The state-of-the-art graph searching algorithm applied to the optimal global path planning problem for mobile robots is the A* algorithm with the heap structured open list. In this paper, we present a novel algorithm, called the L* algorithm, which can be applied to global path planning and is faster than the A* algorithm. The structure of the open list with the use of bidirectional sublists (buckets) ensures the linear computational complexity of the L* algorithm because the nodes in the current bucket can be processed in any sequence and it is not necessary to sort the bucket. Our approach can maintain the optimality and linear computational complexity with the use of the cost expressed by floating-point numbers. The paper presents the requirements of the L* algorithm use and the proof of the admissibility of this algorithm. The experiments confirmed that the L* algorithm is faster than the A* algorithm in various path planning scenarios. We also introduced a method of estimating the execution time of the A* and the L* algorithm. The method was compared with the experimental results.
The issues of medical robots have been approached for 12 years in the Institute of Machine Tools and Production Engineering of the Technical University of Lodz. In the last two years, the scope of research related to the miniaturization of surgical tools, automated changing of these tools with the use of a tool depot designed for this purpose, equipping the robot in the sense of touch and developing the software which provides ergonomic and intuitive robot control with the use of all its functions. In the telemanipulator control, strong emphasis is placed on the intuitiveness of control, which is hard to be ensured due to the fact that the robot tool is observed by a laparoscopic camera, whose orientation and position may vary. That is the reason for developing a new algorithm. It copies the increments of the position and orientation measured in relation to the monitor coordinate system onto the robot tool movement and orientation, which are measured in relation to the camera coordinates system. In this algorithm it is necessary to solve inverse kinematics, which has a discontinuity. Avoiding the discontinuity is achieved by mapping the solution with the cosine function. It causes smooth pass through the area of discontinuity in this way avoiding the singularity
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