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copied!<p>Here are some ideas that may work </p> <p>You can model your path as a piecewise linear curve. If you have 31 line segments then your curve is fully described by 60 numbers. Each of the possible curves have a cost, so the cost is a function on the following form</p> <p>cost(x1, x2, x3 ..... x60)</p> <p>Now your problem is to find the global optimum of a function of 60 variables. You can use standard methods to do this. One idea is to use genetic algorithms. Another idea is to use a monte carlo method such as parallel tempering</p> <p><a href="http://en.wikipedia.org/wiki/Parallel_tempering" rel="nofollow">http://en.wikipedia.org/wiki/Parallel_tempering</a></p> <p>Whenever you have a promising path then you can use it as a starting point to find a local minimum of the cost function. Maybe you can use some interpolation to make your cost function is differentiable. Then you can use Newtons method (or rather BFGS) to find local mimima of the cost function. </p> <p><a href="http://en.wikipedia.org/wiki/Local_minimum" rel="nofollow">http://en.wikipedia.org/wiki/Local_minimum</a></p> <p><a href="http://en.wikipedia.org/wiki/BFGS" rel="nofollow">http://en.wikipedia.org/wiki/BFGS</a></p> <p>Your problem is somewhat similar to the problem of finding reaction paths in chemical systems. Maybe you can find some inspiration in the book "Energy Landscapes" by Davis Wales.</p> <p>But I also have some questions:</p> <ul> <li>Is it necessary for you to find the optimal path, or are you just looking for an path that is OK?</li> <li>How much computer power and time do you have at hand?</li> <li>Can the robot make sharp turns, or do you need extra physics modelling to improve the cost function?</li> </ul>

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