Emergency obstacle avoidance requires a mobile robot to brake or change its heading within the available distance. This paper investigates the dependence of maneuver performance and odometric error on approach speed for a differential-drive robot. A footprint-clearance analysis and a normalized wheel-motion index provide a kinematic description of five braking and turning maneuvers. The principal experiment comprises 540 block-randomized trials on tile, of which 539 are retained, at commanded approach speeds of 45, 55, and 65 cm/s. An overhead camera provides an independent pose reference. When encoder, gyro, and camera heading changes are evaluated over complete motion records, the mean encoder discrepancy increases by 4.7-5.1 degrees for the two reverse-spin maneuvers between the lowest and highest speeds; the arc and brake-assisted pivot change by less than 0.4 degrees. Larger encoder discrepancy is associated with lower avoidance success after adjustment for distance, speed, maneuver, day, and turn direction. Gyro discrepancies remain approximately 3 degrees for the reverse spins. Estimated reaction distances for 90% success and their uncertainty quantify the maneuver trade-offs. The results support speed-specific empirical characterization of emergency maneuvers and distinguish encoder error from recovery motion and measurement-window mismatch.

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