A Technique to Analytically Formulate and to Solve the 2-Dimensional Constrained Trajectory Planning Problem for a Mobile Robot

A new technique for trajectory planning of a mobile robot in a two-dimensional space is presented in this paper. The main concept is to use a special representation of the robot trajectory, namely a parametric curve consisting in a sum of harmonics (sine and cosine functions), and to apply an optimization method to solve the trajectory planning problem for the parameters (i.e., the coefficients) appearing in the sum of harmonics. This type of curve has very nice features with respect to smoothness and continuity of derivatives, of whatever order. Moreover, its analytical expression is available in closed form and is very suitable for both symbolic and numerical computation. This enables one to easily take into account kinematic and dynamic constraints set on the robot motion. Namely, non-holonomic constraints on the robot kinematics as well as requirements on the trajectory curvature can be expressed in closed form, and act as input data for the trajectory planning algorithm. Moreover, obstacle avoidance can be performed by expressing the obstacle boundaries by means of parametric curves as well. Once the expressions of the trajectory and of the constraints have been set, the trajectory planning problem can be formulated as a standard mathematical problem of constrained optimization, which can be solved by any adequate numerical method. The results of several simulations are also reported in the paper to show the effectiveness of the proposed technique to generate trajectories which meet all requirements relative to kinematic and dynamic constraints, as well as to obstacle avoidance.     

基于滚动时域的无人机动态航迹规划

针对带有动力学约束的多旋翼无人机航迹规划问题,提出了一种基于滚动时域控制和快速粒子群优化(RHC-FPSO)方法。该方法引入了基于VORONOI图的代价图方法说明从航迹端点到达目标点的距离估计。根据滚动时域和人工势场法的思想,将路径规划问题转化为优化问题,以最小距离和其他性能指标为代价函数。设计评价函数准则,按照评价准则使用变权重粒子群优化算法求解。针对无人机靠近危险区飞行的问题,将斥力场引入到代价函数中,提升其安全性。仿真实验结果显示,使用文中方法可以有效地在满足约束条件下穿过障碍物区域,以及在复杂环境下可以动态计算。     

基于hp自适应伪谱法的空间机器人路径规划

针对空间机器人运动过程中基座姿态产生较大扰动的问题,基于hp自适应高斯伪谱法提出了一种以基座所受反作用力矩最小为目标函数的空间机器人路径规划方法.首先,综合考虑空间机器人运动过程中存在的关节角度约束、关节角速度约束、控制力矩约束及初始状态和终端状态约束等约束条件,将空间机器人路径规划问题看成满足一系列约束条件和边界条件并实现特定性能指标最优的最优控制问题.其次,结合hp自适应高斯伪谱法（hp-AGPM）与非线性规划技术,求解带有边界约束和路径约束的优化控制问题,得到满足约束且性能指标最优的空间机器人运动轨迹.最后,以平面2自由度空间机械臂为例对所设计方法进行仿真验证,并与其他伪谱法进行对比分析.仿真结果表明：本文算法能在10.6 s的时间内规划出满足各约束条件且容许偏差低于10^-6的最优运动轨迹,并且在计算速度和配点数量上都优于其他伪谱法.     

Hierarchical control of cooperative nonlinear dynamical systems

Cooperative control methods that are scalable with low computational cost are crucial for networked dynamical systems to respond quickly in unknown or cluttered environments. In an attempt to make the problem tractable, many existing cooperative controls are designed with oversimplified assumptions and/or without the capabilities of rapidly handling different environmental and dynamical constraints. In this article, proposed is a two-level hierarchical, cooperative control framework using a divide-and-conquer strategy so that challenges can be separately handled at different levels. It is scalable and has low computational cost. Based on a simplified homogeneous double-integrator dynamic model, the top-level planner first computes cooperative trajectories satisfying obstacle avoidance requirements. Then at the lower level, state and control constraints, nonlinear dynamics and self-collision/obstacle avoidance as related to the real system are addressed through a bio-inspired fast trajectory planning algorithm. The stability of the overall hierarchical structure is proven. Two examples, a differential-drive ground vehicle formation control and an unmanned aerial vehicle formation flight, are used to illustrate the advantages of the proposed hierarchical framework.     

