In this technical brief, we focus on solving trajectory optimization problems that have nonlinear system dynamics and that 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 a quadrotor or computing minimum-jerk trajectories for a robot arm. DirCol5i is a transcription method that is specialized for solving this type of problem. It uses the 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. Although it is slower for some simple optimization problems, when solving problems with high-order derivatives DirCol5i is faster, more numerically robust, and does not require setting up a chain integrator.
DirCol5i: Trajectory Optimization for Problems With High-Order Derivatives
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 16, 2017; final manuscript received September 26, 2018; published online November 8, 2018. Assoc. Editor: Richard Bearee.
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Kelly, M. P. (November 8, 2018). "DirCol5i: Trajectory Optimization for Problems With High-Order Derivatives." ASME. J. Dyn. Sys., Meas., Control. March 2019; 141(3): 034502. https://doi.org/10.1115/1.4041610
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