一种基于Dijkstra算法的机器人避障问题路径规划

移动机器人的避障问题是移动机器人控制领域的研究热点.针对给定的移动机器人避障问题,探讨了最短路径及最短时间路径的路径规划问题.对于最短路径问题,建立了简化的路径网格模型,将其抽象为由节点及边构成的两维图,再使用经典的Dijkstra算法获得可行的最短路径.对于最短时间路径问题,通过分析移动机器人弯道运行的速度曲线,基于几何方法得出了移动时间与过渡圆弧圆心之间严格的数学关系,此后借助MATLAB优化函数获得最佳的移动路径.算法可为类似机器人避障问题的解决提供借鉴.     

基于模糊传感器的机器人动态障碍环境中的运动控制

对自主式机械手在动态和部分已知且存在运动障碍环境中的运动规划和控制进行了研究,解决了自由碰撞运动控制中具有普遍意义的问题。利用人工势能场的机器人导航控制技术由模糊控制实现,系统的稳定性由李雅普诺夫原理保证。模糊控制器为机器人伺服提供控制指令,使机器人在不可预知的环境中能实时地、自主地选择到达目标的路径和方向。在动态环境的实时控制中,基于传感器的运动控制是处理未知模型和障碍物的重要控制方式。     

基于几何分析的机械臂运动路径规划问题研究

设计了分步-搜索逼近算法,解决了六自由度机械臂的位姿逆运算问题,使机械臂完成指尖到达指定目标点、沿指定曲线轨迹移动等动作.针对避障问题,设计了扫描截面的避碰算法.在此基础上,给出了机械臂作业的通用算法,并对所建模型和算法进行了实际检验.最后,分析了机械臂的设计参数,并提出了改进建议.     

六自由度机械臂的运动规划

为了使六自由度机械臂完成特定的动作,需要设计计算相应的指令序列.首先计算了机械臂位姿与指尖位置之间的关系公式,然后针对机械臂的到达问题、沿曲线运动问题和避障问题,分别提出目标位姿预测、曲线离散到达和受限目标到达三种解决方法,其中涉及的关键算法是自适应搜索法,该方法具有效率高、精度高、适用范围广的特点.在产生指令序列时采用贪心算法.通过以上方法得到的执行结果误差很小(<0.8mm),同时搜索收敛速度也很快.     

用旋量方法规划机器人运动轨迹

以姿态旋量描述机器人的位置姿态,在对偶空间中通过姿态旋量映射的点规划机器人的终端轨迹,具有直观、简便的独特优点。规划中直接根据跟踪误差进行收敛,提高了轨迹运行的动态精度,并适合于冗余自由度操作器。     

空间机器人组装超大型结构的动力学分析北大核心CSCD

超大型航天结构具有超大柔性、超低固有频率的特点,空间机器人在轨组装时应尽可能避免激起超大型结构的柔性振动.空间机器人组装超大型结构模块的过程分成抓捕阶段、位姿调整与稳定阶段、安装阶段和爬行阶段.通过对安装阶段的动力学与控制研究,提出共线安装的轨迹规划方法,有效避免了柔性结构振动.首先,采用自然坐标法和绝对节点坐标法建立主结构-空间机器人-待组装结构的在轨组装系统动力学模型.然后,将共线安装的要求转化为空间机器人的轨迹规划约束,要求空间机器人质心到主结构/待组装结构的距离保持不变,实现共线安装的轨迹规划.数值仿真表明:提出的组装方法在组装过程中可有效避免超大型结构的横向运动,降低夹持力矩.最后,分析了系统参数对组装过程动力学响应的影响,为超大型航天器的在轨组装提供了参考.     

