Obstacle Modelling Oriented to Safe Motion Planning and Control for Planar Rigid Robot Manipulators

Trajectory planning and tracking are crucial tasks in any application using robot manipulators. These tasks become particularly challenging when obstacles are present in the manipulator workspace. In this paper a n-joint planar robot manipulator is considered and it is assumed that obstacles located in its workspace can be approximated in a conservative way with circles. The goal is to represent the obstacles in the robot configuration space. The representation allows to obtain an efficient and accurate trajectory planning and tracking. A simple but effective path planning strategy is proposed in the paper. Since path planning depends on tracking accuracy, in this paper an adequate tracking accuracy is guaranteed by means of a suitably designed Second Order Sliding Mode Controller (SOSMC). The proposed approach guarantees a collision-free motion of the manipulator in its workspace in spite of the presence of obstacles, as confirmed by experimental results.     

ON THE PATH PLANNING PROBLEM IN THE VICINITY OF OBSTACLES

This paper presents a new approach to motion planning in the neighborhood of obstacles. The technique presented here, the configuration space vector path planner CSVPP , generates a collision-free path for a robot amongst unknown arbitrarily shaped obstacles. The CSVPP algorithm utilizes discrete vectors in the configuration space of the robot to generate a path between any two points in the robot's dynamic time-varying workspace. The calculation of the robot's path assumes interpolated joint control, and provides a computational speed that enables the algorithm to be implemented in real time. A number of simulations are provided for several varying environments.     

Collision-free motion planning of dual-arm reconfigurable robots

Dual-arm reconfigurable robot is a new type of robot. It can adapt to different tasks by changing its different end-effector modules which have standard connectors. Especially, in fast and flexible assembly, it is very important to research the collision-free planning of dual-arm reconfigurable robots. It is to find a continuous, collision-free path in an environment containing obstacles. A new approach to the real-time collision-free motion planning of dual-arm reconfigurable robots is used in the paper. This method is based on configuration space (C-Space). The method of configuration space and the concepts reachable manifold and contact manifold are successfully applied to the collision-free motion planning of dual-arm robot. The complexity of dual-arm robots’ collision-free planning will reduce to a search in a dispersed C-Space. With this algorithm, a real-time optimum path is found. And when the start point and the end point of the dual-arm robot are specified, the algorithm will successfully get the collision-free path real time. A verification of this algorithm is made in the dual-arm horizontal articulated robot SCARATES, and the simulation and experiment ascertain that the algorithm is feasible and effective.     

Development of a configuration space motion planner for robot in dynamic environment

In this paper, the on-line motion planning of articulated robots in dynamic environment is investigated. We propose a practical on-line robot motion planning approach that is based upon pre-computing the global configuration space (C-space) connectivity with respect to all possible obstacle positions. The proposed motion planner consists of an off-line stage and an on-line stage. In the off-line stage, the obstacles in the C-space (C-obstacle) with respect to the obstacle positions in the workspace are computed, which are then stored using a hierarchical data structure with non-uniform 2^m trees. In the on-line stage, the real obstacle cells in the workspace are identified and the corresponding 2^m trees from the pre-computed database are superposed to construct the real-time C-space. The collision-free path is then searched in this C-space by using the A* algorithm under a multi-resolution strategy which has excellent computational efficiency. In this approach, the most time-consuming operation is performed in the off-line stage, while the on-line computing only need to deal with the real-time obstacles occurring in the dynamic environment. The minimized on-line computational cost makes it feasible for real-time on-line motion planning. The validity and efficiency of this approach is demonstrated using manipulator prototypes with 5 and 7 degree-of-freedom.     

DETERMINING THE PATH SEARCH GRAPH AND FINDING A COLLISION-FREE PATH BY THE MODIFIED A* ALGORITHM FOR A 5-LINK CLOSED CHAIN

Two tightly coordinated 2-link planar manipulators and the straight line between their two bases can be considered as a 5-link closed chain. Since the coordination of robot manipulators has broad applications in manufacturing, hazardous material handling, undersea operation, and space exploration, automatic collision-free path planning for a 5-link closed chain is an important unsolved engineering problem. This paper describes a collision-free path planning algorithm for a 5-link closed chain with revolute joints. In the algorithm the 5-link closed chain is first represented by a path search graph that is built on the basis of the concept of the newly developed C subspace model. Subsequently, a collision-free path is searched upon the graph by the modified A* algorithm. The significance of this path planning algorithm is its convergence and efficiency. The convergence is guaranteed by the C subspace model, which constructs unique mapping between the planned path in C subspaces and that in the world space. The way we build the path search graph and evaluation functions of the A* algorithm is designed to increase the search speed and to preserve the maneuverability of the 5-link closed chain.     

