectiveness of the trajectory optimization criterion.

Multi-IRS and Multi-UAV-Assisted MEC System for 5G/6G Networks: Efficient Joint Trajectory Optimization and Passive Beamforming Framework

This article presents a multi-intelligent reflecting surface (IRS)- and multi-unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system for 5G/6G networks. In the studied system, multiple UAVs are integrated for providing services to large-scale user equipment (UEs) with the help of multiple IRSs. This article aims to minimize the overall cost including energy consumption, completion time, and maintenance cost of UAVs by jointly optimizing the trajectories of UAVs and phase shifts of IRSs. When solving this problem, one has to count in mind the deployment of stop points (SPs) of UAVs, and consider the association among UEs, and UAVs (i.e., which UE will send data to which UAV at which SP), the order of SPs, and the phase shifts of IRSs. Therefore, traditional optimization techniques may not solve the above-mentioned problem in an efficient way. To tackle the above-mentioned problem, this article proposes an algorithm called TPaPBA that consists of four phases. The first phase optimizes the SPs’ deployment via using a differential evolution algorithm having variable population size. As a result, all the SPs of UAVs can be obtained. Then, the second phase optimizes the association among UEs, SPs, and UAVs. Specifically, TPaPBA first adopts a clustering algorithm to optimize the SPs-UAVs association, and then a close criterion is introduced to optimize UEs-SPs association. Subsequently, third phase adopts a low-complexity greedy algorithm to optimize the order of SPs for UAVs. Finally, the phase shifts of IRSs are optimized to enhance the data rate between UEs and UAVs. The simulation results of TPaPBA on ten instances having UEs ranging from 100 to 1000, reveals that TPaPBA has significantly improved the system performance contribution and outperforms other approaches in terms of reducing the overall cost of UAVs.

Time and Energy Optimal Trajectory Planning of Wheeled Mobile Dual-Arm Robot Based on Tip-Over Stability Constraint

Trajectory planning and avoidance of tipping are the main keys to success in the mobile dual-arm manipulation, especially when the dual-arm or moving platform is running fast. The forces and moments between wheel-terrain and body-arm have been analyzed by kinematics and force analysis of a robot to define tip-over stability constraint. Then, an improved tip-over moment stability criterion for a wheeled mobile dual-arm robot is presented and defines tip-over stability constraint based on it. To improve the motion stability of the robot, this paper presents an optimal joint trajectory planning model based on time and energy. The quintic B-spline curve and an improved NSGA-II algorithm, which are time and energy, are applied to multi-objective optimization. The simulation results show that the motion stability of a robot is improved based on the tip-over stability constraint. This trajectory planning method based on the stability constraint can be applied to other mobile robots as well.

Trajectory Optimization and Power Allocation for Cell-Free Satellite-UAV Internet of Things

Massive access outside the coverage of terrestrial cellular networks will be the main feature of the sixth generation (6G) networks. In order to cope with it, the cognitive satellite-UAV network (CSUN) has drawn a lot of attentions. In this paper, we investigate the UAV trajectory optimization and power allocation for the cell-free CSUN consisting of one satellite and a swarm of UAVs. Indeed, due to the on-board energy constraints of UAVs, both the trajectory optimization and the power allocation can significantly save the energy to improve the energy efficiency. The joint trajectory optimization and power allocation problem is formulated as a mixed-integer non-convex optimization problem which is extremely difficult to solve. In order to reduce the computational complexity, we decompose the original optimization problem into two subproblems in terms of the trajectory optimization and power allocation. For the trajectory optimization subproblem, we model it as a Traveling Salesman Problem (TSP), and the PSO is adopted to solve it. When the trajectory variables are fixed, the power allocation subproblem is still difficult to tackle due to its non-convexity and large scale. Firstly, we present a kind of centralized algorithm in which the DC (difference of two convex functions) algorithm is applied to optimize it, and then a distributed algorithm based on auxiliary variables is proposed to reduce the signaling overhead and computational complexity. The simulation results demonstrate the effectiveness of the proposed joint trajectory optimization and power allocation algorithm for the cell-free CSUN.

