基于伪谱法的滑翔轨迹多级迭代优化策略

伪谱法可实时求解具有高度非线性动态特性的飞行器最优轨迹;以X-51A相似飞行器模型为研究对象,采用增量法与查表插值建立纵向气动力模型,伪谱法与序列二次规划算法求解滑翔轨迹最优控制问题;提出使用多级迭代优化策略,为序列二次规划算法求解伪谱法参数化得到的大规模非线性规划问题提供初值,弥补序列二次规划算法在求解大规模非线性规划问题过程中,出现的初值敏感、收敛速度减慢等问题。通过与传统方法求解出的状态量与控制量仿真飞行状态进行对比,证明了多级迭代优化策略的有效性和高效性,该策略在实际工程应用中取得了良好效果。     

基于Radau伪谱法的重复使用运载器再入轨迹优化

为了提高数值解法的收敛速度,本文利用Radau伪谱法求解重复使用运载器的再入轨迹优化问题.该方法在一组Legendre-Gauss-Radau点上构造全局Lagrange插值多项式对状态变量和控制变量进行逼近,在动力学方程中状态变量对时间的导数可由插值多项式的导数来近似,故可将动力学方程约束转化为在Legendre-Gauss-Radau点上的代数微分方程约束.因此,可将连续时间的最优控制问题转化为有限维的非线性规划(NLP)问题,之后通过稀疏NLP求解器SNOPT即可对其进行求解.最后的仿真结果显示,通过该方法优化后的再入轨迹成功满足过程约束与边界约束.由于该方法的高效率和高精度特性,可将其应用于轨迹快速优化工程实际问题中.     

Interactive robot trajectory planning and simulation using Augmented Reality

Human-robot interaction in industrial robotics has largely been confined to finding better ways to reconfigure or program the robots. In this paper, an Augmented Reality based (RPAR-II) system is proposed to facilitate robot programming and trajectory planning considering the dynamic constraints of the robots. Through the various simulation capabilities provided in the proposed AR environment, the users are able to preview the simulated motion, perceive any possible overshoot, and resolve discrepancies between the planned and simulated paths prior to the execution of a task. By performing the simulation, the performance of the trajectory planning and the fitness of the selection of the robot controller model/parameters in the robot programming process can be visually evaluated. Practical issues concerning the system implementation are also discussed.     

A hybrid strategy for the time- and energy-efficient trajectory planning of parallel platform manipulators

In planning the trajectories of motor-driven parallel platform manipulators, the objective is to identify the trajectory which accomplishes the assigned motion with the minimal travel time and energy expenditure subject to the constraints imposed by the kinematics and dynamics of the manipulator structure. In this study, the possible trajectories of the manipulator are modeled using a parametric path representation, and the optimal trajectory is then obtained using a hybrid scheme comprising the particle swarm optimization method and the local conjugate gradient method. The numerical results confirm the feasibility of the optimized trajectories and show that the hybrid scheme is not only more computationally efficient than the standalone particle swarm optimization method, but also yields solutions of a higher quality.     

Adaptive trajectory generation based on real-time estimated parameters for impaired aircraft landing

ABSTRACT

This paper is motivated by a need to address the challenge of securing a safe landing after suffering from inflight impairment. In this paper, a new adaptive generalised model predictive static programming (G-MPSP) is developed to generate a safe emergency landing trajectory for impaired aircraft. Utilising the computationally efficient G-MPSP framework, the proposed algorithm enables adaptation of model parameters based on the prediction errors to ensure reasonable guidance performance. Based on the estimated parameters, a feasible landing trajectory is then generated by the flexible finite-horizon G-MPSP with input constraints. The integrated approach features explicit closed-form solutions for both parameter estimation and trajectory generation. Its effectiveness is demonstrated by simulations in the presence of parameter uncertainties and noises and by comparison studies with the non-adaptive G-MPSP.     

Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots

Trajectory planning in robotics refers to the process of finding a motion law that enables a robot to reach its terminal configuration, with some predefined requirements considered at the same time. This study focuses on planning the time-optimal trajectories for car-like robots. We formulate a dynamic optimization problem, where the kinematic principles are accurately described through differential equations and the constraints are strictly expressed using algebraic inequalities. The formulated dynamic optimization problem is then solved by an interior-point-method-based simultaneous approach. Compared with the prevailing methods in the field of trajectory planning, our proposed method can handle various user-specified requirements and different optimization objectives in a unified manner. Simulation results indicate that our proposal efficiently deals with different kinds of physical constraints, terminal conditions and collision-avoidance requirements that are imposed on the trajectory planning mission. Moreover, we utilize a Hamiltonian-based optimality index to evaluate how close an obtained solution is to being optimal.     

