<p>Mobile robots are being used more widely in various environments, such as households, hospitals, agriculture, and industry. In these spaces, many times the robots are required to cover long distances, at times carrying heavy payloads, resulting in large energy consumption. In order to reduce the energy consumption, this paper presents a set of novel optimal speed profiles for two wheel differential drive robots. The profiles are derived using Hamiltonian formalism, resulting in closed-form speed profiles for both straight and rotational motions. The derivation used a power model that explicitly considers robot and motor dynamic parameters as well as external payload. Energy consumption of a commercial two wheel differential drive robot was experimentally evaluated using various trapezoidal and the proposed optimum speed profiles, showing significant energy savings using the new speed profiles. The paper also presents an analysis on variations of trajectory times and maximum speeds with varying payloads.</p>