Mobile robot with a self-positioning system

This paper describes a general method using configuration space for planning a collision-free path of a manipulator with 6 degrees of freedom (DOF). The basic approach taken in this method is to restrict the free space concerning path planning and to avoid executing unnecessary collision detections, based on the idea that a collision-free path can be planned using only partial information of the configuration space. The configuration space is equally quantized into cells, and the cells concerning path planning are efficiently enumerated based on a heuristic graph search algorithm. A heuristic function which characterizes the search strategy can be defined to give priority to the gross motion using the first few joints. A bi-directional search strategy is also introduced to improve efficiency. The memory is allocated only to the portion of the configuration space concerning path planning, and the data of the free space defined in the 6-dimensional configuration space can be efficiently stored. This algorithm of free space enumeration is independent of the kinematic characteristics of the manipulator. Therefore, this method is generally applicable to any type of manipulator. It has actually been implemented and has been applied to a 6-DOF articulated manipulator.     

基于网格法的机械臂无碰撞轨迹规划

介绍了高压带电作业机械臂在三维空间中进行无碰撞轨迹规划的一种方法,通过对整个作业空间进行网格化划分,完整的描述出自由空间与障碍物空间,并对每一个网格进行索引对应,使其在利用 A＊算法搜索路径是可以迅速准确的得到最优的无碰撞路径,减少系统的运行时间。     

Planning collision-free paths for robotic arm among obstacles

A theory for planning collision-free paths of a moving object among obstacles is described. Using the concepts of state space and rotation mapping, the relationship between the positions and the corresponding collision-free orientations of a moving object among obstacles is represented as some set of a state space. This set is called the rotation mapping graph (RMG) of that object. The problem of finding collision-free paths for an object translating and rotating among obstacles is thus transformed to that of considering the connectivity of the RMG. Since the connectivity of the graph can be solved by topological methods, the problem of planning collision-free paths is easily solved in theory. Using this theory, a topological method for planning collision-free paths of a rod-object translating and rotating among obstacles is presented. If a nonrigid robotic arm is viewed as a composite rod with some degrees of freedom, the planning of collision-free paths of a robotic arm can be solved in a similar way to a rod.     

Motion Planning for Redundant Manipulators Using a Floating Point Genetic Algorithm

This paper deals with the trajectory planning problem for redundant manipulators. A genetic algorithm (GA) using a floating point representation is proposed to search for the optimal end-effector trajectory for a redundant manipulator. An evaluation function is defined based on multiple criteria, including the total displacement of the end-effector, the total angular displacement of all the joints, as well as the uniformity of Cartesian and joint space velocities. These criteria result in minimized, smooth end-effector motions. Simulations are carried out for path planning in free space and in a workspace with obstacles. Results demonstrate the effectiveness and capability of the proposed method in generating optimized collision-free trajectories.     

The complexity of the free space for motion planning amidst fat obstacles

The complexity of motion planning algorithms highly depends on the complexity of the robot's free space, i.e., the set of all collision-free placements of the robot. Theoretically, the complexity of the free space can be very high, resulting in bad worst-case time bounds for motion planning algorithms. In practice, the complexity of the free space tends to be much smaller than the worst-case complexity. Motion planning algorithms with a running time that is determined by the complexity of the free space therefore become feasible in practical situations. We show that, under some realistic assumptions, the complexity of the free space of a robot with any fixed number of degrees of freedom moving around in ad-dimensional Euclidean workspace with fat obstacles is linear in the number of obstacles. The complexity results lead to highly efficient algorithms for motion planning amidst fat obstacles.Research is supported by the Dutch Organization for Scientific Research (NWO) and partially supported by the ESPRIT III BRA Project 6546 (PROMotion).     

