*3.2. The Strategy of Parent Point Priority Determination (PPD)*

In order to save time in traversing the whole random tree in the process of determining the parent point, this paper proposes a strategy of parent point priority determination to simplify this process and thus shorten the path planning time. The strategy of parent point priority determination is an improved strategy based on the RRT algorithm, whose core idea is to prioritize the parent point of the next new point before random sampling. Compared with the RRT algorithm, the improved algorithm based on the PPD strategy saves time in finding the *Pparent* and therefore speeds up the execution of the algorithm. The specific process is shown in Algorithm 2, where *Dnew* and *Dparent* denote the distance from the new point to the target point and the distance from the parent point to the target point, respectively, which can be calculated by Equation (1).

$$\begin{cases} \begin{aligned} D\_{new} &= \sqrt{\left(P\_{ncv(x)} - P\_{goal(x)}\right)^2 + \left(P\_{ncv(y)} - P\_{goal(y)}\right)^2} \\\ D\_{parent} &= \sqrt{\left(P\_{parent(x)} - P\_{goal(x)}\right)^2 + \left(P\_{parent(y)} - P\_{goal(y)}\right)^2} \end{aligned} \tag{1} \end{cases}$$

**Algorithm 2.** PPD-RRT algorithm.

b. Set the point *Pinit* as the parent point *Pparent* of the next expansion.

c. Get four random points *Prand*1∼ *Prand*<sup>4</sup> on the circumference of the circle with the parent point *Pparent* as the center and the step length *ρ* as the radius.

d. Select the closest point to the target point in *Prand*1∼ *Prand*<sup>4</sup> as the random point *Prand*.

e. Connect parent point *Pparent* to the random point *Prand*, the random point *Prand* is the new point *Pnew*.

f. Use Equation (1) to calculate *Dnew* and *Dparent* respectively, and choose the one which is closer to the target point as the parent point *Pparent* for the next expansion.

g. Repeat the above steps c–f until the target point *Pgoal* is added to the random tree.

The random tree expansion diagram of the improved algorithm based on the PPD strategy is shown in Figure 2. In the process of generating new points, as the random tree becomes larger and there are more and more points in the random tree, traversing the random tree to search the parent point consumes a lot of computational time. In this article, the parent point is determined before the new point is generated, which can greatly save the path-planning time, and the larger the random tree gets, the more obvious this effect becomes.

**Figure 2.** Random tree expansion diagram of the improved algorithm based on the PPD strategy. The red circle indicates the starting point, and the green circle indicates the target point. The black circle indicates the path point, the solid black line indicates the path. and the green dashed line indicates the distance from the point to the target point. The blue dashed line indicates the circumference of the circle with the parent point as the center and the step length *ρ* as the radius, which is the random sampling space. *Prand*1~*Prand*<sup>4</sup> denote random sampling points, *Pparent* denotes parent point, and *Pnew* denotes the new point.

a. Initialize the random tree *Pinit*.