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

In this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance.     

桥式吊车系统的伪谱最优控制设计

对于桥式吊车系统的最优控制问题,根据实际的工况要求,性能指标有时不一定是标准的二次形式.同时,在实际的控制问题中,状态和控制输入往往会受到一些边界条件和路径过程中的约束.针对这一问题,本文应用Chebyshev伪谱优化算法来处理,它可以处理状态和控制约束的非线性最优化问题以及一个非标准的目标函数.首先对桥式吊车系统模型进行一系列的坐标变换,将其转变为上三角系统形式的误差模型.然后将桥式吊车最优控制问题转化成具有一系列代数约束的参数优化问题,即非线性规划问题.通过求解离散化后的参数优化问题,得到桥式吊车的最优控制律.本文还给出了Chebyshev伪谱最优解的可行性和一致性分析.最后,在仿真研究中验证该控制器的有效性.     

求解含复杂约束非线性最优控制问题的改进Gauss伪谱法

针对含有复杂约束条件的非线性最优控制问题,提出了一种改进的Gauss伪谱法 (Improved Gauss pseudospectral method, IGPM). 这类问题难以得到解析解,特别是有些问题不存在解析的模型, 一些参数只能通过查表得到,使得传统方法难以求解. 在传统的Gauss伪谱法的基础上,将非线性的终端状态积分约束等价地转化为线性形式,提出了IGPM, 通过协态映射定理可以计算出协态变量,检验最优性,使得IGPM具有间接法一样的精度. 并且给出了初始时刻协态变量和端点时刻控制变量的计算方法. 为了提高解的精度,基于IGPM提出了迭代算法, 最后将该算法应用于求解高超声速飞行器上升段轨迹优化问题,结果表明最优轨迹基本满足路径约束条件和最优性条件.     

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

Optimal trajectory plarmmg 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 roam 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 optimization 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 functiom 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.     

Coordinated trajectory planning for efficient communication relay using multiple UAVs

This paper investigates the use of small UAVs as communication relay nodes for expanding communication links and improving communication quality for a fleet of naval vessels. This paper firstly deals with the UAV deployment for stationary communication nodes, and then, proposes a decentralised nonlinear model predictive trajectory planning strategy for a dynamic environment. By exploiting motion estimates of vessels and states of UAVs, the trajectory planning algorithm finds a control input sequence optimising network connectivity over a certain time horizon. Numerical simulations are performed for both stationary and manoeuvring vessels to verify the feasibility and benefit of the proposed approach.     

基于高斯伪谱法的分区联立动态优化策略

最优控制轨迹通常由不同类型的弧段组成,采用数值方法求解这类问题时,其优化轨迹的不连续性可能导致求解失败,为此基于高斯伪谱法,提出一种分区联立动态优化求解策略.该策略通过对优化时域合理分区,避免了由于控制轨迹不连续而导致的病态优化问题.另外,通过联立求解分区后的优化问题,能够满足各分区间的连接条件,而且可以使用较少的节点获得高质量的优化解.最后以抗生素发酵过程为例验证了所提出算法的有效性.     

多约束条件下空间飞行器姿态机动规划的微分平坦方法

考虑执行机构性能、传感器空间指向等复杂约束,研究了空间飞行器姿态机动的路径规划问题.建立了姿态机动路径规划模型,并通过使用微分平坦理论将其映射到平坦输出空间,消除微分方程约束的同时降低设计空间维数;给出了平坦输出参数化描述的伪谱法,并运用共形映射、重心插值等技术改善了微分矩阵的病态特性,提高了路径规划的精度.仿真表明:该方法能够较快规划出满足约束的姿态机动路径,对工程应用具有一定参考价值.     

A unified framework for the numerical solution of optimal control problems using pseudospectral methods

A unified framework is presented for the numerical solution of optimal control problems using collocation at Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR), and Legendre-Gauss-Lobatto (LGL) points. It is shown that the LG and LGR differentiation matrices are rectangular and full rank whereas the LGL differentiation matrix is square and singular. Consequently, the LG and LGR schemes can be expressed equivalently in either differential or integral form, while the LGL differential and integral forms are not equivalent. Transformations are developed that relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. The LG and LGR discrete costate systems are full rank while the LGL discrete costate system is rank-deficient. The LGL costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the LGL discrete costate system. An example is considered to assess the accuracy and features of each collocation scheme.     

