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Construction of control barrier function and $C^2$ reference trajectory for constrained attitude maneuvers

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Document pages: 9 pages

Abstract: Constrained attitude maneuvers have numerous applications in robotics andaerospace. In our previous work, a general framework to this problem wasproposed with resolution completeness guarantee. However, a smooth referencetrajectory and a low-level safety-critical controller were lacking. In thiswork, we propose a novel construction of a $C^2$ continuous referencetrajectory based on Bézier curves on $ SO(3) $ that evolves withinpredetermined cells and eliminates previous stop-and-go behavior. Moreover, wepropose a novel zeroing control barrier function on $ SO(3) $ that provides asafety certificate over a set of overlapping cells on $ SO(3) $ while avoidingnonsmooth analysis. The safety certificate is given as a linear constraint onthe control input and implemented in real-time. A remedy is proposed to handlethe states where the coefficient of the control input in the linear constraintvanishes. Numerical simulations are given to verify the advantages of theproposed method.

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