HGV平衡滑翔式轨迹可达区域计算方法研究

针对滑翔式高超声速飞行器(HGV)平衡滑翔轨迹可达区域的高精度快速计算问题,研究了一种基于降阶动力学模型和连续凸优化方法的可达区域计算方法。首先,根据“准平衡滑翔假设”条件,将再入飞行器三自由度动力学方程进行降阶处理,得到以速度为自变量的三阶动力学方程。然后,将可达区域计算问题描述为一系列满足再入走廊约束和初、末状态约束下的横程最大优化问题,将动力学方程进行线性化、离散化处理后,采用连续凸优化方法对该问题进行求解,得到了滑翔飞行器不同末端速度下的可达区域。最后,以CAV-H飞行器模型为例进行了仿真验证,结果表明,该方法具有较高的求解效率和可达区域计算精度。     

基于群智能-一致性理论的无人机编队全过程飞行航迹规划方法

针对无人机编队执行任务全过程飞行规划问题,提出一种基于多步粒子群优化的无人机编队航迹规划算法.首先,对无人机和执行任务策略进行建模,将编队执行任务全过程划分为编队成形、执行任务、返航、解散和无人机降落5个阶段,设计不同阶段的飞行策略;其次,针对不同的终端约束条件,设计多类多层优化指标,提出多步粒子群算法,并引入模型预测控制滚动优化航路点,得到适用于不同阶段的能严格满足约束条件的航路规划方法;然后,建立旋转坐标系,将航路点信息转换为编队控制律中的理想航向和高度信息,得到能通过航路点的编队控制算法;最后,利用编队控制算法去执行航路规划方法给出的航路点,生成航迹,得到编队航迹规划算法.仿真结果表明,所提规划方法比传统方法更适用于编队飞行,能为编队规划执行任务全过程的平滑航迹,具有良好的通用性.     

可重复使用航天器时间协同飞行轨迹优化

针对可重复使用航天器(RLV)时间协同飞行轨迹优化问题,提出了一种基于Radau伪谱法的轨迹优化方法。方法以再入飞行时间可知性、可控性为目标,使用Radau伪谱法对RLV的飞行时间进行预测,进而协调出多RLV的再入协同飞行时间,以此再入飞行时间为终端约束使用Radau伪谱法生成满足协同飞行要求的再入轨迹。仿真结果表明,上述轨迹优化方法可以得到满足时间协同约束、状态约束和控制约束的飞行轨迹,具有较高的稳定性和较快的求解速度。所提方法满足多架RLV时间协同再入飞行的需求,具有很强的实用价值。     

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.      

计算机数控系统光滑时间最优轨迹规划

基于控制向量参数化(CVP)方法, 研究了计算机数控(CNC)系统光滑时间最优轨迹规划方法. 通过在规划问题中引入加加速度约束, 实现轨迹的光滑给进. 引入时间归一化因子, 将加加速度约束的时间最优轨迹规划问题转化为固定时间的一般性最优控制问题. 以路径参数对时间的三阶导数(伪加加速度)和终端时刻为优化变量, 并采用分段常数近似伪加加速度, 将最优控制问题转化为一般的非线性规划(NLP)问题进行求解. 针对加加速度、加速度等过程不等式约束, 引入约束凝聚函数, 将过程约束转化为终端时刻约束, 从而显著减少约束计算. 构造目标和约束函数的Hamiltonian函数, 利用伴随方法获得求解NLP问题所需的梯度.     

Constrained multi-objective trajectory planning of parallel kinematic machines

This paper presents a new approach to multi-objective dynamic trajectory planning of parallel kinematic machines (PKM) under task, workspace and manipulator constraints. The robot kinematic and dynamic model, (including actuators) is first developed. Then the proposed trajectory planning system is introduced. It minimizes electrical and kinetic energy, robot traveling time separating two sampling periods, and maximizes a measure of manipulability allowing singularity avoidance. Several technological constraints such as actuator, link length and workspace limitations, and some task requirements, such as passing through imposed poses are simultaneously satisfied. The discrete augmented Lagrangean technique is used to solve the resulting strong nonlinear constrained optimal control problem. A decoupled formulation is proposed in order to cope with some difficulties arising from dynamic parameters computation. A systematic implementation procedure is provided along with some numerical issues. Simulation results proving the effectiveness of the proposed approach are given and discussed.     

