Hiroshi Noborio

A quadtree‐based path‐planning algorithm for a mobile robot

To enable a mobile robot to select automatically a collision-free path in a given workspace, design of a path-planning algorithm which must work efficiently in real-time is crucial. This article proposes a path-planning algorithm that selects a reasonable collision-free path tying start and goal points out of a quadtree representation of the robot workspace. The quadtree is obtained from fast conversion of a real image taken through a camera on the ceiling. It represents obstacles and their allocation in the workspace in good time and hence the algorithm is able to find a collision-free path while following the change of obstacles and their allocation. The algorithm is designed on the basis of “small-is-quick” principle. That is, the smaller a search space of the algorithm is, the faster the algorithm selects the shortest path out of the search space. To put the principle in practice, the algorithm investigates a path graph instead of the quadtree while spreading the path graph on the quadtree as small as possible, and selects fast the shortest collision-free path out of the path graph as a reasonable collision-free path. Thus the algorithm fulfils its function fast even in a workspace that has a number of obstacles with complicated shape. In comparison with several conventional path-planning algorithms presented so far, it is shown from experimental results that the proposed algorithm selects faster a reasonable collision-free robot path than others.

A practical algorithm for planning collision-free coordinated motion of multiple mobile robots

When multiple mobile robots are working in the same environment, planning of collision-free coordinated motion is necessary; here, an algorithm for planning such a motion of two mobile robots, no matter how crude the constraints of obstacles are, is proposed. The situation is modeled as a Petri net, which is considered as a useful model for describing and analyzing a system in which it is possible for some events to occur concurrently but there are constraints on the concurrence. In the Petri net, all motion constraints of robots in their paths are arranged as its firing rules, and hence collision-free coordination between the robots can be easily planning by manipulation of the firing rules. The algorithm always finds a collision-free coordinated path of two robots if there actually exists such a path in the environment. Moreover, because the algorithm does not use any knowledge of movement of the robots, precise time-varying trajectory control is not required and realization of the coordination is easy. The algorithm works efficiently even in a complex environment, indebted to the generic properties of geographical quadtree modeling for the environment. The usefulness of the algorithm is shown by several simulations.<<ETX>>

Fast interference check method using octree representation

The efficiency of off-line robot teaching with a graphics simulator depends on the speed of the interference check algorithm between the model of the robot and the model of its obstacles. This paper proposes an efficient algorithm whose computational complexity does not depend directly on the number of obstacles and the shape complexity of each obstacle. In this work, the octree representation is adopted as the model of the robots environment. It registers all obstacles in the environment with a hierarchical structure in positioning. On the other hand, the boundary representation (B-Reps) is adopted as the robot model. It can represent easily a complex robot motion including rotation by updating its coordinates table every sampling interval. The algorithm consists of a basic process which assigns successively each patch of the B-Reps within a region to some of the eight subregions when the region is divided into them. Then the division is guided recursively by the hierarchical structure of the octree. Wi...

A sufficient condition for designing a family of sensor-based deadlock-free path-planning algorithms

An intelligent automaton should always arrive at its goal automatically while avoiding the obstacles in a two-dimensional (2D) world. If the automaton does not know the shape or location of any obstacle in the world, it gathers information on its neighbourhood from some sensor, and according to the sensor information, it avoids the closer obstacles. In this situation, a sensor-based path-planning algorithm is used to determine the automatons action flexibly according to changes in the sensor information. By this method, the automaton usually avoids the closer obstacles on the basis of the local information but it may circulate around some of the obstacles in the world because of the locality of the sensor information. If deadlock occurs, the automaton does not arrive at the goal at all. To overcome this drawback, we address a sufficient condition for designing a family of deadlock-free sensor-based path-planning algorithms in an uncertain world. Within this family, the automaton basically goes straight t...

A feasible motion-planning algorithm for a mobile robot based on a quadtree representation

A motion-planning algorithm is proposed which fulfils its function fast even if shapes of the robot and its obstacles are complicated. Considering the global obstacle allocation in the robot workspace, the proposed algorithm selects intermediate positions where the mobile robot should pass from a start position to a goal position. Using a systematic motion generation method based on the closest points between the robot and its obstacles, the algorithm generated collision-free robot motions to joint the intermediate positions successively. The algorithm runs on the quadtree representation, obtained from fast conversion of a real image taken through a camera on the ceiling of the workspace. The algorithm can generate collision-free motions while following a change of obstacle allocation. In a comparison with several motion-planning algorithms, it is shown that the proposed algorithm generates fast collision-free robot motions.<<ETX>>

A comparative study of sensor-based path-planning algorithms in an unknown maze

In general, an unknown maze has few collision-free paths to a destination. Therefore, a robot supervised by the classic sensor-based path-planning algorithms Bug2, Class1, Alg1, Alg2 repeatedly enters into long local and global loops excluding and including a destination (goes out of its true way), respectively. For example, in Alg1 and Alg2, we can point out a case that a robot always enters into a global loop one time, and also in Bug(alter.) and Class1(alter.), we can find another case that a robot frequently joins a local loop many times. A complicated maze usually includes such cases, and therefore a robot arrives at a destination via a very long collision-free path. To overcome this, we revisit an algorithm, HD-I, whose following direction is adequately changed by trial and error. In HD-I, a robot hardly selects an inadequate direction and consequently decreases a probability to enter into global and local loops.

