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We study a driftless system on a three-dimensional manifold driven by twoscalar controls. We assume that each scalar control has an independent bound onits modulus and we prove that, locally around every point where the controlledvector fields satisfy some suitable nondegeneracy Lie bracket condition, everytime-optimal trajectory has at most five bang or singular arcs. The result isobtained using first-and second-order necessary conditions for optimality.

Bounds on time-optimal concatenations of arcs for two-input driftless 3D systems