Tunable Trajectory Planner Using G3 Curves

TL;DR

This paper introduces a tunable trajectory planning method for autonomous driving that balances passenger comfort and travel time by optimizing curvature and velocity profiles through discretization and iterative gradient descent.

Contribution

It proposes a simplified, discretized approach to continuous-curvature trajectory planning with a tunable parameter for curvature derivatives, enabling efficient optimization.

Findings

Effective trade-off between comfort and time demonstrated

Fast generation of minimal-length paths using a single parameter

Iterative optimization improves trajectory quality

Abstract

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.