Precise deformation of rheologic object under MSD models with many voxels and calibrating parameters

The MSD (Mass-Spring-Damper) model efficiently calculates shape deformation of many kinds of materials such as elastic, visco-elastic, and rheologic objects. For this reason, dynamic animation can be made in a personal computer and its popular acceleration board within the video-frame rate. The problem of MSD model is how to maintain shape precision of each deformation. For this purpose, we have calibrated coefficients of damper and spring of Voigt part and a coefficient of damper of the other part in the basic MSD element under many surface points capturing a real rheologic object by the randomized algorithm. Nevertheless, the shape precision is not unfortunately enough. To overcome this, we improve our previous approach in the following five points: (1) The number of voxels in the MSD model increases from 75 to 600. (2) The ratio between lengths of Voigt and the other parts in the MSD element is added to three coefficients of spring and dampers of the basic element as calibrating parameters. (3) Four unknown parameters of the basic element are distinguished to calibrate in and on each voxel. In addition, the parameters are distinguished to calibrate among surface and core areas of a virtual rheologic object. (4) In order to speed up the calibration, we use GA (Genetic Algorithm) in replace of RA (Randomized Algorithm). (5) Each or both of local and global volume constant conditions are added into the previous approach. In conclusion, we investigate relations between shape deformation, volume resolution, and number of calibrated parameters in several MSD models representing a rheologic object. Also, we improve deformation precision by increasing not only volume resolution but also number of calibration parameters or by adding each or both of volume constant conditions.

Three or more dimensional sensor-based path-planning algorithm HD-I

To design an online or sensor-based path-planning algorithm, we should decrease its search cost (the number N of visited points of a robot in a known map or the sum S of moving distances of it in an uncertain map). For this purpose, the optimal algorithm, e.g. an A* algorithm is not suitable. Because in order to select an optimal path between start and goal points, the algorithm requests a huge set of visited points or driving distances. On the observation, by decreasing the sum S, we design a new sensor-based path-planning algorithm HD-I. In almost all the sensor-based algorithms, e.g. Class 1, convergence of a robot to its goal is ensured by decreasing the distance. Also in a famous algorithm, best-first (BF), the convergence is also kept by visiting a node whose distance to its goal is the smallest. They are similar because a robot does not take a distance from a start into account. Therefore, their modified versions can be mixed. Especially, BF can investigate around an unknown obstacle whose dimensions are over two. As a result, by mixing modified BF and Class 1, we obtain a three or more dimensional algorithm HD-I.

On the heuristics of A* or A algorithm in ITS and robot path-planning

Based on many large data set, we calibrate a near-optimal heuristic as a constant function for guiding efficiently A or A* algorithm. We claim that this magic number exists as a universal constant for several kinds of data sets. This is perhaps related to the nature of their data sets though it is not theoretically analyzed. In general A* and Dijkstra algorithms always pick up the optimal (e.g., the shortest) path between two nodes on a given graph. However, because they do not use any good heuristics, they spend much time to calculate. To overcome this drawback, we propose A of A* algorithm with a smart heuristics. The algorithm quickly investigates an optimal or near-optimal path. Unfortunately, the heuristics does not always maintain the admissibility, and thus our algorithm does not sometimes pick up the optimal path. Finally, we ascertain superiority of the proposed algorithm to the classic A* and Dijkstra algorithms by two kinds of extremely different data sets.

On the sensor-based navigation by changing a direction to follow an encountered obstacle

In the last decade, many sensor-based navigation algorithms have been proposed. In the sensor-based navigation, a robot arrives at its goal globally while avoiding neighbor obstacles locally by sensor information. In every environment, a mobile robot arrives at its goal surely. However if an environment has complicated shape, a mobile robot sometimes joins a loop and consequently runs long until its goal. In general, a loop consists of routes which a robot follows obstacles in the same direction. Nevertheless in most previous algorithms, a mobile robot follows an encountered obstacle in a constant direction. On this observation, a robot is exempted from participation of a loop by reversing a direction to follow an obstacle. The authors discuss algorithms in which the following direction is alternatively changed. This strategy has been adopted by cockroaches living in a natural environment. They then propose algorithms in which the following direction is randomly reversed. Then they compare paths generated by constant, alternative, and random selections in Bug2 and Classl under a graphics simulator for 2D complicated environments.