**3. Sparse Visibility Graph-Based Path Planner**

Define Q ⊂ <sup>R</sup><sup>3</sup> as the robot navigation space, and S⊂Q as the sensor data from obstacles. A down-sample strategy is used to update and maintain the v-graph, denoted as G, and the grid to store pointcloud is denoted as L. Define the position of robot as *Probot* ∈ Q, the goal *Pgoal* ∈ Q.

The flow chart of the path planner proposed in the paper is shown in Figure 2. And the process consists of three parts: (1) generating the geometric contours of obstacles by LiDAR-to-plane mapping; (2) aggregating and simplifying complex obstacle information to maintain the v-graph at a low cost; and (3) searching for nodes and edges to generate the path from the start point to the goal through the v-graph.

**Figure 2.** The main flow chart of the path planner based on the v-graph.