Biased Stackelberg game‐based UAV relay anti‐jamming communications: Exploiting trajectory optimization and transmission mode selection

Although unmanned aerial vehicle (UAV) relay can provide auxiliary communication due to its flexible mobility, it is vulnerable to jamming attacks. This paper considers the UAV relay anti-jamming communication issue under the threat of a malicious jammer with beam-forming jamming capability. To prevent the relay link from deteriorating, UAV trajectory adjustment and transmission mode switching between half-duplex and full-duplex are two available schemes, while they will incur the additional flying costs and continuous mode switching, respectively. To balance the trade-off between trajectory optimization and mode selection, this paper investigates the joint trajectory optimization and mode selection anti-jamming approach. First, an anti-jamming utility considering the cost-efficient and end-to-end capacity gains is designed. Second, to model the bounded rationality of both the UAV relay and the jammer due to the adversarial context, a biased Stackelberg game to analyse the competitive system interactions is proposed. Moreover, the existence of Stackelberg equilibrium (SE) in the problem is proved. Finally, a joint mode selection and trajectory optimization (JMSTO) algorithm based on the multi-armed bandit is proposed to obtain the SE. It is further demonstrated that the JMSTO algorithm has a logarithmic regret. The results show that our proposed JMSTO algorithm is superior to non-joint optimization methods.

Joints Trajectory Planning of Robot Based on Slime Mould Whale Optimization Algorithm

The joints running trajectory of a robot directly affects it’s working efficiency, stationarity and working quality. To solve the problems of slow convergence speed and weak global search ability in the current commonly used joint trajectory optimization algorithms, a joint trajectory planning method based on slime mould whale optimization algorithm (SMWOA) was researched, which could obtain the joint trajectory within a short time and with low energy consumption. On the basis of analyses of the whale optimization algorithm (WOA) and slime mould algorithm (SMA) in detail, the SMWOA was proposed by combining the two methods. By adjusting dynamic parameters and introducing dynamic weights, the proposed SMWOA increased the probability of obtaining the global optimal solution. The optimized results of 15 benchmark functions verified that the optimization accuracy of the SMWOA is clearly better than that of other classical algorithms. An experiment was carried out in which this algorithm was applied to joint trajectory optimization. Taking 6-DOF UR5 manipulator as an example, the results show that the optimized running time of the joints is reduced by 37.674% compared with that before optimization. The efficiency of robot joint motion was improved. This study provides a theoretical basis for the optimization of other engineering fields.

Cooperative UAV Enabled Relaying Systems: Joint Trajectory and Transmit Power Optimization

Unmanned aerial vehicles (UAVs) can be used as aerial relays to provide quick and on-demand wireless connections for the area without network coverage. Since a UAV’s onboard energy is limited, how to prolong the duration of UAV relaying communication is challenging. In this paper, we consider applying multiple UAVs to extend the duration of communication via UAV collaboration. We first propose a UAV collaboration scheme, namely heuristic UAV substitution, which lets the UAV relays work one by one individually. Then, we propose another scheme called spectral efficient UAV substitution to improve the spectrum efficiency. Furthermore, under these two proposed schemes, we jointly design the trajectories of the UAV relays and the transmit power of the source and the UAV relays, with the goal of end-to-end throughput maximization. Although the considered optimization problem is non-convex and difficult to solve, we propose an efficient algorithm to find a suboptimal solution to it by applying the block coordinate ascent and successive convex approximation methods. Simulation results show that the proposed UAV substitution schemes can effectively extend the relaying communication duration, and the throughput performance of the proposed joint trajectory optimization and transmit power control algorithm outperforms some benchmark algorithms without considering joint design.

