Planning Motion Trajectories for Mobile Robots Using Splines

Abstract

Motion planning for wheeled mobile robots (WMR) in controlled environments is con- sidered a solved problem. Typical solutions are path planning on a 2D grid and reactive collision avoidance. Active research deals with issues regarding the integration of ad- ditional constraints such as dynamics, narrow spaces, or smoothness requirements. Current approaches to motion planning mainly consider a finite number of actions that can be carried out by the robot at a given time. In this work we present an approach that resorts to a parametric trajectory representation to overcome these lim- itations. As representation we choose Quintic Bezier Splines. We conduct global, explicit planning for velocities along the robot’s trajectory – a prerequisite if smooth kinodynamics along the path are to be included into the planning process, yet mainly unaddressed in current work. Our approach guarantees velocity profiles to respect several kinodynamic constraints and resolves accelerational interdependencies without iteration. The proposed approach optimizes a curvature continuous trajectory and maintains anytime capability. For actual execution the trajectory is forwarded to a separate feedback controller. The suggested method is able to smoothly update a trajectory to account for unmapped obstacles, moderate errors in localization, or erroneous plan exe- cution. Evaluation of our method on real robots shows its applicability and advantages over a Dynamic Window-based approach.