Many of the applications pertinent to unmanned vehicles, such as environmental research and analysis, communications, and information-surveillance and reconnaissance, benefit from prolonged vehicle operation time. Conventional efforts to increase the operational time of electric-powered unmanned vehicles have traditionally focused on the design of energy-efficient components and the identification of energy efficient search patterns, while little attention has been paid to the vehicle's mission-level path plan and power management. This thesis explores the formulation and generation of integrated motion-plans and power-schedules for solar-panel equipped mobile robots operating under strict energy constraints, which cannot be effectively addressed through conventional motion planning algorithms. Transit problems are considered to design time-optimal paths using both Balkcom-Mason and Pseudo-Dubins curves. Additionally, a more complicated problem to generate mission plans for vehicles which must persistently travel between certain locations, similar to the traveling salesperson problem (TSP), is presented. A comparison between one of the common motion-planning algorithms and experimental results of the prescribed algorithms, made possible by use of a test environment and mobile robot designed and developed specifically for this research, are presented and discussed.