A Shortest Path Based Path Planning Algorithm for Nonholonomic Mobile Robots

A path planning algorithm for a mobile robot subject to nonholonomic constraints is presented. The algorithmemploys a global- local strategy, and solves the problem in the 2D workspace of the robot, without generating the complexconfiguration space. Firstly, a visibility graph is constructed for finding a collision-free shortest path for a point. Secondly,the path for a point is evaluated to find whether it can be used as a reference to build up a feasible path for the mobile robot.If not, this path is discarded and the next shortest path is selected and evaluated until a right reference path is found. Thirdly,robot configurations are placed along the selected path in the way that the robot can move from one configuration to the nextavoiding obstacles. Lemmas are introduced to ensure that the robot travels using direct, indirect or reversal manoeuvres. Thealgorithm is computationally efficient and runs in time O(nk + n log n) for k obstacles andn vertices. The path found is near optimal in terms of distance travelled. The algorithm is tested in computersimulations and test results are presented to demonstrate its versatility in complex environments.     

3D Collision-Free Motion Based on Collision Index

A collision-free motion planning method for mobile robots moving in 3-dimensional workspace is proposed in this article. To simplify the mathematical representation and reduce the computation complexity for collision detection, objects in the workspace are modeled as ellipsoids. By means of applying a series of coordinate and scaling transformations between the robot and the obstacles in the workspace, intersection check is reduced to test whether the point representing the robot falls outside or inside the transformed ellipsoids representing the obstacles. Therefore, the requirement of the computation time for collision detection is reduced drastically in comparison with the computational geometry method, which computes a distance function of the robot segments and the obstacles. As a measurement of the possible occurrence of collision, the collision index, which is defined by projecting conceptually an ellipsoid onto a 3-dimensional Gaussian distribution contour, plays a significant role in planning the collision-free path. The method based on reinforcement learning search using the defined collision index for collision-free motion is proposed. A simulation example is given in this article to demonstrate the efficiency of the proposed method. The result shows that the mobile robot can pass through the blocking obstacles and reach the desired final position successfully after several trials.     

A Generalized Real-Time Obstacle Avoidance Method Without the Cspace Calculation

An important concept proposed in the early stage of robot path planning field is the shrinking of a robot to a point and meanwhile the expanding of obstacles in the workspace as a set of new obstacles. The resulting grown obstacles are called the Configuration Space (Cspace) obstacles. The find-path problem is then transformed into that of finding a collision-free path for a point robot among the Cspace obstacles. However, the research experiences have shown that the Cspace transform is very hard when the following situations occur: 1) both the robot and obstacles are not polygons, and 2) the robot is allowed to rotate. This situation gets even worse when the robot and obstacles are three dimensional (3D) objects with various shapes. For this reason, direct path planning approaches without the Cspace transformation is quite useful and expected.Motivated by the practical requirements of robot path planning, a generalized constrained optimization problem (GCOP) with not only logic AND but also logic OR relationships was proposed and a mathematical solution developed previously. This paper inherits the fundamental ideas of inequality and optimization techniques from the previous work, converts the obstacle avoidance problem into a semi-infinite constrained optimization problem with the help of the mathematical transformation, and proposes a direct path planning approach without Cspace calculation, which is quite different from traditional methods. To show its merits, simulation results in 3D space have been presented.     

基于有序二叉决策图的路径规划可行性研究

对全局环境未知且存在障碍物情况下的移动机器人路径规划问题进行了研究.借助有序二又决策图的原理,首次采用有序二叉决策图数据结构来表示机器人工作空间中的信息环境模型,并对它们进行了二进制编码,建立一个有效紧凑的OBDD环境模型.利用该OBDD模型能自动规划了免碰撞路径,获取一条从起始状态(包括位置及姿态)到达目标状态的安全、高效的无碰路径.实验仿真结果表明,所提出的方法是正确和有效的.     

ROBOT PATH PLANNING BASED ON MODIFIED GREY RELATIONAL ANALYSIS

In this paper, a simple searching approach integrated the nonlinear programming problem and the modified grey relational analysis is proposed to find the near-optimal and collision-free path for a robot, from an initial position to a goal position, in which the robot can be acted in the known or unknown workspace with multiple circular obstacles. The proposed find-path procedure consists of at least one trial. Each trial includes three main stages, i.e., a forward search stage, a backward search stage, and an inference stage. After all trials are completed, a decision-making stage is introduced to determine the near-optimal and collision-free path which is guaranteed to reach the goal. Besides, the presented method is applicable for the on-line applications and, furthermore, can solve the local minimal problems. Simulation results for circular obstacles demonstrate the performances of the proposed approach and its potential as an on-line path planner.     

