SCR-Normalize: A novel trajectory planning method based on explicit quintic polynomial curves

This paper presents a framework for generating explicit quintic polynomial curves as the trajectory of autonomous vehicles. The method is called SCR-Normalize and is founded on two novel ideas. The first concept is to rotate the coordinate reference, regarding the boundary conditions, in order to reach a special coordinate reference called Secondary Coordinate Reference (SCR). In the SCR, the explicit quintic polynomial curve has short length and low curvature values (i.e. the curve is not wiggly). The second concept is to normalize the trajectory in order to speed up the framework. Two kinds of problems are considered to be solved in this paper: (a) generating a length optimal trajectory for arbitrary boundary conditions subject to a curvature constraint; and (b) path smoothing. For case (a), for the lane change manoeuvre, the problem is solved explicitly. In addition, the familiar expression for the optimal interval of the lane change manoeuvre is analytically proved for the first time. For arbitrary swerving manoeuvres, two algorithms are presented and their performance is compared with each other and with two other algorithms. Similarly, for case (b), an algorithm is presented and its performance is compared with three other methods. Evaluating the algorithms in the examples, and comparing the results with other methods illustrates the efficiency of the SCR-Normalize framework to generate optimal trajectories in real time.