基于伪谱法的双摆吊车时间最优消摆轨迹规划策略

在工业生产过程中,桥式吊车系统经常会体现出双摆系统的特性,导致更多欠驱动状态量的出现,增大控制难度.基于此,论文提出了一种针对双摆桥式吊车系统的时间最优轨迹规划方法,可以得到全局时间最优且具有消摆能力的轨迹.具体而言,为方便地构造以时间为代价函数的优化问题,首先对系统运动学模型进行相应的变换;在此基础上,考虑包括两级摆角及台车速度和加速度上限值在内的多种约束,构造出相应的优化问题;然后,利用高斯伪谱法(Gauss-pseudospectral method, GPM)将该带约束的优化问题转化为更易于求解的非线性规划问题,且在转化过程中,可以非常方便地考虑轨迹约束.求解该非线性规划问题,即可得到时间最优的台车轨迹.不同于已有的大多数方法,该方法可获得全局时间最优的结果.最后,通过仿真与实验结果验证了这种时间最优轨迹规划方法具有满意的控制性能.     

多无人机自适应编队协同航迹规划

针对多无人机(UAV)协同航迹规划中因编队队形约束而忽略部分较窄通道的问题,提出了一种基于自适应分布式模型预测控制的快速粒子群优化(ADMPC-FPSO)方法。该方法利用领航跟随法和虚拟结构法相结合的编队策略构造出虚拟编队引导点,以完成自适应编队协同控制任务。根据模型预测控制的思想,结合分布式控制方法,将协同航迹规划转化为滚动在线优化问题,且以最小距离等性能指标为代价函数。通过设计评价函数准则,使用变权重快速粒子群优化算法对问题进行求解。仿真结果表明,通过所提算法能够有效实现多无人机协同航迹规划,并可根据环境变化快速完成自适应编队变换,同时较传统编队策略代价更低。     

空间机器人最优能耗捕获目标的自适应跟踪控制

提出了一种能够引导末端执行器以期望速度跟踪目标的轨迹规划方法。该方法可以实现避障并满足关节限制要求。基于轨迹规划方法,设计了一种利用自由飘浮空间机器人跟踪与捕获章动自旋卫星的自适应控制策略。此外,该控制策略还考虑了最优能耗、测量误差和优化误差。首先,为了使执行器的跟踪误差和机械臂的能耗最小,将空间机器人的控制策略描述为一个关于关节速度、力矩和避障距离的不等式约束优化问题。然后,推导出一个系数为下三角矩阵的显式状态方程,并对目标函数进行解耦和线性化。设计了一种关节速度和力矩分段优化方法去代替传统的凸二次规划方法求解最优问题,这种方法具有较高的计算效率。最后,利用李雅普诺夫稳定性理论验证了所提控制方法的收敛性。     

反临拦截弹中制导弹道在线优化设计

为了实现反临拦截弹中制导段的弹道在线优化,基于邻域最优控制(NOC)理论和改进间接高斯伪谱法(GPM)设计一种弹道在线生成算法.根据临近空间拦截作战特点设计弹道优化模型,基于NOC理论推导关于修正状态量和协态量的两点边值问题.对横截条件进行二阶变分,通过逆向递推将终端最优协态修正值表示成跟踪偏差和终端约束修正量的表达式.将拦截弹的当前状态量作为初始约束值,终端最优协态修正值作为干扰量,利用标称弹道数据,基于改进间接GPM求得控制修正量.仿真结果表明,所提出的方法可以快速生成一条修正弹道,且具有较高的终端修正精度.     

基于改进约束差分进化算法的动态航迹规划

为解决三维复杂环境下无人机动态航迹规划问题,提出一种基于改进约束差分进化算法的动态航迹规划方法,以满足对实时性及动态搜索精度的要求.首先,根据无人机航迹规划特点将其描述为包括飞行约束及威胁约束在内的约束优化问题,并构造目标代价函数和约束限制函数;其次,将广义反向学习和自适应排序变异操作引入到约束差分进化算法中,以提高算法的多样性、收敛速度和寻优精度;最后,利用自适应权衡模型对各状态下的约束限制进行处理,充分利用“精英”个体信息,实现对目标适应值的合理转换.通过仿真实验以及与3种先进约束差分进化算法比较表明:所提方法能够有效实现静态及动态威胁回避,规划出安全适航的飞行路径,实现地形跟随;相较于其他3种算法,所提方法具有寻优性能好、鲁棒性强、收敛速度快和可靠性高等优势.     

