Feasible RRT-based path planning using seventh order Bézier curves

This paper presents a methodology based on a variation of the Rapidly-exploring Random Trees (RRTs) that generates feasible trajectories for autonomous vehicles with holonomic constraints in environments with obstacles. Our approach is based on seventh order Bézier curves to connect vertexes of the tree, generating paths that do not violate the main kinematic constraints of the vehicle. The methodology also does not require complex kinematic and dynamic models of the vehicle. The smoothness of the acceleration profile of the entire path is directly guaranteed by controlling the curvature values at the extreme points of each Bézier that composes the tree. The proposed algorithm provides fast convergence to the final result with several other advantages, such as the reduction in the number of vertexes of the tree because the method enable connections between vertexes of the tree with unlimited range. In an environment with few obstacles, a very small quantity of vertexes (sometimes only two) is sufficient to take the robot between two points. The properties of the seventh order Bézier formulation are also used to avoid collisions with static obstacles in the environment.