Correction to “Joint Trajectory Optimization and User Scheduling for Rotary-Wing UAV-Enabled Wireless Powered Communication Networks”

Correction to “Joint Trajectory Optimization and User Scheduling for Rotary-Wing UAV-Enabled Wireless Powered Communication Networks”

Trajectory Optimization of CAVs in Freeway Work Zone considering Car-Following Behaviors Using Online Multiagent Reinforcement Learning

Work zone areas are frequent congested sections considered as the freeway bottleneck. Connected and autonomous vehicle (CAV) trajectory optimization can improve the operating efficiency in bottleneck areas by harmonizing vehicles’ manipulations. This study presents a joint trajectory optimization of cooperative lane changing, merging, and car-following actions for CAV control at a local merging point together with upstream points. The multiagent reinforcement learning (MARL) method is applied in this system, with one agent providing a merging advisory service at the merging point and controlling the inner-lane vehicles’ headway for smooth outer-lane vehicle merging, while other agents provide lane-changing advisory services at advance lane-changing points to control how vehicles make lane changes in advance and perform corresponding headway adjustment, similar to and jointly with the merging advisory service. Uniting all agents, the coordination graph (CG) method is applied to seek the global optimum, overcoming the exponential growth problem in MARL. Using MATLAB and the VISSIM COM interface, an online simulation platform is established. The simulation results show that MARL is effective for online computation with in-timing response. More importantly, comparisons of the results obtained in various scenarios demonstrate that the proposed system obtained smoother vehicle trajectories in all controlled sections, rather than only in the merging area, indicating that it can achieve better traffic conditions in freeway work zone areas.

Exploiting Redundancies for Workspace Enlargement and Joint Trajectory Optimization of a Kinematically Redundant Hybrid Parallel Robot

Abstract In this paper, possibilities for workspace enlargement and joint trajectory optimization of a (6 + 3)-degree-of-freedom kinematically redundant hybrid parallel robot are investigated. The inverse kinematic problem of the robot can be solved analytically, which is a desirable property of redundant robots, and is implemented in the investigations. A new method for detecting mechanical interferences between two links which are not directly connected is proposed for evaluating the workspace. Redundant degrees-of-freedom are optimized in order to further expand the workspace. An approach for determining the desired redundant joint coordinates is developed so that a performance index can be minimized approximately when the robot is following a prescribed Cartesian trajectory. The presented approaches are readily applicable to other kinematically redundant hybrid parallel robots proposed by the authors.

Motion and trajectory planning modeling for mobile landing mechanism systems based on improved genetic algorithm.

In many traditional soft-landing missions, researchers design the lander and the rover as two separate individuals, which has its limitations. At present, research on landers mainly focuses on the performance analysis of those who cannot move, and the motion of legged mobile lander has not yet been studied. In this paper, a novel Mobile Landing Mechanism (MLM) is proposed. Firstly, the monte-Carlo method is used to solve the workspace, and the motion feasibility of the mechanism is verified. Secondly, combining with the constraints of velocity, acceleration and secondary acceleration of each driving joint of the MLM, the trajectory of its joint space is planned by using cubic spline curve. And based on the weighted coefficient method, an optimal time-jerk pedestal trajectory planning model is established. Finally, by comparing the genetic algorithm (GA) with the adaptive genetic algorithm (AGA), an optimization algorithm is proposed to solve the joint trajectory optimization problem of the MLM, which can obtain better trajectory under constraints. Simulation shows that the motion performance of the mechanism is continuous and stable, which proves the rationality and effectiveness of the foot trajectory planning method.

Joint Trajectory Optimization and Spectrum Access for Cognitive UAV Networks

In this article, we consider a cognitive unmanned aerial vehicle network (CUAVN), which consists of a leading unmanned aerial vehicle (LUAV) and a group of following unmanned aerial vehicles (FUAVs), and where the FUAVs fly irregularly from a data collection point to the next data collection point and transmit collected data to the LUAV. Our goal is to maximize the achievable throughput of the CUAVN by jointly adapting the FUAVs sensing duration, the trajectory of the FUAVs, and the transmit power of the FUAVs under the constraints of maximum interference, maximum UAV speed, UAV collision avoidance and the total flying periods. In the challenging scenarios, the original non-convex problem is addressed by iteratively optimizing three decoupled subproblems: sensing duration optimization, FUAVs trajectory optimization, and FUAVs power allocation optimization. Since there are highly non-convex objective function and constraints in the FUAV trajectory optimization subproblem, we convert it into a more tractable convex problem by utilizing difference-of-convex (DC) functions. Furthermore, a three dimensional (3D) spatial-temporal sensing scheme based on UAVs is introduced into cognitive UAV systems with multiple primary transmit-receive pairs (PTRs) to further improve spectrum efficiency. Simulation results show that the achievable throughput of the FUAVs with the proposed scheme rises by approximately 53% compared with the FUAV fixed trajectory flight scheme and by approximately 58% in comparison with the only time-dimension spectrum sensing scheme.

