This dissertation is concerned with the question of autonomously and efficiently exploring three-dimensional environments. Hence, three robotics problems are studied in this work: the motion planning problem, the coverage problem and the exploration problem. The work provides a better understanding of motion and exploration problems with regard to their mathematical formulation and computational complexity, and proposes solutions in the form of algorithms capable of being implemented on a wide range of robotic systems.;Because robots generally operate on a limited power source, the primary focus is on minimizing energy while moving or navigating in the environment. Many approaches address motion planning in the literature, however few attempt to provide a motion that aims at reducing the amount of energy expended during that process. We present a new approach, we call integral-squared torque approximation, that can be integrated with existing motion planners to find low-energy and collision-free paths in the robot's configuration space.;The robotics coverage problem has many real-world applications such as removing landmines or surveilling an area. We prove that this problem is inherently difficult to solve in its general case, and we provide an approach that is shown to be probabilistically complete, and that aims at minimizing a cost function (such as energy).;The remainder of the dissertation focuses on minimum-energy exploration, and offers a novel formulation for the problem. The formulation can be directly applied to compare exploration algorithms. In addition, an approach that aims at reducing energy during the exploration process is presented, and is shown through simulation to perform better than existing algorithms.
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