Fig. 1 ( a ) A sample grid map (size: 10,000 × 10,000) for path planning problems. The area in white are obstacles, and the area in white is free space. The starting point is marked by the square, and the goal point is marked by the circle; ( b ) a solution to the problem is shown; and ( c ) the o... More about this image found in ( a ) A sample grid map (size: 10,000 × 10,000) for path planning problems....

Fig. 2 ( a ) Quadtree decomposition of the map shown in Fig. 1 . The black blocks are free space, and the gray blocks are obstacle blocks and ( b ) the collision cost of the line segment is the sum of areas of the bright blocks. More about this image found in ( a ) Quadtree decomposition of the map shown in Fig. 1 . The black blocks...

Fig. 3 A sample of crossover operation. The two solid paths on the left-hand side are the two parents. The two hollow dots on the right-hand side are the selected crossover points, and the offspring is the new solid path. More about this image found in A sample of crossover operation. The two solid paths on the left-hand side ...

Fig. 4 Five mutation operations used in this study: ( a ) add waypoint, ( b ) delete waypoint, ( c ) move waypoint, ( d ) split segment, and ( e ) cut corner More about this image found in Five mutation operations used in this study: ( a ) add waypoint, ( b ) dele...

Fig. 5 Multiple steps of mutation operations are needed to escape a local optimum: ( a ) before mutation, ( b ) after one mutation operation (delete waypoint), and ( c ) after the second mutation operation (add waypoint) More about this image found in Multiple steps of mutation operations are needed to escape a local optimum:...

Fig. 6 Split-and-focus operation. The fixed waypoints are shown with the lock icon. More about this image found in Split-and-focus operation. The fixed waypoints are shown with the lock icon...

Fig. 7 The grid map of case study 1 and the solutions by the three algorithms: ( a ) the starting point and goal point are at the upper-left and upper-right corners, respectively, ( b ) the ten solutions given by GA-linear, ( c ) the ten solutions given by GA-area, and ( d ) the ten solutions give... More about this image found in The grid map of case study 1 and the solutions by the three algorithms: ( a...

Fig. 8 The fitness history of the three methods in case study 1. The x -axis is the generation number and is scaled to [0, 1]. The curve shows the mean ± STD. More about this image found in The fitness history of the three methods in case study 1. The x -axis is t...

Fig. 9 The solutions to the two environments. The starting point and goal point are marked by the blue square and red dot, respectively: ( a ) ten solutions by GA-focus on the box environment, ( b ) a sample solution and the generated tree by RRT* on the box environment, ( c ) ten solutions by GA-... More about this image found in The solutions to the two environments. The starting point and goal point ar...

Fig. 10 The bar plot comparison of the path length and time consumption. The error bar shows the standard deviation: ( a ) comparison of path length in both environments and ( b ) comparison of time consumption in both environments. More about this image found in The bar plot comparison of the path length and time consumption. The error ...

Fig. 11 The solutions to four tough tasks by GA-focus. The starting point and goal point are marked by a square and a dot, respectively: ( a ) an indoor environment, ( b ) a non-square maze environment, ( c ) an environment with pocket-shaped obstacles and narrow passages, and ( d ) an environment... More about this image found in The solutions to four tough tasks by GA-focus. The starting point and goal ...

Fig. 12 The grid map of case study 4 and the solutions by GA-focus: ( a ) the speed field in the environment. The darker color means that the agent can move faster in these areas, and ( b ) the ten solutions given by GA-focus. The starting point and goal point are at the upper-left (the square) an... More about this image found in The grid map of case study 4 and the solutions by GA-focus: ( a ) the speed...

Fig. 1 System components and workflow of the masonry robot More about this image found in System components and workflow of the masonry robot

Fig. 2 Kinematic model of the masonry robot and the manipulator: ( a ) kinematics of the masonry robot and ( b ) kinematics of the 6R robot arm More about this image found in Kinematic model of the masonry robot and the manipulator: ( a ) kinematics ...

Fig. 3 The kinematic model of the omnidirectional vehicle More about this image found in The kinematic model of the omnidirectional vehicle

Fig. 4 Masonry robot masonry operation process More about this image found in Masonry robot masonry operation process

Fig. 5 Working planes and coordinate systems of the masonry robot More about this image found in Working planes and coordinate systems of the masonry robot