Low-cost autonomous robots suffer from limited onboard computing power, resulting in excessive computation time when navigating in cluttered environments. This paper presents Edge Accelerated Robot Navigation, or EARN for short, to achieve real-time collision avoidance by adopting hierarchical motion planning (HMP). In contrast to existing local or edge motion planning solutions that ignore the interdependency between low-level motion planning and high-level resource allocation, EARN adopts model predictive switching (MPS) that maximizes the expected switching gain w.r.t. robot states and actions under computation and communication resource constraints. As such, each robot can dynamically switch between a point-mass motion planner executed locally to guarantee safety (e.g., path-following) and a full-shape motion planner executed non-locally to guarantee efficiency (e.g., overtaking). The crux to EARN is a two-time scale integrated decision-planning algorithm based on bilevel mixed-integer optimization, and a fast conditional collision avoidance algorithm based on penalty dual decomposition. We validate the performance of EARN in indoor simulation, outdoor simulation, and real-world environments. Experiments show that EARN achieves significantly smaller navigation time and collision ratios than state-of-the-art navigation approaches.