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DAMON leverages manifold learning and variational autoencoding to achieve obstacle avoidance, allowing for motion planning through adaptive graph traversal in a pre-learned low-dimensional hierarchically-structured manifold graph that captures intricate motion dynamics between a robotic arm and its obstacles. This versatile and reusable approach is applicable to various collaboration scenarios. The primary advantage of DAMON is its ability to embed information in a low-dimensional graph, eliminating the need for repeated computation required by current sampling-based methods. As a result, it offers faster and more efficient motion planning with significantly lower computational overhead and memory footprint. In summary, DAMON is a breakthrough methodology that addresses the challenge of dynamic obstacle avoidance in robotic systems and offers a promising solution for safe and efficient human-robot collaboration. Our approach has been experimentally validated on a 7-DoF robotic manipulator in both simulation and physical settings. DAMON enables the robot to learn and generate skills for avoiding previously-unseen obstacles while achieving predefined objectives. We also optimize DAMON's design parameters and performance using an analytical framework. Our approach outperforms mainstream methodologies, including RRT, RRT*, Dynamic RRT*, L2RRT, and MpNet, with 40\% more trajectory smoothness and over 65\% improved latency performance, on average.