Nonholonomic Motion Planning of Mobile Robots
Nonholonomic Motion Planning of Mobile Robots
复制标题
移动机器人的非完整运动规划
DOI：
10.1007/978-1-84882-985-5_25
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
M. Galicki
中科院分区：
文献类型：
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作者：
M. Galicki
轮式移动机器人最近因其实用的任务而引起了人们的极大兴趣，例如机器人叉车在工厂中处理托盘或避障。根据负载的位置，必须生成一个轨迹，该轨迹必须精确地在叉孔的前面结束，并与叉孔对齐。机器人的速度在终点必须为零。在实际操作中，移动机器人在路上行驶时经常需要避开障碍物。在这种情况下，机器人应该尽可能靠近障碍物，这可能导致确定最小长度的无碰撞路径的必要性。上述任务属于一类运动规划问题。运动规划涉及在不违反非完整约束的情况下，获得将平台从初始构型（状态）引导到最终构型（状态）的开环控制。此外，在运动过程中还应考虑由驱动车轮的致动器的物理能力引起的控制约束。此外，如果工作空间中存在障碍物（状态不等式约束），则控制器应引导机器人避免与障碍物碰撞。在这种情况下，可以区分出解决这一问题的两种基本方法。一类是基于非完整运动规划的全局方法，可分为离散和连续两种。离散化技术是对基于离散化控制空间生成边的图进行顺序搜索。[1,2,3]中提出的图搜索方法生成全局最优运动。使用图搜索技术生成轨迹的缺点是由于状态和/或控制空间的离散化而导致分辨率损失。全局连续方法可以分为两类。第一类使用最优控制理论生成机器人轨迹。在[4]中使用了庞特里亚金极大值原理来确定无阻碍工作空间中的时间最优轨迹。结果控制是不连续的，而且砰砰砰。works[5,6]利用变分法和参数化控制，将连续最优控制公式转化为等效的非线性规划问题。作品[7,8]中提供的第二类非完整运动规划技术是基于牛顿方法的使用。其对避碰的适应性包含在[9]中。然而，它需要一个耗时的迭代计算过程。并且，在搜索机器人轨迹时，只对某一性能指标进行局部优化。在[10]中提出了一种接近实时的最优控制轨迹生成器，它求解了11个受状态约束的一阶微分方程。介绍了平均法在[11]运动规划中的应用。[11]的作者提出用截断傅立叶级数来表示转向输入，并基于射击法求解。在[12]中，提出了一种合适的非完整约束和轨迹参数化的变换，以避免障碍物。然而，这种方法没有考虑控制约束。对于具有非完整平台的移动机械臂，文献[13,14]提出了控制反馈层面的运动规划算法。第二种方法是基于局部方法的非完整运动规划。其中，基于系统在给定点求值的李代数的方法最具代表性。它在工作bbb中得到了发展。然而，GCBHD公式[16]的计算似乎是时间…
IntroductionWheeled mobile robots have attracted a lot of interest recently due to useful practical tasks such as robot fork trucks handling palettes in factories or obstacle avoidance. Based on the location of the load, a trajectory must be generated which ends precisely in front of, and aligned with the fork holes. The robot velocity must be zero at terminal point. It is often practically desirable that the mobile robot should avoid an obstacle while staying on the road. In such a case the robot should approach the obstacle as close as possible, which may lead to the necessity of determining the collision-free paths of minimum lengths. The aforementioned tasks belong to a class of motion planning problems. Motion planning is concerned with obtaining open loop controls which steer a platform from an initial configuration (state) to a final one, without violating the nonholonomic constraints. In addition, control constraints resulting from the physical abilities of the actuators driving the wheels should also be taken into account during the motion. Moreover, if there exist obstacles in the work space (state inequality constraints), the controls should steer the robot in such a way as to avoid collisions with obstacles. In such a context, two basic approaches to solving this problem may be distinguished. One is based on global methods of nonholonomic motion planning, which may be divided into discretized and continuous. The discretized technique is a sequential search of a graph whose edges are generated based on a discretized control space. Graph search methods proposed in [1, 2, 3] generate the globally optimal motion. The drawback of using graph-search techniques for trajectory generation is the resolution lost due to discretization of state and/or control space. Global continuous methods may be categorized into two classes. The first class uses an optimal control theory to generate robot trajectories. The Pontryagin maximum principle has been used in [4] to determine the time optimal trajectory in the unobstructed work space. The resulting controls are discontinuous and bang-bang. Using the calculus of variations and parameterization of controls, works [5, 6] convert the continuous optimal control formulation into an equivalent nonlinear programming problem. The second class of nonholonomic motion planning techniques offered in works [7, 8] is based on the use of Newton’s method. Its adaptation to collision avoidance is contained in [9]. However, it requires a time consuming iterative computational procedure. Moreover, only local optimization of a performance index is carried out when searching for the robot trajectory. A near realtime optimal control trajectory generator is presented in [10] which solves eleven first-order differential equations subject to the state constraints. Application of averaging method to motion planning is presented in [11]. The author of [11] proposed the use of truncated Fourier series to express the steering input and found the solution based on a shooting method. A suitable transformation of nonholonomic constraints and trajectory parameterization has been proposed in [12] to avoid obstacles. Nevertheless, this method does not take into account control constraints. In the context of mobile manipulators with nonholonomic platform, motion planning algorithms at the control feedback level have been proposed in works [13, 14]. The second approach to the nonholonomic motion planning is based on local methods. Among them, a method based on a Lie algebra of system evaluated at a given point is the most representative. It has been developed in work [15]. However, the computation of the GCBHD formula [16] seems to be time …