A Three dimensional Path Planning algorithm

Transcription

1 A Three dimensional Path Planning algorithm OUARDA HACHOUR Department Of Electrical and Electronics Engineering Faculty Of Engineering Sciences Signal and System Laboratory Boumerdes University Boulevard de l independence Boumerdes ALGERIA hachour_ouarda@yahoo.fr Abstract: Motion planning is one of the important tasks in intelligent control of an autonomous mobile robot. Path planning is to generate a collision free path in an environment with obstacles with respect to some criterion. Trajectory planning is to schedule the movement of a mobile robot along the planned path. Several approaches have been proposed to address the problem of motion planning of a mobile robot. If the environment is a known static terrain and it generates a path in advance it said to be off-line algorithm. It is said to be on-line if it is capable of producing a new path in response to environmental changes. This paper presents an algorithm for three dimensional (3D) path planning to a target for mobile robot in unknown environment. A few path planning algorithms are described here followed by the aim work of research in detail. Our autonomous mobile robot is able to achieve these tasks: avoiding 3D obstacles, taking a suitable decision, and attending the target which are the main factors to be realized of autonomy requirements. Using our principle of set creation IP and the results of SET(2*n); the 3D algorithm returns the best response of any entering map parameters. The key idea is around the main line from the source to the destination and the m th obstacle causing the collision where they construct the 3D feasible path (a set of non linear segments) which is the neighbour of non linear safety size robot segments. The concept is explained in detail. The robot moves within the unknown 3D environment by sensing and avoiding the obstacles coming across its way towards the target. The proposed algorithm deals with 3D environment complexity and finds the optimal feasible path. Key-Words: - Intelligent Autonomous Mobiles Robots, Path planning, 3D objects, Workspace, obstacle avoidance, Intelligence. 1 Introduction Path planning is one of the important tasks in intelligent control of an autonomous mobile robot. Several approaches have been proposed to address the problem of motion planning of a mobile robot. It is often decomposed into path planning and trajectory planning. Path planning is to generate a collision free path in an environment with obstacles and optimize it with respect to some criterion. Trajectory planning is to schedule the movement of a mobile robot along the planned path. If the environment is a known static terrain and it generates a path in advance it said to be off-line algorithm. It is said to be on-line if it is capable of producing a new path in response to environmental changes. Therefore, the major main work for path planning for autonomous mobile robot is to search a collision free path. Many works on this topic have been carried out for the path planning of autonomous mobile robot. A key prerequisite for a truly autonomous robot is that it can navigate safely within its environment. The problem of achieving this is one of the most active areas in mobile robotics research, which is stated as finding the answers to the three questions where am I?, where do I go?, and how do I get there?. For an autonomous mobile robot these questions refer to the tasks of selflocalization, map building, and path planning. The difficulty of this problem depends on the characteristics of the robot s environment, the characteristics of its sensors, and the map representation required by the application at the same time. The autonomous robot navigation problem has been studied thoroughly by the robotics research community over the last years. The basic feature of an autonomous mobile robot is its capability to operate independently in unknown or partially known environments. The autonomy implies that the robot is capable of reacting to static obstacles and unpredictable dynamic events that may impede the successful execution of a task. To achieve this level of robustness, methods need to be developed to provide solutions to localization, map building, planning and control [1,2,3,4,5]. The robot has to find a collision-free trajectory between the starting configuration and the goal configuration in a static or dynamic environment containing some obstacles.the goal of the navigation process of mobile robots is to ISSN: ISBN:

