MatthewPeterKelly/OptimTraj

GPOPS-II Interpolation Function Handle returned by OptimTraj

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#20 opened on Sep 9, 2016

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Description

In gpopsWrapper.m, OptimTraj provides an interpolation function handle for the GPOPS-II solution using pchip, as per the code below. Is pchip the most accurate way to interpolate the GPOPS-II solution?

soln.interp.state = @(t)( interp1(tSoln',xSoln',t','pchip',nan)' ); soln.interp.control = @(t)( interp1(tSoln',uSoln',t','pchip',nan)' );

The formula for the GPOPS-II state is given in equation (25) of the GPOPS-II paper:

Patterson, Michael A., and Anil V. Rao. "GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming." ACM Transactions on Mathematical Software (TOMS) 41.1 (2014): 1.

http://dl.acm.org/citation.cfm?id=2558904

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Issue type
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DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
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half day
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ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
clear
Prerequisites
MATLABnumerical interpolationGPOPS II paper
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
30
Research direction
The issue questions the accuracy of pchip interpolation used in gpopsWrapper.m. A contributor should review equation (25) in the GPOPS II paper (Patterson & Rao, 2014) to determine if a more accurate interpolation method (e.g., spline or direct evaluation of polynomials) should be used. The file gpopsWrapper.m contains the relevant interpolation code. The contributor could implement and test alternative interpolation methods, comparing results against known solutions.
GPOPS-II Interpolation Function Handle returned by OptimTraj · MatthewPeterKelly/OptimTraj#20 | Good First Issue