Head-mounted displays (HMDs) and large area position tracking systems can enable users to navigate virtual worlds through natural walking. Redirected walking (RDW) imperceptibly steers immersed users away from physical world obstacles allowing them to explore unbounded virtual worlds while walking in limited physical space. In cases of imminent collisions, resetting techniques can reorient them into open space. This work introduces categorically new RDW and resetting algorithms based on the use of artificial potential fields that "push" users away from obstacles and other users. Data from human subject experiments indicate that these methods reduce potential single-user resets by 66% and increase the average distance between resets by 86% compared to previous techniques. A live multi-user study demonstrates the viability of the algorithm with up to 3 concurrent users, and simulation results indicate that the algorithm scales efficiently up to at least 8 users and is effective with larger groups.