UAV-assisted wireless powered Internet of Things: Joint trajectory optimization and resource allocation

Due to affordable price, high mobility and flexible maneuverability, Unmanned Aerial Vehicle (UAV)-assisted communication can play an important role in the deployment of the Internet of Things (IoT) in emergency. Since UAV network performance is highly dependent on UAV deployment location, trajectory design becomes the research hotspot in UAV-assisted communication. To this end, a UAV-assisted multicarrier wireless powered communication model is proposed for IoT scenarios in this paper. Specifically, as an aerial base station, the UAV transmits Orthogonal Frequency Division Multiplexing (OFDM) signals to IoT nodes, while IoT nodes decode information and harvest energy from the signals. Afterwards, IoT nodes transmit information to the UAV by using the harvested energy. A joint UAV trajectory optimization and resource allocation scheme based on OFDM is proposed. The aim is to maximize the minimum achievable rate in the uplink among all IoT nodes by jointly optimizing UAV trajectory, subcarrier, power and subslot allocation, subject to the achievable sum rate of all IoT nodes in the downlink. Due to the non-convexity and complexity of the formulated optimization problem, an alternative iteration algorithm is proposed to deal with the problem. Simulation results that the proposed algorithm can optimize the UAV trajectory and adapt to the node movement. Compared with conventional resource allocation schemes, the proposed scheme not only significantly enhances the minimum achievable rate, but also works well for two flight modes.

Noncausal trajectory optimization for real-time range-only target localization by multiple UAVs

This study proposes a new method namely noncausal trajectory optimization which is developed to obtain superior performance in range-only (i.e. distance and received signal strength based) target localization by multiple unmanned aerial vehicles (UAVs). Noncausal trajectory optimization suggests to optimize the next waypoint considering not only the past waypoints already visited but also the future remaining trajectory of the UAV. Therefore, based on the analogy of noncausal filters in signal processing, the new proposed method is named as “noncausal trajectory optimization”. In the previous literature, because only the past trajectory is taken into account, the UAVs are mostly suggested to make circular or spiral motions around the target. However, this study suggests that the UAV must create a linear trajectory as much as possible when total travel length is shorter than initial distance to the target. For a single UAV, this study proves that the ideal direction of this linear path is only the function of the ratio of the total length of trajectory over the initial distance to the target. To prove this, the summation operators in Fisher information matrices (FIM) are converted to line integrals and then D-optimality criterion is applied. Next, noncausal trajectory optimization is introduced which is dedicated to obtain a higher final localization capability by sacrificing immediate or early advantages. Then, noncausal joint trajectory optimization for multiple UAVs is illustrated. Finally, trajectory optimization for moving target as well as three dimensional trajectory optimization are discussed. Monte Carlo simulations showed that the proposed optimization method obtains a higher final accuracy level compared to the ordinary trajectory optimization.

