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• First study to capture shopping behavior of food desert and food oasis residents. • Explores shopping behavior in terms of both in-person trips and internet orders. • Compares the acceptance of autonomous delivery to replace physical shopping. • Residents planning to use ADRs for their internet order prefer them for all physical shopping trips. • Offers actionable guidance to overcome the mobility inequalities in food deserts. Food desert communities in the US have a widely recognized gap between the demand for healthy foods and the minimum order size that makes it worthwhile for food purveyors to deliver to such neighborhoods, thereby creating delivery deficiencies. A diverse set of mobility constraints and activity-travel patterns exist for disadvantaged segments in these communities, especially the elderly, unemployed, and socially excluded. Appreciating this complexity, an effective solution would be to improve the food access of such communities by providing faster, inexpensive, and flexible online deliveries of healthy foods. However, little is currently known about the shopping travel pattern in food desert communities and the associated mobility inequalities. This paper fulfills this critical research gap and quantifies the differences in shopping travel behavior observed among consumers residing in food deserts and food oases using data collected from Portland and Nashville Metropolitan areas. The paper subsequently captures the perceived acceptance of autonomous delivery robots (ADRs) among these consumers to overcome their mobility inequalities. The results indicate that food desert residents aged between 18 and 25 years, African Americans and those earning more than $75,000 are more likely to engage in internet shopping than food oasis residents. Despite the perceived potential of ADRs to reduce the mobility inequalities in food deserts, acceptance levels for this emerging technology are found to be significantly less among food desert residents, especially among older generational cohorts and less qualified. This study will provide key takeaways to e-commerce companies to expand their delivery service through ADRs in underserved areas. [ABSTRACT FROM AUTHOR]