2 move the robot to a named place in a known, unknown or partially known environment. In most practical situations, the mobile robot can not take the most direct path from the start to the goal point. So, path planning techniques must be used in this situation, and the simplified kinds of planning mission involve going from the start point to the goal point while minimizing some cost such as time spent, chance of detection, or fuel consumption. Often, a path is planned off-line for the robot to follow, which can lead the robot to its destination assuming that the environment is perfectly known and stationary and the robot can rack perfectly. Early path planners were such off-line planners or were only suitable for such off-line planning. However, the limitations of off-line planning led researchers to study on-line planning, which relies on knowledge acquired from sensing the local environment to handle unknown obstacles as the robot traverses the environment. Moreover, when a robot moves in a specific space, it is necessary to select a most reasonable path so as to avoid collisions with obstacles. Several approaches for path planning exist for mobile robots, whose suitability depends on a particular problem in an application. For example, behavior-based reactive methods are good choice for robust collision avoidance. Path planning in spatial representation often requires the integration of several approaches. This can provide efficient, accurate, and consistent navigation of a mobile robot. The major task for path-planning for single mobile robot is to search a collision free path. The work in path planning has led into issues of map representation for a real world. Therefore, this problem considered as one of challenges in the field of mobile robots because of its direct effect for having a simple and computationally efficient path planning strategy [12, 13]. For path planning areas, it is sufficient for the robot to use a topological map that represents only the different areas without details such as office rooms. The possibility to use topological maps with different abstraction levels helps to save processing time. The static aspect of topological maps enables rather the creation of paths without information that is relevant at runtime. The created schedule, which is based on a topological map, holds nothing about objects which occupy the path. In that case it is not possible to perform the schedule. To get further actual information, the schedule should be enriched by the use of more up-to date plans like egocentric maps [8,9,10,11]. Systems that control the navigation of a mobile robot are based on several paradigms. Biologically motivated applications, for example, adopt the assumed behavior of animals. Geometric representations use geometrical elements like rectangles, polygons, and cylinders for the modeling of an environment. Also, systems for mobile robot exist that do not use a representation of their environment. The behavior of the robot is determined by the sensor data actually taken. Further approaches were introduced which use icons to represent the environment. A few advanced researches have been addressed to the problem of 3D navigation where the problem is focused how to pass from 2D to 3D concept. As an example the article in [7] exposes a new visual servoing technique based on two-dimensional (2-D) ultrasound (US) image is proposed in order to control the motion of an US probe held by a medical robot. In opposition to a standard camera which provides a projection of the three-dimensional (3-D) scene to a 2-D image, a consequently visual servoing techniques have been adapted. Another example is explained in [6] where a 3D Efficient navigation of mobile platforms in dynamic human-centered environments is done with 3D principle. In Summary, the key is focused on 3D geometrical surfaces or in 3D map knowledge. For each one, the scientists solve the 3D problem which sometimes can be reduced to a problem of two dimensions by projecting the objects on the plan containing obstacles. In this present work, a simple and efficient three dimensional collision free-path planning approach for autonomous mobile robot is proposed in which the robot navigates, avoids obstacles and attends its target. Note that, the algorithm described here is just to find a feasible and flexible 3D path from initial area source to destination target area, flexible because the user can change the position of obstacles and it has no effect since the environment is unknown. This robust method can deal a wide number of environments and gives to our robot the autonomous decision of how to avoid 3 D obstacles and how to attend the target. More, the 3D path planning procedure covers the environments structure and the propagate distances through free space from the source position. For any starting point within the environment representing the initial position of the mobile robot, the shortest path to the goal is traced. The proposed 3D path finding strategy is designed in 3D map form. The aim of this work is to develop an algorithm which allows a mobile robot to navigate through static obstacles, and finding the path in order to reach a specified target. We propose an algorithm that provides the robot a trajectory to be followed to move from the initial position to the specified target. The robot trajectory is designed in an unknown environment with static obstacles. The problem can basically be divided into positioning and path planning. Navigation is a major challenge for autonomous mobile robots. Starting out from a predefined position and orientation in the map, the mobile robot can autonomously head for destination position in the 3D scene of navigation. ISSN: ISBN:

