B-Spline Trajectory Planning with Curvature Constraint

Abstract

We consider a problem of trajectory planning for mobile robot in a two-dimensional plane. In particular, we develop a method for constructing trajectories with the curvature satisfying given upper bound. The trajectories are constructed as smoothing splines employing B-splines as the basis functions and are planned for road-like path with piece-wise linear boundaries. Expressing the curvature in terms of the control points of B-splines, the problem is formulated as a nonlinear semi-infinite optimization problem. Constraints on velocity and acceleration can also be included. The effectiveness of the proposed method is verified by numerical experiments, first by a simple crank-like path in details and then by more complex path with sharp corners.