Inverse motion planning method for overhead crane systems with state constraints

The trajectory planning problem with state constraints of overhead crane systems is considered in this paper. A new method, that is, an inverse motion planning method, is proposed. On this basis, a new trajectory planner is designed. The payload swing angle trajectory is designed first, and then by substituting it into the dynamic equations, the trolley trajectory is derived. For any transportation tasks, the adjustable parameter of the planner is computed by solving the state constraints such that the system states; that is, the trolley acceleration, trolley speed, and payload swing angle will not exceed their predefined constraints. Several experimental tests are conducted to verify the swing elimination performance of the proposed method.     

挠性卫星姿态机动三段式轨迹规划与滚动跟踪控制

以新颖成像模式对挠性敏捷卫星姿态的快速机动控制为需求,本文针对金字塔构型控制力矩陀螺(CMG)群为执行机构的挠性卫星,提出基于三段式正弦角加速度的姿态路径规划方法及具有滚动优化思想的跟踪算法。在姿态路径规划方法设计中,融合谱分析及非线性优化方法,设计了兼顾卫星姿态机动快速性及抑制挠性附件振动性能的姿态轨迹;为实现对规划姿态轨迹的高精度跟踪,综合加权优化指标及奇异性、执行机构能力等约束,设计了金字塔构型CMG群框架角速度的非线性模型预测(NMPC)跟踪控制律。在转动惯量存在测量误差及空间干扰情况下,多种姿态机动仿真表明,本文提出的控制方法是有效的,且表现出较强的鲁棒性。     

Minimum-time trajectory planning of mechanical manipulators under dynamic constraints

The paper presents a global optimization approach to the trajectory planning problem of mechanical manipulators. The purpose is to obtain a minimum-time cubic spline trajectory subject to constraints given by limited joint torques and torque derivatives taking into account the non-linear manipulator dynamics. It is shown how, without conservativeness, a semi-infinite optimization problem emerges. Conditions ensuring that the formalized problem admits a solution are given. The estimated global solution can be actually obtained by means of an hybrid genetic/interval algorithm that guarantees the feasibility of the found solution. The methodology is illustrated with numerical details for a two-link planar arm and a PUMA six-link manipulator; for the former, comparisons with an alternative optimization solver are exposed.     

基于PER-APF算法的无人驾驶汽车换道轨迹规划

针对传统人工势场算法在解决无人驾驶汽车换道轨迹规划过程中存在的不足,提出一种基于势能重构人工势场 (Potential Energy Reconstruction- Artificial Potential Field, PER-APF) 的无人驾驶汽车换道轨迹规划算法。首先,建立了具有斥力区分的道路边界约束条件和多约束换道轨迹规划模型,通过判断障碍车辆与道路边沿的距离来保证换道过程的安全性与有效性;其次,提出了基于势能重构的改进APF算法,通过构建虚拟区域以及重构物理势能力场,有效的解决了目标不可达以及局部最优问题。仿真结果表明,所设计的PER-APF算法能够快速有效地为无人驾驶汽车规划一条安全合理的换道轨迹。     

A novel trajectory planning strategy for aircraft emergency landing using Gauss pseudospectral method

To improve the survivability during an emergency situation, an algorithm for aircraft forced landing trajectory planning is proposed. The method integrates damaged aircraft modelling and trajectory planning into an optimal control framework, in order to deal with the complex aircraft flight dynamics, a solving strategy based on Gauss pseudospetral method （GPM） is presented. A 3-DOF nonlinear mass-point model taking into account the wind is developed to approximate the aircraft flight dynamics after loss of thrust. The solution minimizes the forced landing duration, with respect to the constraints that translate the changed dynamics, flight envelope limitation and operational safety requirements. The GPM is used to convert the trajectory planning problem to a nonlinear programming problem （NLP）, which is solved by sequential quadratic programming algorithm. Simulation results show that the proposed algorithm can generate the minimum-time forced landing trajectory in event of engine-out with high efficiency and precision.