外文翻译 空间机器人防碰路径规划.docx

1、外文翻译 空间机器人防碰路径规划 课 程 名 称： 计算机集成制造系统 作 业 名 称： ROBOT 学 生 班 级： K数控 学 生 学 号： 学 生 姓 名： 成 绩 评 定： 教 师 签 字： Space Robot Path Planningfor Collision AvoidanceYuya Yanoshita and Shinichi TsudaAbstract This paper deals with a path planning of space robot which includes a collision avoidance algorithm. For the f

2、uture space robot operation, autonomous and self-contained path planning is mandatory to capture a target without the aid of ground station. Especially the collision avoidance with target itself must be always considered. Once the location, shape and grasp point of the target are identified, those w

3、ill be expressed in the configuration space. And in this paper a potential method, Laplace potential function, is applied to obtain the path in the configuration space in order to avoid so-called deadlock phenomenon. Some improvement on the generation of the path has been observed by applying path s

4、moothing method, which utilizes the spline function interpolation. This reduces the computational load and generates the smooth path of the space robot. The validity of this approach is shown by a few numerical simulations.Key Words Space Robot, Path Planning, Collision Avoidance, Potential Function

5、, Spline InterpolationI. INTRODUCTIONIn the future space development, the space robot and its autonomy will be key features of the space technology. The space robot will play roles to construct space structures and perform inspections and maintenance of spacecrafts. These operations are expected to

6、be performed in an autonomous manner in place of extravehicular activities by astronauts.In the above space robot operations, a basic and important task is to capture free flying targets on orbit by the robotic arm. For the safe capturing operation, it will be required to move the arm from initial p

7、osture to final posture without collisions with the target.The configuration space and artificial potential methods are often applied to the operation planning of the usual robot. This enables the robot arm to evade the obstacle and to move toward the target. Khatib proposed a motion planning method

8、, in which between each link of the robot and the obstacle the repulsive potential is defined and between the end-effecter of the robot and the goal the attractive potential is defined and by summing both of the potentials and using the gradient of this potential field the path is generated. This me

9、thod is advantageous by its simplicity and applicability for real-time operation. However there might be points at which the repulsive force and the attractive force are equal and this will lead to the so-called deadlock.In order to resolve the above issue, a few methods are proposed where the solut

10、ion of Laplace equation is utilized. This method assures the potential fields without the local minimum, i.e., no deadlock. In this method by numerical computation Laplace equation will be solved and generates potential field. The potential field is divided into small cells and on each node the disc

11、rete value of the potential will be specified. In this paper for the elimination of the above defects, spline interpolation technique is proposed. The nodal point which is given as a point of path will be defined to be a part of smoothed spline function. And numerical simulations are conducted for t

12、he path planning of the space robot to capture the target, in which the potential by solving the Laplace equation is applied and generates the smooth and continuous path by the spline interpolation from the initial to the final posture.II. ROBOT MODELThe model of space robot is illustrated in Fig.1.

13、The robot is mounted on a spacecraft and has two rotary joints which allow the in-plane motion of the end-effecter. In this case we have an additional freedom of the spacecraft attitude angle and this will be considered the additional rotary joint. This means that the space robot is three linked wit

14、h 3 DOF (Degree Of Freedom). The length of each link and the angle of each rotary joint are given byand (i = 1,2,3) , respectively. In order to simplify the discussions a few assumptions are made in this paper:-the motion of the space robot is in-plane,i.e., two dimensional one.-effect of robot arm

15、motion to the spacecraft attitude is negligible.-robot motion is given by the relation of static geometry and not explicitly depending on time.-the target satellite is inertially stabilized.In general in-plane motion and out-of-plane motion will be separately performed. So we are able to assume the

16、above first one without loss of generality. The second assumption derives from the comparison of the ratio of mass between the robot arm and the spacecraft body. With respect to the third assumption we focus on generating the path planning of the robot and this is basically given by the static natur