一种新的实时智能汽车轨迹规划方法

针对智能汽车的驾驶决策和轨迹规划问题, 将轨迹表示为轨迹曲线和加速度变化两部分, 以优化轨迹的行驶效率、安全性、舒适性和经济性为目标建立非线性规划模型. 基于序优化思想, 提出混合智能优化算法OODE, 分内、外两层分别优化加速度变化和轨迹曲线, 通过“粗糙” 评价轨迹曲线实现轨迹曲线的快速择优. 仿真结果表明, 所提出的方法能够处理包含多动态障碍物的复杂交通场景, 且具备实时应用能力, 模型的精度和求解速度均优于传统方法.

     

A novel coordinated path planning method using k-degree smoothing for multi-UAVs

Coordinated path planning for multiple unmanned aerial vehicles (multi-UAVs) is a highly significant problem encountered in their coordinated control. In the interests of completing mission securely and efficiently, the advanced multi-UAVs control technology requires a universal smoothing method as well as a precise coordination strategy. In this paper, we propose a novel multi-UAVs coordinated path planning method based on the k-degree smoothing, a more complex environment consists of multiple threat sources of which is constructed. By employing the Improved Ant Colony Optimization algorithm, a k-degree smoothing method is also presented aiming at obtaining a more flyable path. Additionally, the multi-UAVs coordination algorithm is induced by k-degree smoothing, allowing the UAVs to arrive at the destination simultaneously or in an acceptable time interval. Finally, simulations of the comparison between the Improved Ant Colony Optimization and classic algorithm, the detailed smoothing method, and the coordination are respectively conducted to validate that the proposed approach is feasible and effective in multi-UAVs coordinated path planning problems.     

An algorithm based on bidirectional searching and geometric constrained sampling for automatic manipulation planning in aircraft cable assembly

Robotic manipulation of deformable linear objects has potential application in aircraft cable assembly. However, it is difficult to be implemented in real tasks due to requiring prediction of the object’s deformation and obstacle-free manipulation planning with high efficiency. Aiming at exploring automatic assembly planning for aircraft cables assembly in narrow cabins with obstacles, this paper proposes a novel planning algorithm named RRT-BwC (Bi-direction with Constrain). Firstly, formulation of the question and the manipulation objects are presented with geometric definitions. Then a bi-RRT-tree searching method is developed to design the planner for overcoming obstacles in the high dimensional planning space. The numerical distance between configurations in the cable shape space are defined to measure the demands for their transition in consideration of the manipulation logics. And the sampling zone constrains to the shape configuration nodes are also discussed. Finally, the algorithm presents a valid manipulation sequence for robotic manipulation. The functionality and performance of the improved RRT approach are demonstrated with a simulated real-world problem of aircraft cable assembly, exhibiting computation efficiency promotion.     

A novel cartesian trajectory planning method by using triple NURBS curves for industrial robots

This article presents a novel method of robot pose trajectory synchronization planning. First of all, based on triple NURBS curves, a method of describing the position and orientation synchronization of the robot is proposed. Then, through considering geometric and kinematic constraints, especially angular velocity constraint, and employing bidirectional interpolation algorithm, a robot pose trajectory planning approach is developed, which has limited linear jerk, continuous bounded angular velocity and approximate optimal time, and does not need an optimization program. Ultimately, two robot pose paths, blade-shaped curve and fan-shaped curve, are utilized for simulations, and the results indicate that the proposed trajectory planning method can satisfy the given constraint conditions, i.e. the linear jerk is limited and the angular velocity is continuous bounded. The trajectory tracking experiments are further carried out on a 6-DOF industrial robot, and the results show that the proposed planning method can generate smooth trajectories to ensure the stability of the robot motion without impact in practical situations.     

A method for real-time trajectory monitoring to improve taxi service using GPS big data

As taxi service is supervised by certain electronic equipment (e.g., global positioning system (GPS) equipment) and network technique (e.g., cab reservation through Uber in USA or DIDI in China), taxi business is a typical electronic commerce mode. For a long time, taxi service is facing a typical challenge, that is, passengers may be detoured and overcharged by some unethical taxi drivers, especially when traveling in unfamiliar cities. As a result, it is important to detect taxi drivers’ misbehavior through taxi’s GPS big data analysis in a real-time manner for enhancing the quality of taxi services. In view of this challenge, an online anomalous trajectory detection method, named OnATrade (pronounced “on a trade,” which means activities in a taxi trade on the fly), is investigated in this paper for improving taxi service using GPS big data. The method mainly consists of two steps: route recommendation and online detection. In the first step, route candidates are generated by using a route recommendation algorithm. In the second step, an online anomalous trajectory detection approach is presented to find taxis that have driving anomalies. Experiments evaluate the validity of our method on large-scale, real-world taxi GPS trajectories. Finally, several value-added applications benefiting from big data analysis over taxi’s GPS data sets are discussed for potential commercial applications.