# Difference between Collision Cone and Velocity Obstacle

I'm trying to understand these two classic approaches to path planning in dynamic environments/with moving obstacles. According to some review papers, there seems to be quite a difference between them, e.g. so that the collision cone approach (as presented in [1]) can be used for non-circular objects as well. But to me they seem very analogous:

In my understanding, given a point robot and a circle obstacle, both moving at constant velocities $$v_A$$ and $$v_B$$, the collision cone $$CC$$ is defined by two rays through the robot, tangentially containing the whole obstacle. If the relative velocity $$v_r = v_A - v_B$$ is contained in this cone, a collision will eventually happen, otherwise they will pass without collision. Now, the velocity obstacle seems to be just the collision cone moved by $$v_B$$, i.e. $$VO = CC \bigoplus v_B$$ where $$\bigoplus$$ is the Minkowski sum. Therefore, any velocity of the robot in $$VO$$ will result in an collision, all the others won't.

Is there something I'm misunderstanding here or is it that simple? Here is a figure from [2] that seems to fit to my understandings.

[1]: Chakravarthy, A., & Ghose, D. (1998). Obstacle avoidance in a dynamic environment: a collision cone approach. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 28(5), 562–574. https://doi.org/10.1109/3468.709600

[2]: Wilkie, D., van den Berg, J., & Manocha, D. (2009). Generalized velocity obstacles. In 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems (S. 5573–5578). IEEE. https://doi.org/10.1109/IROS.2009.5354175