Improved A-star algorithm for robot path planning in static environment

A-star algorithm is a kind of simple path planning algorithm without solving the calculus, which has a high application. However, compared with other path planning algorithms, it occupies a large memory space. To solve this problem, this paper proposes three new concepts such as the bidirectional search, a guide line and a list of key points. A-star algorithm is optimized and rasterize on indoor environment modeling method, finally through the MATLAB simulation experiments prove that the optimized algorithm feasible experimental results show that the improved algorithm in target different under the two kinds of experiment are able to reduce memory footprint by more than 60%.


Introduction
Robot path planning has always been a hot research topic in the field of artificial intelligence [1,2,3,4]. Traditional algorithms mainly include genetic algorithm (Ga), artificial potential field algorithm, and free space method [5].Intelligent algorithm mainly has a fuzzy logic algorithm of artificial neural network algorithm A-star algorithm [6], even though the solution of the problem and many, but the algorithm has disadvantages to improve [7] no matter what kind of algorithm, its core idea is to make the robot through a minimum cost, finding the shortest path in the specific environment for the guidelines, planning out a continuous and collision free path as a result, planning path before the need to model construction of environment, the main building and map model are raster map method [8] can attempt to method [9] structure space method [10], etc. Generally speaking, path planning methods are classified according to planning ideas and can be divided into global path planning and local path planning [11]. Global path planning can usually plan an optimal path for the robot, but it requires prior information of the environment and requires a large amount of calculation. Sensors local path planning is access to environmental information, and can make real-time adjustment along with the change of environment, by contrast, if the actual situation is not very strict to the optimal path, local path planning is more practical and real-time performance for A-star algorithm [12] is a local path planning algorithm of heuristic search, its calculation is simple, without solving calculus and applicability widely etc., as the main algorithm for research because of its unique way of computing cost of search and take up a direct link between the storage space, inspired by the literature [13]. In this paper, the cost function is improved by introducing the concept of wire to reduce the unnecessary search area in the two-dimensional static environment, so as to reduce the search cost, and improve the search efficiency in the use of MATLAB carries on the simulation experiment.

Environment modeling
Taking indoor environment as an example, two-dimensional plane simulation was carried out (grid method was used for Map modeling, and the advantage was that the search area was displayed with Astar algorithm, which was easy to calculate). The white grid represented barrier-free and accessible area raster ap M was set up by grid ij M : ap In the grid diagram, "0" is the white grid (barrier-free accessible area), and "1" is the black grid (area with obstacle impassable area). Establish a 40×40 grid map as shown in Figure 1:

A-star algorithm
The traditional A-star algorithm comprehensively evaluates each node (i.e. search area) around the current position in the grid by setting the evaluation function. Each node is the position that the robot can reach. after intelligent assessment of each position point, the optimal position point can be found, and the position can be replaced until the target position is found. Its evaluation function is as follows: represents the actual cost of the current node to the next node; ) (n H Represents the estimated cost of predicting the destination of the current node. The formula of Manhattan estimation method is as follows:

.Improved algorithm
Based on the A-star algorithm, the constraint function ) (n C is introduced, which is similar to the estimated cost ) (n H .The evaluation function formula of the improved algorithm is as follows: ) (n C is the vertical distance between the node and the "boot line". as shown in Figure 2, a straight line is drawn to connect the starting point and the target point, which is called the "guide line". Solid  In this way, the search points for the next two steps in Figure 2 are shown in Figure 4 and Figure 5, where the red square is the optimal node, that is, the node where the next step replaces the starting point.

Explanation of experiment
In this paper, Intel(R) Core(TM) I7-8750h CPU @2.20ghz 2.21ghz,RaM 8.00GB, 64 operating system, Windows 10 home Chinese version computer and MATLAB 2018B were used for experimental simulation. as shown in FIG. 6 and FIG. 7, before the simulation experiment of the improved algorithm, the A-star algorithm simulation experiment to be compared was carried out first.

Improved algorithm simulation experiment
The improved algorithm is used to change the position of the target point when other conditions are unchanged. as shown in FIG. 8 and FIG. 9, respectively correspond to FIG. 6 and FIG. 7 for simulation experiments.  (2) of the two algorithms, it is found that the improved algorithm changes the position of the target point, and falls into the misunderstanding of not being able to find the target point after increasing the difficulty of searching. Therefore, we have carried out the second improvement, and the idea is as follows: Step 1: analyze the path to find the transition nodes that have fallen into a misunderstanding. according to the nodes surrounded by the solid blue line in Figure 10, the simulated robot made a wrong judgment when searching for the point and turned on the wrong road, so it got into a misunderstanding. Step 2: after finding the turning point according to step 1, we introduce a new concept, which is as follows: When the A-star algorithm is executed, it will create two lists, one is an open list, which is used to store the surrounding 8 unextended nodes; Is a closed list, to hold the extension of the end of Key point setting method is as follows: as shown in figure 11, figure 12, the search to the node to establish a coordinate system, the connection of the node and the target point (blue dotted line), to determine the nodes around (blue ring dashed lines), if a target point with the obstacles in the blue dashed line of quadrant, and no obstacles other quadrants, referred to as the "key", the node will be in the "key points list".
Step 3: Carry out preliminary simulation of the improved algorithm on the experimental figure (2) of the improved algorithm, as shown in Figure 13. Through the experimental results, after secondary to improve simulation robot can solve misunderstanding, find the target point, and the search area less than a star algorithm, a star algorithm search area for 483, the second time improved algorithm search area for 162, considering the occupy storage space and the open list, closed list and related key points list, so the actual storage space decreased by 65.83%However, the experimental results show that the step length value of the quadratic improved algorithm is 54, which is 1.6 more than that of the A-star algorithm and there are unnecessary turning points on the path, so we continue to improve it. Step 4: Through the previous experiment, we found that in the improved algorithm, There may be two nodes have the same value, the algorithm under the condition of default based on the probability of 1/2 randomly select a node as the situation continue to search optimal, combined with the introduction of the concept of "critical point" at the same time, we decided to let algorithm in both cases a bidirectional search, when a direction search to the target point, the other party to stop, because the first search to the direction of the target must be the fastest shortest path. Finally, MATLAB simulation experiment was carried out, and the results were shown in Figure 14. The experimental results show that the step size of the final improved algorithm is 46.6, which reduces the step size by 11.06% and the search area by 169 compared with the A-star algorithm. also considering the influence of "key point list", the final storage space is reduced by 64.38%.  Table 1, through comparison of experimental data, the final improved algorithm is superior to A-star algorithm in terms of step size, search area and search time.

Conclusion
against A-star algorithm on occupy storage space problem, in this paper, by introducing a "guide line", "key points list", "two-way search" three new ways, such as the A-star algorithm is optimized, finally through MATLAB to indoor environment simulation, the simulation experiment, the two target different situations, take up the storage space by 62.04% and 64.38%, step length value and the search time are better than A-star algorithm, proving the feasibility of improvement.