Mechanizing the manual harvesting of fresh market fruits constitutes one of the biggest challenges to the sustainability of the fruit industry. During manual harvesting of some fresh-market crops like strawberries and table grapes, pickers spend significant amounts of time walking to carry full trays to a collection station at the edge of the field. A step toward increasing harvest automation for such crops is to deploy harvest-aid collaborative robots (co-bots) that transport the empty and full trays, thus increasing harvest efficiency by reducing pickers' non-productive walking times. This work presents the development of a co-robotic harvest-aid system and its evaluation during commercial strawberry harvesting. At the heart of the system lies a predictive stochastic scheduling algorithm that minimizes the expected non-picking time, thus maximizing the harvest efficiency. During the evaluation experiments, the co-robots improved the mean harvesting efficiency by around 10% and reduced the mean non-productive time by 60%, when the robot-to-picker ratio was 1:3. The concepts developed in this work can be applied to robotic harvest-aids for other manually harvested crops that involve walking for crop transportation.