正交轨线问题的计算机代数研究

用数学软件 Mathematica 3.0实现单参数曲线族的正交轨线的求解 .使常微分方程中的这一类常见问题得到迅速的解决     

Efficient Computation of Rectilinear Geodesic Voronoi Neighbor in the Presence of Obstacles

In this paper we present an algorithm to compute the rectilinear geodesic voronoi neighbor of an arbitrary query pointqamong a setSofmpoints in the presence of a set ofnvertical line segment obstacles inside a rectangular floor. The distance between a pair of points α and β is the shortest rectilinear distance avoiding the obstacles in and is denoted by δ(α, β). The rectilinear geodesic voronoi neighbor of an arbitrary query pointq,RGVN(q) is the pointp_i ∈ Ssuch that δ(q, p_i) is minimum. The algorithm suggests a preprocessing of the elements of the setsSand inO((m + n)log(m + n)) time such that for an arbitrary query pointq, theRGVNquery can be answered inO(log(m + n)) time. The space required for storing the preprocessed information isO(n + m log m). If the points inSare placed on the boundary of the rectangular floor, a different technique is adopted to decrease the space complexity toO(m + n). This technique works even if the obstacles are rectangles instead of line segments. Finally, the parallelization of the preprocessing steps for the latter algorithm is suggested, which takesO(log³(m + n)) time, usingO((m + n)^1.5/log²(m + n)) processors andO(log(m + n)) query time.     

机器人避障问题

研究机器人在平面区域中绕过静态障碍物到达指定目的地的问题, 分别考虑了路程最短和时间最短两种目标下的最优路径, 给出了计算机自动搜索最优路径的模型和算法。     

Dynamic Modeling of Spatial Cooperation Between Dual-Arm Mobile Manipulators北大核心CSCD

移动机械臂进行空间协作时会产生复杂的非线性耦合,使得采用Lagrange方程或Newton-Euler法直接进行建模极为繁琐。针对双移动机械臂空间协作问题,提出了一种结合Udwadia-Kalaba (U-K)方法与Lagrange方程建立动力学模型的方法。在建模过程中,将负载简化为连杆,选择负载中心断开的方式对系统进行分解,从而避免了机械臂末端关节断开导致的末端关节转角与连杆转角的约束信息缺失问题;将分割形成的两个子系统通过Lagrange方程进行建模,得到了子系统的动力学模型;再将协作系统的固有几何关系通过约束形式引入,应用U-K方法得到了协作系统动力学模型,减少了建立动力学模型所需要的计算量;最后通过数值仿真验证了该方法所得到的动力学模型的准确性。     

污染环境中两种群竞争模型的轨线研究

讨论了污染环境中体内毒素浓度不同的两种群竞争模型,通过构造适当的L iapunov函数,研究了模型的轨线并且给出了轨线的位置.     

Asymptotic Behaviour of Trajectory Fitting Estimators for Certain Non-ergodic SDE

Suppose one observes a path of a stochastic processX = (X_t)_t≥0 driven by the equation dX_t=θ a(X_t)dt + dW_t, t≥0, θ ≥ 0 with a(x) = x or a(x) = |x|^α for some α ∈ [0,1) and given initial condition X ₀. If the true but unknown parameter θ₀ is positive then X is non-ergodic. It is shown that in this situation a trajectory fitting estimator for θ₀ is strongly consistent and has the same limiting distribution as the maximum likelihood estimator, but converges of minor order. This revised version was published online in August 2006 with corrections to the Cover Date.     

旋量法在机器人动力学分析中的应用

本文用旋量方法研究机器人的动力学模型，将速度和角速度，力和力矩的内在联系有机地融合为一体，使Ｎｅｗｔｏｎ－Ｅｕｌｅｒ方法更加简明有效率．文中相对于机器人各臂质心建立参考系，使惯性张量和质心加速度计算简化，进一步减少计算量，达到快速实时计算．     

State constraints in the linear regulator problem: Case study

In this paper, we consider the problem of minimum-norm control of the double integrator with bilateral inequality constraints for the output. We approximate the constraints by piecewise linear functions and prove that the Langrange multipliers associated with the state constraints of the approximating problem are discrete measures, concentrated in at most two points in every interval of discretization. This allows us to reduce the problem to a convex finite-dimensional optimization problem. An algorithm based on this reduction is proposed and its convergence is examined. Numerical examples illustrate our approach. We also discuss regularity properties of the optimal control for a higher-dimensional state-constrained linear regulator problem.The first author was supported by the National Science Foundation, Grant No. DMS-9404431. The second author was supported by a François-Xavier Bagnoud Doctoral Fellowship and by NSF Grants DMS-9404431 and MSS-9114630.     

