Kinodynamic Planning Using Probabalistic Road Maps Steven M. LaValle James J. Kuffner, Jr. Presented by Petter Frykman

What is the difference? Dynamic equations of motion and physical constraints

What is the difference? Dynamic equations of motion and physical constraints Higher dimensional state space k b u m

v v x x goalstart v

How it works... We are now controling u instead of q Numerical integration of x = f(x,u)  By knowing:  We want to calculate: Which could be done by a standars form of Runge-Kutta asuming that u is constant

Obstacles in the state space Regular obstacles  As we have seen them before Region of Inevitable Collision  Where no input we can give the robot can prevent a collision

v

Rapidly-exploring trees Nothing else than we have seen before  Select a point in state space at random  Select the point in the tree that is nearest  Try to expand towards the new point

Find new state Given two points x, and x´ Try to find u that takes the robot from x towards x´  Reached Found u that takes the robot all the way  Advanced Found u that takes the robot closer  Trapped Can’t find any u that is any good...

Metrics Time and energy is two of the possible metrics used. The problem is that an ideal metric is often as difficult to find as solving the original problem. The performance and the solution depends very much on the choice of the metric ρ.

Nearest neighbor This is also a bottleneck. The implementation used in the paper searches all states in the trees for the nearest one. There are other techniques that are better at doing this, at least approximatly. They often require some addisional data structure to represent the state space. This representation must be compatible with the problem in hand.

Bidirectional search Good for faster algorithms Bad when time is explicitly needed

Experimental results  5 different experiments, 4 – 12 dimensions  Control inputs were defined for each setup Planar translating body4D Planar body with rotation6D Translating 3D body6D 3D satellite12D 3D spacecraft12D

Planar translating body 400 – 2500 nodes explored Approximatly 5 seconds

Planar body with rotation ~13600 nodes explored 5 minutes

Translating 3D body ~16300 nodes explored 1 minute

3D body with rotation, satellite ~23800 nodes explored 6 minutes

3D body with rotation, space craft ? nodes explored 11 minutes

Further development More efficient metrics Efficient nearest neighbor Collision detection

David Hsu