For sampled-data first-order robots with matched safety margins and a linear class-κ function, the complementarity QP and the CBF-QP have the same optimal velocity command.
Oc3: A reactive velocity level motion planner with complementarity constraint-based obstacle avoid- ance for mobile robots,
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Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control
For sampled-data first-order robots with matched safety margins and a linear class-κ function, the complementarity QP and the CBF-QP have the same optimal velocity command.