Tham khảo tài liệu 'advances in robot navigation part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | SLAM and Exploration using Differential Evolution and Fast Marching 89 Fig. 5. Trajectories calculated applying the proposed algorithm with Fast Marching over the Logarithm Extended Voronoi Transform. measured in seconds and each step of the algorithm for different trajectory lengths to calculate the computational cost depends on the number of points of the image . Alg. Step Trajectory length Long Medium Short Obst. Enlarging Ext. Voronoi Transf. FM Exploration Path Extraction Total time Table 1. Computational cost seconds for the room environment 966x120 pixels Smooth trajectories. The planner must be able to provide a smooth motion plan which can be executed by the robot motion controller. In other words the plan does not need to be refined avoiding the need for a local refinement of the trajectory. The solution of the eikonal equation used in the proposed method is given by the solution of the wave equation 0e k0 nx-c0t As this solution is an exponential if the potential n x is C then the potential is also C and therefore the trajectories calculated by the gradient method over this potential would be of the same class. This smoothness property can be observed in fig. 5 where the trajectory is clearly good safe and smooth. One advantage of the method is that it not only generates the optimum path but also the velocity of the robot at each point of the path. The velocity reaches its highest values in the light areas and minimum values in the greyer zones. The VFM Method simultaneously provides the path and maximum allowable velocity for a mobile robot between the current location and the goal. Reliable trajectories. The proposed planner provides a safe reasonably far from detected obstacles and reliable trajectory free from local traps . This is due to the refraction index which causes higher velocities far from obstacles. Completeness. As the method consists of the .
