A motion planning algorithm for a nonholonomic vehicle using vector potential functions in triangular regions

A motion planning algorithm for a nonholonomic vehicle in triangular regions is investigated. The regions are the result of splitting a larger and complex workspace, and are classified into three classes, that are, empty regions, obstacle-inside regions, and goal regions. The vehicle has to achieve a goal configuration from any initial configuration in the workspace. A set of procedures to generate velocity vector fields by utilizing vector potential functions is proposed. The vector fields are categorized as those generated by the edges of regions, obstacles, and goal points. To deal with some constraints, i.e., maximum velocities, a set of parameter-scaling rules is provided. A state-feedback controller for a unicycle vehicle is used to show that the generated motion plan can be tracked by the vehicle. Simulation results showing the motion planning from different initial configuration are presented.