Velocity Obstacle

【Velocity Obstacle】

　　Two circular objects A,B, at time t(0), with velocity V(A),V(B). A represent the robot, and B represent obstacle.

　　　　

　　Collision Cone：

　　　　　

　　V(A,B) is the relative velocity of A&B. V(A,B) = V(A) - V(B). And λ(A,B) is the line of V(A,B).

　　　　　　　

　　By translating CC(A,B) by V(B)，we get absolute Velocity Obstacle VO：

　　　　

　　　　

　　The VO partitions the absolute velocities of A into avoiding & colliding velocities. Selecting V(A) outside of VO would avoid collision with B：

　　　　

　　Velocities on the boundaries of VO would result in A grazing B.

　　To avoid multiple obstacles, we consider the union of the individual velocity obstacles：

　　　　

　　Since VO is based on a linear approximation of the obstacle's trajectory, using it to predict remote collisions may be inaccurate.
　　To account for imminent collisions：

　　　　

　　　

【Avoidance Maneuver】

　　躲避策略。

　　

　　Feasible Acceleration: 　　

　　RV: Reachable Velocity:

　　

　　

　　Reachable Avoidance Velocity (RAV):

　　　　

　　

　　 A maneuver avoiding obstacle B can be computed by selecting any velocity in RAV.

【Structure of the Avoidance Maneuvers】

　　躲避策略的结构。