# Smart Obstacle Avoidance Using a Danger Index for a Dynamic Environment
## 1 Introduction  
Moving in free space while avoiding collisions within the dynamic environment is known as obstacle avoidance or path planning, which is the backbone of mobile robots. Many well-known path planning algorithms have been proposed in robotics research literature. The reward-based planning algorithms [1; 2; 3] propose to give the robot a positive reward when it reaches the target, and give the robot a negative reward when it collides with the obstacle. The path is then obtained by maximizing the cumulative future reward. However, due to the discretization of the state and control space, their trajectories are mostly not smooth [4]. The sampling-base planning algorithms, such as the Rapidly exploring Random Tree (RRT) [5] and the Probabilistic Road Maps (PRM) [6], generally connect a series of randomly sampled points from a barrier-free space, and attempt to establish a path from the initial position to the target position. Although their time cost is less, the random sampling introduces the randomness of the planned path. Therefore, we cannot predict the result of the path planner, which is not optimal in general. The grid-based planning algorithms, such as the A\({}^{*}\)[7] and the [PERSON]'s [8] algorithm, which have been used in the robotic operating systems (ROS), can find the optimal trajectory, but their time cost and memory usage grow exponentially with the dimension of the state space [4]. The novel artificial potential field (APF) developed by [PERSON] [9; 10; 11] is a simple and effective path planning method. The theory behind APF is simple and straightforward: it has an attractive potential field for attracting the robot to the target point, and a repulsive potential field for pushing the robot away from obstacles. The APF approach can be used for global and local path planning. However, there are some inherent problems in traditional artificial potential field approaches: (1) oscillations in the presence of obstacles due to the large move step of the robot; (2) goal nonreachable with obstacles nearby (GNRON); (3) trapped in a local minimum region; and (4) moving obstacles avoidance. Solving these problems has become an interesting topic in the field of APF based path planning [12; 13]. [PERSON] et al. [14] deal with the local minimum region by filling it with the virtual obstacle. [PERSON] et al. [15] introduce simulated annealing to look for the global minimum and escape the local minimum region. [PERSON] et al. [16] use the Deterministic Annealing (DA) approach to avoid local minima in APF by adding a temperature parameter into the cost function of the APF approach. The value of the temperature parameter starts to increase until the robot goes away from the local minimum region. [PERSON] et al. [17] propose to use two modes to control the APF, i.e., one mode is to go directly to the target using traditional APF and the other mode uses a new point APF algorithm to avoid collisions with the static obstacle. Mode 1 can be switched to mode 2 when the robot is trapped in a local minimum region or blocked in front of the obstacle. A new direction is synthesized using the robot motion information and direction between the robot and the goal point, which can guide the robot to escape the local minimum region. [PERSON] et al. [18] propose an improved repulsive force for overcoming a local minima problem, which generates a new repulsive force to the primary force when the robot detects an obstacle within its sensory range. The new repulsive force component turns the robot smoothly away from the obstacles. [PERSON] et al. [19] modify the APF approach with the collision cone approach, which adds an artificial force to the existing attractive and repulsive forces when the relative velocity vector between the robot and obstacle is included in a collision cone. The improved resultant force can guide the robot to reach the goal.