Off-Line and On-Line Trajectory Planning

The basic problem of motion planning is to select a path, or trajectory, from a given initial state to a destination state, while avoiding collisions with known static and moving obstacles. Ideally, it is desirable that the trajectory to the goal be computed online, during motion, to allow the robot react to changes in the environment, to a moving target, and to errors encountered during motion. However, the inherent difficulty in solving this problem, which stems from the high dimensionality of the search space, the geometric and kinematic properties of the obstacles, the cost function to be optimized, and the robot’s kinematic and dynamic model, may hinder a sufficiently fast solution to be computed online, given reasonable computational resources. As a result, existing work on motion planning can be classified into off-line and on-line planning. Off-line planners compute the entire path or trajectory to the goal before motion begins, whereas on-line planners generate the trajectory to the goal incrementally, during motion. This chapter reviews the main approaches to off-line and on-line planning, and presents one solution for each.