Time-Optimal Curvature Continuous Path to a Line for Robot Steering

This paper proposes a novel method for solving the time-optimal path for a Curvature Continous (CC) robot toward a given line, which is called the Line-Targeted Curvature Continous (LTCC) path. Such an LTCC path can be directly used in lane changes and departure applications and can participate in the planning of complex scenarios as the steering function. Instead of solving by optimization method, this paper derives a closed-form representation of the path under any boundary constraints, which is an essential and computationally-friendly approach. A rigorous mathematical deduction is used to prove the correctness of the proposed method, meanwhile, numerous experiments are performed for verification. The experiment results reveal that the algorithm can generate the same path as the optimization-based method but much faster. On this basis, the proposed method is tested as the steering function with the RRT∗ method in complex scenarios, which reveals its advantage over the CC path, and the great potential for the applications in the real world.