Motion planning

Motion planning (also known as the navigation problem or the piano mover's problem) is a term used in robotics is to find a sequence of valid configurations that moves the robot from the source to destination. For example, consider navigating a mobile robot inside a building to a distant waypoint. It should execute this task while avoiding walls and not falling down stairs. A motion planning algorithm would take a description of these tasks as input, and produce the speed and turning commands sent to the robot's wheels. Motion planning algorithms might address robots with a larger number of joints (e.g., industrial manipulators), more complex tasks (e.g. manipulation of objects), different constraints (e.g., a car that can only drive forward), and uncertainty (e.g. imperfect models of the environment or robot). Motion planning has several robotics applications, such as autonomy, automation, and robot design in CAD software, as well as applications in other fields, such as animating digital characters, video game, artificial intelligence, architectural design, robotic surgery, and the study of biological molecules. A basic motion planning problem is to produce a continuous motion that connects a start configuration S and a goal configuration G, while avoiding collision with known obstacles. The robot and obstacle geometry is described in a 2D or 3D workspace, while the motion is represented as a path in (possibly higher-dimensional) configuration space. A configuration describes the pose of the robot, and the configuration space C is the set of all possible configurations. For example: The set of configurations that avoids collision with obstacles is called the free space Cfree. The complement of Cfree in C is called the obstacle or forbidden region. Often, it is prohibitively difficult to explicitly compute the shape of Cfree. However, testing whether a given configuration is in Cfree is efficient. First, forward kinematics determine the position of the robot's geometry, and collision detection tests if the robot's geometry collides with the environment's geometry.