3 2 The proposed 3D path planning The path in 3D environment is considered as an object which has the width and the height of the robot. From stating point to the target point, it supposes that there is one straight line ST, see the figure 1. When the robot linear path trajectory collides the obstacles, we create a set of intersection points IP which are belonging to the polygonal perimeter of the shape of the obstacle (see the figure2). If it is a circular shape we trace a polygon that Includes or around the circular shape. As we can see the linear path ST creates two sub linear or non linear paths connecting the segments of each elements belonging to the set of IP( it depends of the situation of the obstacles). If two intersection points are in the same position (or belonging to one straight line) we take only one to continue the building of sub paths. The first edge of the new sub path is created by the following formula: d 1 Sin θ = (1) x Hence d 1 x = (2) Sin θ Where x represents the first segment of the sub path, See the figure 3. Figure 1: an example of a free path without collision with obstacles Fig. 1: an example of a free path without collision with obstacles S S Figure 2: an example of a collision with obstacles: two segments of intersection T T Figure 3: an example of the open list obstacles In the workspace, we can define the position of the obstacles with respect to the line ST, and there exist three cases: the obstacles which cut the line ST, which are above the line ST and which are below the line ST.for the case of 3D we have to take the width of the robot to consideration as it is shown in the figure 4. The path in 3D environment is considered as an object which has the width and the height of the robot. 2.1 The 3D algorithm The proposed 3D algorithm is based on the number of intersection points that are belonging above or below the linear path ST in collision with the obstacle. We select two (02) sets of linear intersections belonging to the extremity of each obstacle causing the collision. The mode of selection is focused on the n number of non linear segments( sometimes linear depending on the format of obstacles and the connection between the source S and the target T) that are above or below the linear path ST in collision with the obstacle SET(2*n). We multiply by (02) two because each time we check two selected intersection points that are belonging the perimeter of the obstacle and are in the open list of new intersection of the another obstacle. Our algorithm consists of the following steps: 1-Generate a free path as quickly as possible connecting the source to the destination (trace a direct line connecting the source to the destination ST). In this ISSN: ISBN:

4 context it supposes that there is no collision and it exists a 3D free path directly to destination (an easiness mode checking). The first set of segment connection is empty and it is given by SET(2*n)=0 and IP={}. 2-This step is done when a collision occurs. Two single points are created in the open list: these points are the intersection of two segments going from the source that collide the first obstacle see the figure 4. The coordinates of intersection are saved in the open list to be treated after with up coming coordinates of the new intersection: IP={2p}. When the starts the checking for interferences, a temporary interference objects are created and included to last created selection set explained before. In order to avoid the obstacle, the direct path must be rotated around the starting point S, by a small angle Teta, 0<Teta<360, see the figure 4. After this rotation, the temporary interference objects that are created during the interference checking are deleted. Thus the interference selection set becomes empty. The process iterates again by another rotation Delta_Teta and checks for collision by testing the interference selection set. The open list SET(2*n)= m * collisions., where m is the number of iteration. When the linear path is in collision with obstacles unless the selection set is not empty. It keeps rotating until the interference selection becomes empty. When the selection set is not empty, the created interference objects must be removed before the next iteration. 3-find the fewest number of segments path. In this context, whenever a collision occurs, the algorithm creates two new points one right and one left the obstacle causing the collision. It then recursively both sets of line segments and checks each line for collision. 