Robotics-trajectory planning (Artificial potential)

Today finally completed the robot trajectory planning of the Last class, goodbye to bring B-box Prof TJ Taylor.

The last lesson is to use potential field for trajectory planning. The idea of this method is very clear, for the configration Space inside the obstacle of the DT transformation, with the DT transformation value as the input of the penalty function, so that the robot as far away from the obstacles, while the end of the design parabolic function, so that the robot has a trend toward the end of the near. Finally, a feasible motion trajectory of the robot is obtained. Because this trajectory is gradient descent, and the penalty function is continuous, so if the robot does not fall into the local optimal, then you can get the global optimal path (I do not hold this view, second-order Hessian matrix capitalization of the disobedience, what greedy algorithm is the shortest path? ）

1. Generating penalty function graph based on DT transform

The DT transform is an algorithm in the 2D2 value image that is used to find the distance from a pixel to a recent non-0 pixel. In other words, the distance the robot is to the nearest obstacle. This distance is very easy to obtain in the robot movement, as long as there is a real-time distance sensor, you can find the robot in different locations, to the nearest obstacle distance. Thus generating f-map (penalty function graph)

　　

The robot's configuration Space and F-map as shown.

2, pull to the end of the potential

In addition to the penalty function, the robot also needs a potential--configuration Space with an end-centered paraboloid. After adding it to the F-map, the final artificial potential can be obtained.

　　

3. Gradient Descent

A gradient descent algorithm is performed on artificial potential to obtain the trajectory of robot motion.

4. Summary

Robotic trajectory planning is a promising discipline, with future directions including the following:

Non-gay robots: No car can reverse at any time

Planning under dynamic constraints: considering acceleration and deceleration of the robot

Multi-robot trajectory planning

Trajectory planning for mobility barriers

Trajectory planning for uncertain environments

Robotics-trajectory planning (Artificial potential)