Velocity and acceleration constrained trajectory planning by smoothing splines

Abstract

We develop a trajectory planning method of mobile robots in a two-dimensional plane. Trajectories are constructed as vector smoothing splines using B-splines as the basis functions. We plan trajectory for road-like path specified by piecewise linear boundaries as treated in our recent paper, and our specific focus in this paper is on introducing quadratic inequality constraints on the trajectory as well as on its derivatives. It is shown that such constraints are systematically included in the smoothing spline settings and the problem is formulated as quadratically constrained quadratic programming problem. This problem can be solved numerically by MATLAB based software CVX efficiently. Such a quadratic constraint can be used, e.g. to limit the maximum speed and acceleration of the robot motion, and the usefulness and effectiveness of the developed method are confirmed by numerical experiments.