An Information Roadmap Method for Robotic Sensor Path Planning

A new probabilistic roadmap method is presented for planning the path of a robotic sensor deployed in order to classify multiple fixed targets located in an obstacle-populated workspace. Existing roadmap methods have been successful at planning a robot path for the purpose of moving from an initial to a final configuration in a workspace by a minimum distance. But they are not directly applicable to robots whose primary objective is to gather target information with an on-board sensor. In this paper, a novel information roadmap method is developed in which obstacles, targets, sensor’s platform and field-of-view are represented as closed and bounded subsets of an Euclidean workspace. The information roadmap is sampled from a normalized information theoretic function that favors samples with a high expected value of information in configuration space. The method is applied to a landmine classification problem to plan the path of a robotic ground-penetrating radar, based on prior remote measurements and other geospatial data. Experiments show that paths obtained from the information roadmap exhibit a classification efficiency several times higher than that of existing search strategies. Also, the information roadmap can be used to deploy non-overpass capable robots that must avoid targets as well as obstacles.     

A search algorithm for motion planning with six degrees of freedom

The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given high-level specifications of tasks and geometric models of the robot and obstacles. The “Movers'” problem is to find a continuous, collision-free path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the three-dimensional Movers' problem: Given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a continuous, collision-free path taking P from some initial configuration to a desired goal configuration.This paper describes an implementation of a complete algorithm (at a given resolution) for the full six degree of freedom Movers' problem. The algorithm transforms the six degree of freedom planning problem into a point navigation problem in a six-dimensional configuration space (called C-space). The C-space obstacles, which characterize the physically unachievable configurations, are directly represented by six-dimensional manifolds whose boundaries are five-dimensional C-surfaces. By characterizing these surfaces and their intersections, collision-free paths may be found by the closure of three operators which (i) slide along five-dimensional level C-surfaces parallel to C-space obstacles; (ii) slide along one- to four-dimensional intersections of level C-surfaces; and (iii) jump between six-dimensional obstacles. These operators are employed by a best-first search algorithm in C-space. We will discuss theoretical properties of the algorithm, including completeness (at a resolution). This paper describes the heuristic search, with particular emphasis on the heuristic strategies that evaluate local geometric information. At the heart of this paper lie the design and implementation of these strategies for planning paths along level C-surfaces and their intersection manifolds, and for reasoning about motions with three degrees of rotational freedom. The problems of controlling the interaction of these strategies, and of integrating diverse local experts for geometric reasoning provide an interesting application of search to a difficult domain with significant practical implications. The representations and algorithms we develop impact many geometric planning problems, and extend to Cartesian manipulators with six degrees of freedom.     

Efficient manipulator collision avoidance by dynamic programming

This paper describes a research effort in the area of collision avoidance path planning for robotic manipulators. A robotic arm with known geometry is to perform a spatial manipulation in the presence of known obstacles in its workspace. The task is to generate a series of waypoints for its path to pass through which will guarantee a safe, collision-free trajectory from its predefined starting point to its predefined goal position.This is an important topic in the area of automated manufacturing. Automated factories are becoming increasingly important for the goals of greater manufacturing efficiency, better equipment utilization, and lower overall manufacturing costs. Robotic devices, including manipulator arms and assembly devices, are finding more uses in these factories.The approach is to discretize the robot's workspace into a transition network. The optimal path through this network, in terms of angular displacement of the manipulator's joints, is generated by dynamic programming. While this approach has been used previously, this paper adds the innovation of variable-node spacing, with the node density in various parts of the network reflecting the need for precise position control in each local area of the workspace. In this way, precise motion control is possible without an undue computational burden.     

Terrain-evaluation-based motion planning for legged locomotion on irregular terrain

The path planning of legged locomotion is complex in that path generation is based on constraints not only from body motion, but also from leg motion. A general approach to path planning will fail in generating a feasible path for walking machines when facing the huge searching space of legged locomotion. In this paper, an effective method of path planning is introduced by virtue of terrain evaluation. It maps obstacles into the robot configuration space by evaluating the obstacles' influence on the legged locomotion. The evaluation produces an index of terrain, called terrain complexity, for path planning. Using potential-guided searching, the terrain with mapped obstacles is searched to generate a feasible path.