4- finding the fewest number of line segments. This is done in order to find the shortest possible path without collisions from the source to the destination. The optimisation here is in term of meaning short distance. It supposes that having the minimum number of the connected segments, we get the optimal path.these segments are not linear at the end, taking into account the dimension of the robot: the segments are rounded by the size of the robot and we obtain a non linear size safety segments. See the figure 5 and 6 to understand better. The first step of the 3D algorithm is the easiest and the simple one. It is asked to trace a direct line from the source to the destination. The second and the third steps depend on the number of collisions and generate the segment paths. These steps are realized when there is one or more collisions. The third checks recursively the number of segment paths that are created during he creation. Finally, the fourth returns the optimal and feasible path of navigation without collision. The function SET(2*n) returns the number of collisions and the coordinates of intersection points created above or below the obstacle causing the collisions and are saved in the set of intersection points IP. S Segment1 teta obstacle Segment2 Figure 4: an example of creation of two segments 3 Simulation results The robot starts from any position then it must move by sensing and avoiding the obstacles. We use our algorithm containing the information about the target position, and the robot will move accordingly. To determine the nature of space of navigation, the sub_ paths of position of the robot are marked as either free or occupied; otherwise unknown. We can therefore divide our search area into free and occupied area. By selecting a goal that lies within free space, we ensure that the free sub-path will not be in collision with the environment, and that there exists some sub-paths to get the target. If the algorithm does not converge, an error is returned in the variable Error Message. If there is no possible way to get the target, the program returns (no way) as message box response indicating that after much computing there is no possible configuration to the target. This is very important in all navigation process, because instead of stopping the program or waiting without issue, the user gets the answer which is logical as answer to show that no way towards the target. The input parameters Map contain the ground information In order to evaluate, the performance of navigation algorithm of autonomous mobile robots over various environments, we observed simulation of the navigation in different environments. We can change the position of obstacles so we get other different environments. These environments were randomly generated. To find a new path after insertion of deletion ISSN: ISBN:

5 of an obstacle. Hence, a mobile robot detects unknown hazardous obstacle on the path and find its free path without collision. More, after the generation of several paths given by the process of navigation, the robot reaches its target intelligibly by deciding itself how to navigate, how to avoid obstacle, and how to reach carefully his goal. This navigation approach has an advantage of adaptivity such that the mobile robot algorithm works perfectly even if an environment is unknown. This proposed approach has made the robot able to achieve these tasks: avoid obstacles, deciding, perception, and recognition and to attend the target which are the main factors to be realized of autonomy requirements Conceptually speaking, our 3D algorithm is quite simple: it is an algorithm of finding a feasible path on the ground from a starting location to a target location, avoiding the obstacles and minimizing the cost in 3D workspace. The concept is to find the low cost for each sub path (short path) taking into account the collision principle. The sub paths are generated from he generation of (2*n) segments that is explained before. In 3D workspace, the path is considered as an object which has the width and the height of the robot. First we consider that it exits a free direct path ST that we will select it. Then we select all obstacles in the environment. Finally, we create an initially empty set: the algorithm checks the intersection between obstacles in the first selection set against those in the second selection set. the path ST must be rotated around the starting point S, by a small angle. After this rotation, the temporary sub paths are created during the intersection. The process iterates again by another rotation Delta_Teta and checks for collision by testing the remaining obstacles belonging to the line ST. It keeps rotating until the mth number of obstacles created in this line are detected and checked. This section concerned with the simulation of our algorithm in different 3D environment.the path given in the figure 5 shows the path as a 3D modelling trajectory planning. To consider the width of the robot we should create a region from a set of entities. To take the height of the robot into consideration we have to extrude the region by the height of the robot. In the figure 5 the obstacle Obs2 is avoided by detecting one checking point and finding the best optimal path from the two segments (sub_paths) discussed above. Note that here IP={2p}( IP takes one point between the two points of collision) and SET(2*n)= (m==1)* collisions. To get the shortest possible path we