most recent 30 from http://mathoverflow.net 2013-05-23T12:27:04Z http://mathoverflow.net/feeds/question/82502 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/82502/minimum-time-planar-paths-under-a-bound-on-magnitude-of-acceleration Stewart Johnson 2011-12-02T19:21:16Z 2011-12-02T21:53:03Z

<p>On a plane, given initial position (x1,y1), initial velocity (u1,v1), final position (x2,y2), and final velocity (u2,v2), compute the solution to x''= cos(z), y''=sin(z) that has these endpoint conditions and minimizes time. </p> <p>The control function z can be taken as piecewise continuous.</p> <p>Pontryagin's optimality criteria implies the fractional linear tangent law: z must be of the form z=arctan((at+b)/(ct+d)).</p> <p>Starting from this, how do you actually (numerically) compute the optimal path (x(t),y(t))? </p> <p>This stems from a research paper “Baserunner’s Optimal Path,” published online in The Mathematical Intelligencer, November, 2009, by Frank Morgan and myself. </p> <p>We did find one old reference: Acceleration-Constrained Time-Optimal Control in N-dimensions, by Feng and Krogh, IEEE Transactions on automatic control, Vol 31, Issue 10, Pages 955-958, Published Oct 1986. </p> <p>Anyone know any newer work or numerical solutions? </p>