17、e of geometry relationship and is therefore not depending on the time explicitly. The last one means the satellite is cooperative.Fig.1 Model of Two-link Space RobotIII. PATH PLANNING GALGORITHMA. Laplace Potential GuidanceThe solution of the Laplace equation (1) is called a Harmonic potential funct

18、ion, and its and minimum values take place only on the boundary. In the robot path generation the boundary means obstacle and goal. Therefore inside the region where the potential is defined, no local minimum takes place except the goal. This eliminates the deadlock phenomenon for path generation. （

19、1）The Laplace equation can be solved numerically. We define two dimensional Laplace equation as below: （2）And this will be converted into the difference equation and then solved by Gauss -Seidel method. In equation (2) if we take the central difference formula for second derivatives, the following e

20、quation will be obtained: （3）where， are the step (cell) sizes between adjacent nodes for each x, y direction. If the step size is assumed equal and the following notation is used:Then equation (3) is expressed in the following manner: （4）And as a result, two dimensional Laplace equation will be conv

21、erted into the equation (5) as below: （5）In the same manner as in the three dimensional case, the difference equation for the three dimensional Laplace equation will be easily obtained by the following: （6）In order to solve the above equations we apply Gauss-Seidel method and have equations as follo

22、ws: （7）where is the computational result from the ( n +1 )-th iterative calculations of the potential. In the above computations, as the boundary conditions, a certain positive number is defined for the obstacle and 0 for the goal. And as the initial conditions the same number is also given for all

23、of the free nodes. By this approach during iterative computations the value of the boundary nodes will not change and the values only for free nodes will be varying. Applying the same potential values as the obstacle and in accordance with the iterative computational process, the small potential aro

24、und the goal will be gradually propagating like surrounding the obstacle. The potential field will be built based on the above procedure.Using the above potential field from 4 nodal points adjacent to the node on which the space robot exists, the smallest node is selected for the point to move to. T

25、his procedure finally leads the space robot to the goal without collision.B. Spline InterpolationThe path given by the above approach does not assure the smoothly connected one. And if the goal is not given on the nodal point, we have to partition the cells into much more smaller cells. This will in

26、crease the computational load and time.In order to eliminate the above drawbacks we propose the utilization of spline interpolation technique. By assigning the nodal points given by the solution to via points on the path, we try to obtain the smoothly connected path with accurate initial and final p

27、oints.In this paper the cubic spline was applied by using MATLAB command.C. Configuration SpaceWhen we apply the Laplace potential, the path search is assured only in the case where the robot is expressed to be a point in the searching space. The configuration space(C-Space), where the robot is expr

28、essed as a point, is used for the path search. To convert the real space into the C-Space the calculation to judge the condition of collision is performed and if the collision exists, the corresponding point in the C-space is regarded as the obstacle. In this paper when the potential field was gener

29、ated, the conditions of all the points in the real space, corresponding to all the nodes, were calculated. The judgment of intersection between a segment constituting the robot arm and a segment constituting the obstacle at each node was made and if the intersection takes place, this node is treated

30、 as the obstacle in the C-Space.IV.NUMERICAL SIMULATIONSBased on the above approach the path planning for capturing a target satellite was examined using a space robot model. In this paper we assume the space robot with two dimensional and 2 DOF robotic arm as shown in Fig.1.The length of each link

31、is given as follows:l1 =1.4m, l2 = 2.0m, l3 = 2.0m ,and the target satellite was assumed 1m square. The grasp handle, 0.1 m square, was located at a center of one side of the target. So this handle is a goal of the path. Let us explain the geometrical relation between the space robot and the target

32、satellite. When we consider the operation after capturing the target, it is desirable for the space robot to have the large manipulability. Therefore in this paper the end-effecter will reach the target when the manipulability is maximized. In the 3DOF case, not depending on the spacecraft body attitude, the manipulability is measured by. And if we assume the end-effector of the space robot should be vertical to the target, then all of the joints angles are predetermined as follows:As all the joints angles