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Figure 6. Vector decomposition using the projection of vectors for the first gap border (i=1) V,: velocity vector of an obstacle creating the first gap border, ¥,,: the projected vector). Considering the same triangle, the third side of the triangle (d3) and the angles G, and Gz can be calculated by using the law of Cosines, represented in Equations (8)- (10).

Figure 6 Vector decomposition using the projection of vectors for the first gap border (i=1) V,: velocity vector of an obstacle creating the first gap border, ¥,,: the projected vector). Considering the same triangle, the third side of the triangle (d3) and the angles G, and Gz can be calculated by using the law of Cosines, represented in Equations (8)- (10).

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The new FDGM gap selection approach is a two-stage procedure, shown in Fig. 3. Calculation of the possible prediction time based on time to collision is explained in section III-A, and the prediction of gap changes by the desired time is discussed in part III-B. Figure 1. Robot-obstacle configuration, gaps, the midpoint of the largest gaps, goal point, and final heading angle.
The new FDGM gap selection approach is a two-stage procedure, shown in Fig. 3. Calculation of the possible prediction time based on time to collision is explained in section III-A, and the prediction of gap changes by the desired time is discussed in part III-B. Figure 1. Robot-obstacle configuration, gaps, the midpoint of the largest gaps, goal point, and final heading angle.
Figure 2. Robot-obstacle configuration with a dynamic obstacle moving with velocity vector V_1 in the free-space. A. Calculation of the Possible Prediction Time Based on Time to Collision
Figure 2. Robot-obstacle configuration with a dynamic obstacle moving with velocity vector V_1 in the free-space. A. Calculation of the Possible Prediction Time Based on Time to Collision
Figure 3. The new gap selection procedure
Figure 3. The new gap selection procedure
Figure 4. Robot-obstacle configuration for calculation of possible prediction time (R: robot, Obs1:obstacle, Obs2: obstacle 2, t,: prediction time).
Figure 4. Robot-obstacle configuration for calculation of possible prediction time (R: robot, Obs1:obstacle, Obs2: obstacle 2, t,: prediction time).
Figure 5. Example of the robot-obstacle configuration where there is no intersection.
Figure 5. Example of the robot-obstacle configuration where there is no intersection.
The angles between the gap borders and _ the perpendicular segment h can be calculated as follows:
The angles between the gap borders and _ the perpendicular segment h can be calculated as follows:
Figure 7. Robot-gap configuration for calculating the future gap changes. The FDGM algorithm selects the largest predicted gap along with the other predicted gaps and passes it to the FGM. The simulation results of two different robot- obstacle configurations containing two dynamic obstacles and multiple static obstacles are illustrated in Fig 8. As shown in Fig. 8-a, the traveled paths for both FGM and FDGM algorithms from the starting time until time t, are the same.
Figure 7. Robot-gap configuration for calculating the future gap changes. The FDGM algorithm selects the largest predicted gap along with the other predicted gaps and passes it to the FGM. The simulation results of two different robot- obstacle configurations containing two dynamic obstacles and multiple static obstacles are illustrated in Fig 8. As shown in Fig. 8-a, the traveled paths for both FGM and FDGM algorithms from the starting time until time t, are the same.
To assess the efficiency of the proposed algorithm, 300 Monte Carlo simulations are performed for FGM and FDGM, where the coordinate of obstacles are specified randomly. A LIDAR with a total 180° field of view (FOV) is used in the simulations and the total area of the environment is selected as 7m x 14m, and the initial and the goal coordinates are chosen as [11.8-13] and [16.5- 13], respectively. The results are compared in terms of obstacle avoidance safety and length of the path. The metric used for the obstacle avoidance safety expressed in Eq. (22), is the same as used in [19], [20], and [24]. the environment and the robot dynamics. This safety metric is a function which is inversely proportional to the distance to the obstacle, dj»jn. So, comparing multiple scenarios, smaller values of safety-metric means it is safer.
To assess the efficiency of the proposed algorithm, 300 Monte Carlo simulations are performed for FGM and FDGM, where the coordinate of obstacles are specified randomly. A LIDAR with a total 180° field of view (FOV) is used in the simulations and the total area of the environment is selected as 7m x 14m, and the initial and the goal coordinates are chosen as [11.8-13] and [16.5- 13], respectively. The results are compared in terms of obstacle avoidance safety and length of the path. The metric used for the obstacle avoidance safety expressed in Eq. (22), is the same as used in [19], [20], and [24]. the environment and the robot dynamics. This safety metric is a function which is inversely proportional to the distance to the obstacle, dj»jn. So, comparing multiple scenarios, smaller values of safety-metric means it is safer.
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