have used the concept of minimum_segment of the both portion of intersection with the obstacle caused the collision. It supposed that having the shortest neighbour segments (above or below the line ST) we construct the feasible optimal path which is the set of these segments from source to the destination and returns the best path from the set of segments). Whereas, in the case of the figure 6 the two obstacles Obs1 and Obs2 are avoided by inserting two intersection points. Furthermore, IP={4p}( IP takes one point between the two points of collision of the m th neighboured obstacle caused the collision} and SET(2*n)= (m==2)* collisions. Figure 5: Free 3D path realization by the collision of one point Figure 6 : Free 3D path realization by the collision of two points 4 Conclusion In this present work we have studied the problem of path planning in a 3-dimentional surface with obstacles avoidance. A complete path planning algorithm guarantees that the robot can reach the target if possible, or returns a message that indicates that there The robot moves within the unknown environment by sensing and avoiding the obstacles coming across its way towards ISSN: ISBN:

6 the target. The obtained path is the shortest path from all possible free trajectories. The proposed 3D algorithm has the advantage of being generic and can be changed at the user demand. The obstacles can take any shape since the algorithm is general for any 3D obstacle detection. This approach works perfectly even if an environment is unknown. We have run our simulation in several environments where the robot succeeds to reach its target in each situation and avoids the obstacles capturing the behaviour of intelligent expert system. For the main idea we propose to use simple projection sensors to measure the robot position and orientation. Our autonomous mobile robot is able to achieve these tasks: avoid 3D obstacles, taking a suitable decision, perception, and recognition and to attend the target which are the main factors to be realized of autonomy requirements. Using the principle of set creation IP and the results of SET(2*n); the 3D algorithm returns the best response of any entering map parameters. The key idea is around the main line ST and the m th obstacle causing the collision where they construct the 3D feasible path (a set of non linear segments) which is the neighbour of non linear safety size robot segments. The concept is explained in detail. However in the future, it is necessary to use a robot in hostile environment and space exploration or other applications by using advanced micro-product control systems that can be dealt in 3D dimensions surfaces. References: [1]B.P.Gerkey, M.J MatariĆ, Principled Communication for Dynamic Multi-Robot Task Allocation, Experimental Robotics VII, LNCIS 271, Springer Verlag Berlin Heidelberg, 2001,pp [2]S.Saripalli, G.S.Sukhatme, and J.F.Montgomery, an Experimental Study Of The Autonomous Helicopter Landing Problem, the Eight International Symposium on Experimental Robotics, July 2002,pp [3]B.P.Gerkey, M.J MatariĆ, and G.S.Sukhatme, Exploiting Physical Dynamics for concurrent control of a mobile robot, In Proceeding of the IEEE International Conference on Robotics and Automation ( ICRA 2002), Washington, DC, May 2002, pp [4]T.Willeke, C.Kunz, I.Nourbakhsh, The Personal Rover Project : The comprehensive Design Of a dometic personal robot, Robotics and Autonomous Systems (4), Elsevier Science, 2003, pp [5]A.Howard, M.J MatariĆ and G.S.Sukhatme, An Incremental Self-Deployment Algorithm for mobile Sensor Networks, autonomous robots, special Issue on Intelligent Embedded Systems, 13(2), September 2002, pp [6]P.Steinhaus, M.Strand, and R.Dillmann, Autonomous Robot Navigation in Human-Centered Environments Based on 3D Data Fusion, Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing, Volume 2007, Article ID 86831, 10 pages [7]A.KRUPA and F.CHAUMETTE, Guidance of an ultrasound probe by visual servoing, Advanced Robotics,2006, Vol. 20, No. 11, pp [8] S.Florczyk, Robot VisionVideo-based Indoor Exploration with Autonomous and Mobile Robots, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, [9] O.Hachour and N.Mastorakis, IAV : A VHDL methodology for FPGA implementation, WSEAS transaction on circuits and systems, Issue5, Volume3,ISSN , pp [10] O.Hachour AND N. Mastorakis, FPGA implementation of navigation approach, WSEAS international multiconference 4 th WSEAS robotics, distance learning and intelligent communication systems (ICRODIC 2004), in Rio de Janeiro Brazil, October 1-15, 2004, pp x WSEAS January 2004,pp [11]O.Hachour, Pth planning of autonomous mobile robot, International Journal Of System Applications, Engineering & Developments, issue4, volume2,2008,pp [12] S.M.LaValle, Planning Algorithms, University of Illinois, Cambridge University Press,2006. [13] J. Velagic,B. Lacevic,B. Perunicic, A 3-level autonomous mobile robot navigation system designed by using Reasoning /search approaches, Sciences direct, Robotics and Autonomous Systems 54 (2006) , ELSEVIER. ISSN: ISBN: