We study the Acceleration Obstacle (AO) as a concept to enable a robot's navigation in human crowds. The AO's geometric properties are analyzed and a direct sampling-free algorithm is proposed to approximate its boundary by linear constraints. The resulting controller is formulated as a quadratic program and evaluated in interaction with simulated bi-directional crowd flow in a corridor. We compare it to alternative robotic controllers, considering the robot's and the crowd's performance and the robot's behavior with respect to emergent lanes. Our results indicate that the robot can achieve higher efficiency when being less integrated in lanes.