Motion in local coordinates

This chapter discusses the problem of online motion planning and navigation where the robot’s position is defined either with respect to locally accessible landmarks or with respect to other robots in two and three dimensions. The discourse reviews the methods of motion planning for ground and aerial vehicles and, in particular, considers the methods of positioning by the use of local maps and localization with respect to the common target. The chapter also presents a general idea of simultaneous localization and mapping methods that allow navigation of the robots in initially unknown environment and creating the environmental maps during the motion. It overviews the methods and algorithms of navigation in 3D space and mentions the rapid-expanding tree algorithm, the decoupled trajectory planning and control algorithms, as well as the methods for reducing computational complexity of the motion-planning problem.