Trajectory planning based on minimum absolute input energy for an LCD glass-handling robot

The main idea of this paper is to design a novel point-to-point (PTP) trajectory based on minimum absolute input energy (MAIE) for an LCD glass-handing robot, which is driven by a permanent magnet synchronous motor (PMSM). The mechatronic system is described by a mathematical model of electrical and mechanical coupling equations. To generate the MAIE PTP trajectory, we employ a high-degree polynomial and compare with the trapezoidal, cycloidal and zero-jerk trajectories for various constraint conditions, which satisfy their corresponding desired constraints of angular displacement, speed, acceleration and jerk at the start and end times. The real-coded genetic algorithm (RGA) is used to search for the coefficients of high-degree polynomials for the PTP trajectories, and the inverse of absolute input electrical energy is adopted as a fitness function. From numerical simulations, it is found that either increasing the degree number of polynomials or decreasing the constraints at the start and end times will decrease the absolute input electrical energy. The proposed methodology for designing the MAIE PTP trajectory can also be applied to any mechatronic system driven by a PMSM.     

Dynamics and stability of a hybrid serial-parallel mobile robot

Kinematics, dynamics, and stability analysis of a hybrid serial-parallel wheeled mobile robot is detailed in this paper. Privileging the advantages of both serial and parallel robots, the suggested structure will provide higher stability for heavy object manipulation by a mobile robotic system. The proposed system is made of a differentially-driven wheeled platform, a planar parallel manipulator, which is called here as star-triangle (ST) mechanism, and a serial Puma-type manipulator arm. In order to develop a comprehensive kinematics model of the robot; first it is divided into three modules, i.e. a mobile platform, a parallel ST mechanism, and a serial robot. Next, a closed-form dynamics model is derived for the whole hybrid system based on a combined Newton–Euler and Lagrange formulation. Then, a careful validation procedure is presented to verify the obtained dynamics model. Finally, using the new postural stability metric named as moment-height stability (MHS), the important role of the parallel ST mechanism for stabilizing the mobile robotic system is demonstrated. The obtained results show that the proposed hybrid serial–parallel arrangement effectively enhances the tip-over stability of the overall mobile robotic system. Hence, it can be successfully exploited to prevent tip-over instability particularly during heavy object manipulation tasks.     

微分包含的单调轨道

该文研究微分包含单调轨道的存在性.基于一个新的逼近方法,作者证明了无限维空间中的一个存在性,其特殊情形包含了已有的若于生存定理.     

Analysis of a Linear Sampling Method for Identification of Obstacles

Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.     

Mathematical simulation of combined trajectory paths of a seven link biped robot

The following article focuses on biped robot simulation and control over combined trajectory paths with the aid of mathematical modeling methods focusing on the effects of hip height over torso’s modified motion. The mathematical simulation has been exploited to interpolate the combined trajectory of the robot path with the given breakpoints using inverse kinematic and dynamic methods to determine ZMP and stability treatments. After the robot’s combined path determination, a third-order spline is utilized because of its high precision and ability to calculate the kinematic, dynamic and control parameters. With the aid of this software, common parameters such as joint angles and inertial forces for the given specifications and nominal conditions are calculated and simulated.     

Cell-to-cell mapping method for time-optimal trajectory planning of multiple robot arm systems

This paper presents the results obtained by applying the cell-to-cell mapping method to solve the problem of the time-optimal trajectory planning for coordinated multiple robotic arms handling a common object along a specified geometric path. Based on the structure of the time-optimal trajectory control law, the continuous dynamic model of multiple arms is first approximated by a discrete and finite cell-to-cell mapping on a two-dimensional cell space over a phase plane. The optimal trajectory and the corresponding control are then determined by using the cell-to-cell mapping and a simple search algorithm. To further improve the computational efficiency and to allow for parallel computation, a hierarchical search algorithm consisting of a multiple-variable optimization on the top level and a number of cell-to-cell searches on the bottom level is proposed and implemented in the paper. Besides its simplicity, another distinguishing feature of the cell-to-cell mapping methods is the generation of all optimal trajectories for a given final state and all possible initial states through a single searching process. For most of the existing trajectory planning methods, the planning process can be started only when both the initial and final states have been specified. The cell-to-cell method can be generalized to any optimal trajectory planning problem for a multiple robotic arms system.