Orientation control on SO(3) with piecewise sinusoids

Wang, Shaoqian; Hoagg, Jesse B.; Seigler, T. Michael

doi:10.1016/j.automatica.2018.11.007

Cited by 13 publications

(1 citation statement)

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“…A common approach to non-holonomic motion planning is to use sinusoidal control function to, roughly speaking, generate the "Lie bracket" directions. See for example [10], and [15] for a very recent work on how oscillations can be used for orientation control in SO(3). This idea is also used in derivative-free optimization [4,13].…”

Section: Introductionmentioning

confidence: 99%

Affine Geometric Heat Flow and Motion Planning for Dynamic Systems

2019

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We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and non-holonomic constraints, drift dynamics, obstacle constraints and constraints on the magnitudes of the applied controls. The method, which finds its inspiration in recent work on the so-called geometric heat flows and curve shortening flows, relies on a hereby introduced partial differential equation, which we call the affine geometric heat flow, which evolves an arbitrary differentiable path joining initial to final state in configuration space to a path that meets the constraints imposed on the problem. From this path, controls to be applied on the system can be extracted. We provide conditions guaranteeing that the controls extracted will drive the system arbitrarily close to the desired final state, while meeting the imposed constraints and illustrate the method on three canonical examples.

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Section: Introductionmentioning

confidence: 99%