Optimal trajectory planning of industrial robot for improving positional accuracy

Purpose The purpose of this paper is to improve the positional accuracy, smoothness on motion and productivity of industrial robot through the proposed optimal joint trajectory planning method. Also a new improved algorithm, i.e. non-dominated sorting genetic algorithm-II (NSGA-II) with achievement scalarizing function (ASF) has been proposed to obtain better optimal results compared to previously used optimization methods. Design/methodology/approach The end effector positional errors can be reduced by limiting the uncertainties of dynamic parameter variations like torque rate of joints. The jerk induced in robot joints due to acceleration variations are need to be minimized which otherwise induces vibrations in the manipulator that causes deviation in the encoders. But these lead to a vast increase in total travel time which affects the cost function of trajectory planning. Therefore, these three objectives need to be minimized individually so that an optimal trajectory path can be achieved with minimum positional error. Findings The simulation results have been obtained by running the proposed hybrid NSGA-II with ASF in MATLAB R2017a software. The optimal time intervals have been used to calculate jerk, acceleration and torque values for consecutive points on the trajectory path. From the simulation and experimental results, it can be concluded that the optimization technique could be used effectively for the trajectory planning of six-axis industrial manipulator in the joint space on the basis of minimum time-jerk-torque rate criteria. Originality/value In this paper, a new approach based on hybrid multi-objective optimization technique by combining NSGA-II with ASF has been applied to find the minimal time-jerk- torque rate joint trajectory of a six-axis industrial robot for obtaining higher positional accuracy. The results obtained from the execution of algorithm have been validated through experimentation using Kawasaki RS06L industrial robot for a particular defined path.

Optimal trajectory generation of an industrial welding robot with kinematic and dynamic constraints

PurposeThis paper aims to present an optimal trajectory planning for industrial MOTOMAN MA1440A gas metal arc welding system. A new and efficient evolutionary algorithm, enhanced multi-objective teaching learning-based optimization (EMOTLBO) method, i.e. TLBO with non-dominated sorting approach has been proposed to obtain the optimal joint trajectory for the defined weld seam path.Design/methodology/approachThe joint trajectory of the welding robot need to be computed in an optimal manner for proper torch orientation, smooth travel of the robot along the weld path and for achieving higher positional accuracy. This can be achieved by limiting the kinematic and dynamic variations of the robot joints like joint jerks, squared acceleration and torque induced in the joints while travel of the robot along the weld path. Also, the robot travel should be done within minimum possible time for maintaining productivity. This leads to a multi-objective optimization problem which needs to be solved for maintaining proper orientation of the robot end effector. EMOTLBO has been proposed to obtain the Pareto front consisting of optimal solutions. The fuzzy membership function has been used to obtain the optimal solution from the Pareto front with best trade-off between objectives.FindingsThe proposed method has been implanted in MATLAB R2017a for simulation results. The joint positions have been used to program the robot for performing welding operation along the weld seam. From the simulation and experimental results, it can be concluded that the proposed approach can be effectively used for optimal trajectory planning of MOTOMAN MA 1440 A arc welding robot system as a very smooth and uniform weld bead has been obtained with maximum weld quality.Originality/valueIn this paper, a novel approach for optimal trajectory planning welding arc robot has been performed. Though trajectory planning of industrial robots has been done before, it has not been done yet for welding robot. The objectives are formulated taking in consideration of requirement of welding process like minimization of joint jerks and torques induced during welding operation due to travel of robot with the effect of arc spatter, minimization of squared acceleration for maintaining constant joint velocity and finally minimization of total travel time for maintaining productivity.

Joint Trajectory Optimization and User Scheduling for Rotary-Wing UAV-Enabled Wireless Powered Communication Networks

Wireless powered communication networks are promising in the next generation wireless communication systems since they can prolong the communication time of users. However, the wireless powered performance is limited due to the low energy harvesting efficiency caused by channel fading. In order to tackle this issue, rotary-wing unmanned aerial vehicle (UAV) enabled wireless powered communication network (WPCN) is first proposed to provide energy harvesting and information transmission to multiple ground users. Then, the energy consumption minimization problem for the UAV-enabled WPCN is formulated subject to the speed, initial and final positions of the UAV, the energy harvesting causality and user scheduling constraints. Finally, an efficient algorithm by employing the path discretization and successive convex approximation techniques is proposed to solve the challenging non-convex problem. Simulation results show that our proposed scheme can efficiently balance the energy harvesting phase and transmission phase based on the optimal trajectory design, moreover, it outperforms other benchmark schemes in terms of the energy consumption.