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Technical Brief

DirCol5i: trajectory optimization for problems with high-order derivatives

[+] Author and Article Information
Matthew Kelly

Biorobotics and Locomotion Lab, Department of Mechanical Engineering, Cornell University, Ithaca, NY, USA
mpk72@cornell.edu

1Corresponding author.

ASME doi:10.1115/1.4041610 History: Received September 16, 2017; Revised September 26, 2018

Abstract

In this paper we focus on solving trajectory optimization problems that have non-linear system dynamics and include high-order derivatives in the objective function. This type of problem comes up in robotics --- for example when computing minimum-snap reference trajectories for quadrotor helicopters or computing minimum-jerk trajectories for robot arms. DirCol5i is a transcription method that is specialized for solving this type of problem. It uses fifth-order splines and analytic differentiation to compute higher-derivatives, rather than using a chain-integrator as would be required by traditional methods. We compare DirCol5i to traditional transcription methods. DirCol5i is slower when solving some simple optimization problems, but when solving optimization problems with high-order derivatives, DirCol5i is faster, more numerically robust, and does not require setting up a chain integrator.

Copyright (c) 2018 by ASME
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