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I have a my mobile robot and plan to use the dynamic window approach to collision avoidance. I have read the paper ,but have one inequality i can't derive it. enter image description here could you tell me? thanks!

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This falls out of the basic equations of motion for a body under constant acceleration. The simplest thing is to start with this equation: $$ v^2 = v_o^2 + 2ad $$ Where we are starting at some velocity $v$, and decelerating at $a$ (or $\dot{v}$ in your equation) to a stop. (So $v_o$ = 0). The distance traveled, $d$, must be less than the distance to the obstacle, $dist(v,w)$.

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  • $\begingroup$ Hi, Ben. Thanks for your reply. But, how to explain the angular velocity w? Further more, once the mobile robot start to slow down, the trajectory must be changed. $\endgroup$ Apr 17 '15 at 8:57
  • $\begingroup$ The same equations apply to angular velocity. You decelerate at some constant angular acceleration, and your angular velocity must be small enough so that you will not collide with the object before you stop. I believe these equations assume the trajectory is constant and not changing. They are only used for verifying a given trajectory is admissible. $\endgroup$
    – Ben
    Apr 17 '15 at 13:54

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